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		<id>https://www.explainxkcd.com/wiki/index.php?action=history&amp;feed=atom&amp;title=882%3A_Significant</id>
		<title>882: Significant - Revision history</title>
		<link rel="self" type="application/atom+xml" href="https://www.explainxkcd.com/wiki/index.php?action=history&amp;feed=atom&amp;title=882%3A_Significant"/>
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		<updated>2026-04-04T09:14:25Z</updated>
		<subtitle>Revision history for this page on the wiki</subtitle>
		<generator>MediaWiki 1.30.0</generator>

	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=882:_Significant&amp;diff=401527&amp;oldid=prev</id>
		<title>Lettherebedarklight: /* Transcript */ add Category:Comics with a Spanish translation</title>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=882:_Significant&amp;diff=401527&amp;oldid=prev"/>
				<updated>2025-12-15T08:57:20Z</updated>
		
		<summary type="html">&lt;p&gt;‎&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Transcript: &lt;/span&gt; add &lt;a href=&quot;/wiki/index.php/Category:Comics_with_a_Spanish_translation&quot; title=&quot;Category:Comics with a Spanish translation&quot;&gt;Category:Comics with a Spanish translation&lt;/a&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 08:57, 15 December 2025&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l105&quot; &gt;Line 105:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 105:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Category:Scientific research]]&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Category:Scientific research]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Category:Minecraft]]&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Category:Minecraft]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[Category:Comics with a Spanish translation]]&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Lettherebedarklight</name></author>	</entry>

	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=882:_Significant&amp;diff=381553&amp;oldid=prev</id>
		<title>92.23.2.228: /* Explanation */ Mdashes with more obvious 'not-a-hyphen' spacing.</title>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=882:_Significant&amp;diff=381553&amp;oldid=prev"/>
				<updated>2025-07-21T10:32:25Z</updated>
		
		<summary type="html">&lt;p&gt;‎&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Explanation: &lt;/span&gt; Mdashes with more obvious &amp;#039;not-a-hyphen&amp;#039; spacing.&lt;/span&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 10:32, 21 July 2025&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l10&quot; &gt;Line 10:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 10:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;This comic is about {{w|data dredging}} (aka ''p''-hacking), and the misrepresentation of science and statistics in the media. A girl with a black ponytail comes to [[Cueball]] with her claim that {{w|jelly beans}} cause {{w|acne}}, and Cueball then commissions two scientists (a man with goggles and [[Megan]]) to do some research on the link between jelly beans and acne. They find no link, but in the end the real result of this research is bad news reporting!&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;This comic is about {{w|data dredging}} (aka ''p''-hacking), and the misrepresentation of science and statistics in the media. A girl with a black ponytail comes to [[Cueball]] with her claim that {{w|jelly beans}} cause {{w|acne}}, and Cueball then commissions two scientists (a man with goggles and [[Megan]]) to do some research on the link between jelly beans and acne. They find no link, but in the end the real result of this research is bad news reporting!&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;First, some basic statistical theory. Let’s imagine you are trying to find out if jelly beans cause acne. To do this you could find a group of people and randomly split them into two &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;groups—one &lt;/del&gt;group who you get to eat lots of jelly beans and a second group who are banned from eating jelly beans. After some time you compare whether the group that eat jelly beans have more acne than those who do not. If more people in the group that eat jelly beans have acne, then you might think that jelly beans cause acne. However, there is a problem.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;First, some basic statistical theory. Let’s imagine you are trying to find out if jelly beans cause acne. To do this you could find a group of people and randomly split them into two &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;groups — one &lt;/ins&gt;group who you get to eat lots of jelly beans and a second group who are banned from eating jelly beans. After some time you compare whether the group that eat jelly beans have more acne than those who do not. If more people in the group that eat jelly beans have acne, then you might think that jelly beans cause acne. However, there is a problem.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Some people will suffer from acne whether they eat jelly beans or not, and some will never have acne even if they do eat jelly beans. There is an element of chance in how many people prone to acne are in each group. What if, purely by chance, all the group we selected to eat jelly beans would have had acne anyway while those who didn’t eat jelly beans were the lucky sort of people who never get spots? Then, even if jelly beans did not cause acne, we would conclude that jelly beans did cause acne. Of course, it is very unlikely that all the acne prone people end up in one group by chance, especially if we have enough people in each group. However, to give more confidence in the result of this type of experiment, scientists use statistics to see how likely it is that the result they find is purely by chance. This is known as {{w|statistical hypothesis testing}}. Before we start the experiment, we choose a threshold known as the significance level. In the comic the scientists choose a threshold of 5&amp;amp;thinsp;%. If they find that more of the people who ate jelly beans had acne and the chance it was a purely random result is less than 1 in 20, they will say that jelly beans do cause acne. If, however, the chance that their result was purely by random chance is greater than 5&amp;amp;thinsp;%, they will say they have found no evidence of a link. The important point is this: '''there could still be a 1 in 20 chance that this result was purely a statistical fluke.'''&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Some people will suffer from acne whether they eat jelly beans or not, and some will never have acne even if they do eat jelly beans. There is an element of chance in how many people prone to acne are in each group. What if, purely by chance, all the group we selected to eat jelly beans would have had acne anyway while those who didn’t eat jelly beans were the lucky sort of people who never get spots? Then, even if jelly beans did not cause acne, we would conclude that jelly beans did cause acne. Of course, it is very unlikely that all the acne prone people end up in one group by chance, especially if we have enough people in each group. However, to give more confidence in the result of this type of experiment, scientists use statistics to see how likely it is that the result they find is purely by chance. This is known as {{w|statistical hypothesis testing}}. Before we start the experiment, we choose a threshold known as the significance level. In the comic the scientists choose a threshold of 5&amp;amp;thinsp;%. If they find that more of the people who ate jelly beans had acne and the chance it was a purely random result is less than 1 in 20, they will say that jelly beans do cause acne. If, however, the chance that their result was purely by random chance is greater than 5&amp;amp;thinsp;%, they will say they have found no evidence of a link. The important point is this: '''there could still be a 1 in 20 chance that this result was purely a statistical fluke.'''&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l24&quot; &gt;Line 24:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 24:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;To elaborate on the statistical theory behind this issue:&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;To elaborate on the statistical theory behind this issue:&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;If the probability that each trial gives a false positive result is 1 in 20, then by testing 20 different colors it is now likely that at least one jelly bean test will give a false positive. To be precise, the probability of having ''zero'' false positives in 20 tests is 0.95&amp;lt;sup&amp;gt;20&amp;lt;/sup&amp;gt; = 35.85&amp;amp;thinsp;% while the probability of having at least 1 false positive in 20 tests is 64.15&amp;amp;thinsp;% (the probability of having ''zero'' false positive in 21 tests (counting the test without color discrimination) is 0.95&amp;lt;sup&amp;gt;21&amp;lt;/sup&amp;gt; = 34.06&amp;amp;thinsp;%).&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;If the probability that each trial gives a false positive result is 1 in 20, then by testing 20 different colors it is now likely that at least one jelly bean test will give a false positive. To be precise, the probability of having ''zero'' false positives in 20 tests is 0.95&amp;lt;sup&amp;gt;20&amp;lt;/sup&amp;gt; = 35.85&amp;amp;thinsp;% while the probability of having at least 1 false positive in 20 tests is 64.15&amp;amp;thinsp;% (the probability of having ''zero'' false positive in 21 tests (counting the test without color discrimination) is 0.95&amp;lt;sup&amp;gt;21&amp;lt;/sup&amp;gt; = 34.06&amp;amp;thinsp;%).&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;In scientific fields that perform many simultaneous tests on large amounts of data it is therefore common to adjust for the effect of {{w|Multiple_comparisons_problem|multiple testing}}; typically by controlling the {{w|False_discovery_rate|False Discovery Rate}} which is the number of (expected) false positives compared to all positive results (here, it would be 1/1&amp;amp;nbsp;= 1). For this, you bundle your tests into a single “test of tests” and adjust your single-test p-values such that the chance of your “test of tests” reporting a significant result falls below a certain threshold. Typically, that threshold is 0.&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;05—the &lt;/del&gt;same as the conventional p-value for a single test, and it can be interpreted the same way: that only 1 in 20 “tests of tests” would report a result at this level of significance even if the null hypothesis were true.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;In scientific fields that perform many simultaneous tests on large amounts of data it is therefore common to adjust for the effect of {{w|Multiple_comparisons_problem|multiple testing}}; typically by controlling the {{w|False_discovery_rate|False Discovery Rate}} which is the number of (expected) false positives compared to all positive results (here, it would be 1/1&amp;amp;nbsp;= 1). For this, you bundle your tests into a single “test of tests” and adjust your single-test p-values such that the chance of your “test of tests” reporting a significant result falls below a certain threshold. Typically, that threshold is 0.&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;05 — the &lt;/ins&gt;same as the conventional p-value for a single test, and it can be interpreted the same way: that only 1 in 20 “tests of tests” would report a result at this level of significance even if the null hypothesis were true.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Applying the {{w|False_discovery_rate#Benjamini–Hochberg_procedure|Benjamini–Hochberg procedure}}, the lowest p-value of a set of 20 tests would need to be smaller than (1/20)&amp;amp;nbsp;× 0.05&amp;amp;nbsp;= 0.0025 to be accepted as significant. Such an adjustment would likely have prevented the situation depicted in the comic.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Applying the {{w|False_discovery_rate#Benjamini–Hochberg_procedure|Benjamini–Hochberg procedure}}, the lowest p-value of a set of 20 tests would need to be smaller than (1/20)&amp;amp;nbsp;× 0.05&amp;amp;nbsp;= 0.0025 to be accepted as significant. Such an adjustment would likely have prevented the situation depicted in the comic.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;This general situation is (sadly) often an issue with more serious matters than jelly beans and &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;acne—at &lt;/del&gt;any one time there are many studies about possible links between substances (e.&amp;amp;thinsp;g. red wine) and illness (e.&amp;amp;thinsp;g. cancer). Because only the positive results get reported, this limits the value any single study &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;has—especially &lt;/del&gt;if the mechanism linking the two things is not known.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;This general situation is (sadly) often an issue with more serious matters than jelly beans and &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;acne — at &lt;/ins&gt;any one time there are many studies about possible links between substances (e.&amp;amp;thinsp;g. red wine) and illness (e.&amp;amp;thinsp;g. cancer). Because only the positive results get reported, this limits the value any single study &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;has — especially &lt;/ins&gt;if the mechanism linking the two things is not known.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;=== p-hacking and bad news reporting in real life ===&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;=== p-hacking and bad news reporting in real life ===&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>92.23.2.228</name></author>	</entry>

	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=882:_Significant&amp;diff=381537&amp;oldid=prev</id>
		<title>134.60.67.135: /* Explanation */</title>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=882:_Significant&amp;diff=381537&amp;oldid=prev"/>
				<updated>2025-07-21T07:17:48Z</updated>
		
		<summary type="html">&lt;p&gt;‎&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Explanation&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 07:17, 21 July 2025&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l10&quot; &gt;Line 10:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 10:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;This comic is about {{w|data dredging}} (aka ''p''-hacking), and the misrepresentation of science and statistics in the media. A girl with a black ponytail comes to [[Cueball]] with her claim that {{w|jelly beans}} cause {{w|acne}}, and Cueball then commissions two scientists (a man with goggles and [[Megan]]) to do some research on the link between jelly beans and acne. They find no link, but in the end the real result of this research is bad news reporting!&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;This comic is about {{w|data dredging}} (aka ''p''-hacking), and the misrepresentation of science and statistics in the media. A girl with a black ponytail comes to [[Cueball]] with her claim that {{w|jelly beans}} cause {{w|acne}}, and Cueball then commissions two scientists (a man with goggles and [[Megan]]) to do some research on the link between jelly beans and acne. They find no link, but in the end the real result of this research is bad news reporting!&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;First, some basic statistical theory. &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;Let's &lt;/del&gt;imagine you are trying to find out if jelly beans cause acne. To do this you could find a group of people and randomly split them into two &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;groups - one &lt;/del&gt;group who you get to eat lots of jelly beans and a second group who are banned from eating jelly beans. After some time you compare whether the group that eat jelly beans have more acne than those who do not. If more people in the group that eat jelly beans have acne, then you might think that jelly beans cause acne. However, there is a problem.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;First, some basic statistical theory. &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;Let’s &lt;/ins&gt;imagine you are trying to find out if jelly beans cause acne. To do this you could find a group of people and randomly split them into two &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;groups—one &lt;/ins&gt;group who you get to eat lots of jelly beans and a second group who are banned from eating jelly beans. After some time you compare whether the group that eat jelly beans have more acne than those who do not. If more people in the group that eat jelly beans have acne, then you might think that jelly beans cause acne. However, there is a problem.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Some people will suffer from acne whether they eat jelly beans or not, and some will never have acne even if they do eat jelly beans. There is an element of chance in how many people prone to acne are in each group. What if, purely by chance, all the group we selected to eat jelly beans would have had acne anyway while those who &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;didn't &lt;/del&gt;eat jelly beans were the lucky sort of people who never get spots? Then, even if jelly beans did not cause acne, we would conclude that jelly beans did cause acne. Of course, it is very unlikely that all the acne prone people end up in one group by chance, especially if we have enough people in each group. However, to give more confidence in the result of this type of experiment, scientists use statistics to see how likely it is that the result they find is purely by chance. This is known as {{w|statistical hypothesis testing}}. Before we start the experiment, we choose a threshold known as the significance level. In the comic the scientists choose a threshold of 5%. If they find that more of the people who ate jelly beans had acne and the chance it was a purely random result is less than 1 in 20, they will say that jelly beans do cause acne. If, however, the chance that their result was purely by random chance is greater than 5%, they will say they have found no evidence of a link. The important point is this &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;– &lt;/del&gt;'''there could still be a 1 in 20 chance that this result was purely a statistical fluke'''&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;.&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Some people will suffer from acne whether they eat jelly beans or not, and some will never have acne even if they do eat jelly beans. There is an element of chance in how many people prone to acne are in each group. What if, purely by chance, all the group we selected to eat jelly beans would have had acne anyway while those who &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;didn’t &lt;/ins&gt;eat jelly beans were the lucky sort of people who never get spots? Then, even if jelly beans did not cause acne, we would conclude that jelly beans did cause acne. Of course, it is very unlikely that all the acne prone people end up in one group by chance, especially if we have enough people in each group. However, to give more confidence in the result of this type of experiment, scientists use statistics to see how likely it is that the result they find is purely by chance. This is known as {{w|statistical hypothesis testing}}. Before we start the experiment, we choose a threshold known as the significance level. In the comic the scientists choose a threshold of 5&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;amp;thinsp;&lt;/ins&gt;%. If they find that more of the people who ate jelly beans had acne and the chance it was a purely random result is less than 1 in 20, they will say that jelly beans do cause acne. If, however, the chance that their result was purely by random chance is greater than 5&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;amp;thinsp;&lt;/ins&gt;%, they will say they have found no evidence of a link. The important point is this&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;: &lt;/ins&gt;'''there could still be a 1 in 20 chance that this result was purely a statistical fluke&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;.&lt;/ins&gt;'''&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;At first, the scientists do not want to stop playing ''{{w|Minecraft}}'', but they do eventually start. Minecraft was previously referenced in [[861: Wisdom Teeth]].&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;At first, the scientists do not want to stop playing ''{{w|Minecraft}}'', but they do eventually start. Minecraft was previously referenced in [[861: Wisdom Teeth]].&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The scientists find no link between jelly beans and acne (the probability that the result is by chance is more than 5% i.e. ''p'' &amp;gt; 0.05), but then Megan and Cueball ask them to see if only one color of jelly beans is responsible. They test 20 different colors, each at a significance level of 5%. &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The scientists find no link between jelly beans and acne (the probability that the result is by chance is more than 5&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;amp;thinsp;&lt;/ins&gt;%&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;, &lt;/ins&gt;i.&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;amp;thinsp;&lt;/ins&gt;e. ''p'' &amp;gt; 0.05), but then Megan and Cueball ask them to see if only one color of jelly beans is responsible. They test 20 different colors, each at a significance level of 5&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;amp;thinsp;&lt;/ins&gt;%. &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;This finding leads to a big newspaper headline saying '''Green Jelly Beans Linked To Acne''' where it is said that they have 95 percent confidence with only a 5% chance of a coincidence. Unfortunately, while the p-values reported by the scientists are (presumably) mathematically correct, the wording in the newspaper is misleading and would only apply if green jelly beans were the only ones tested. Common sense should tell you that when you do a whole bunch of tests, it becomes much more likely that &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;you'll &lt;/del&gt;get a false positive result.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;This finding leads to a big newspaper headline saying '''Green Jelly Beans Linked To Acne''' where it is said that they have 95 percent confidence with only a 5&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;amp;thinsp;&lt;/ins&gt;% chance of a coincidence. Unfortunately, while the p-values reported by the scientists are (presumably) mathematically correct, the wording in the newspaper is misleading and would only apply if green jelly beans were the only ones tested. Common sense should tell you that when you do a whole bunch of tests, it becomes much more likely that &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;you’ll &lt;/ins&gt;get a false positive result.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;In the title text, we find out that the scientists {{w|Reproducibility|repeated the experiment}} (another key part of the scientific method), but now they no longer find any evidence for the link between acne and green jelly beans. They try to tell the reporter something, maybe that it was probably a coincidence, but the reporters are not interested since that is not news, and refuse to listen. Instead, they make another major headline from the repeat study saying '''Research conflicted''' (which is not accurate, the scientists doubted their results and had their doubts ''confirmed'') and recommend more study on the link (which is what the scientist just did).&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;In the title text, we find out that the scientists {{w|Reproducibility|repeated the experiment}} (another key part of the scientific method), but now they no longer find any evidence for the link between acne and green jelly beans. They try to tell the reporter something, maybe that it was probably a coincidence, but the reporters are not interested since that is not news, and refuse to listen. Instead, they make another major headline from the repeat study saying '''Research conflicted''' (which is not accurate, the scientists doubted their results and had their doubts ''confirmed'') and recommend more study on the link (which is what the scientist just did).&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;To elaborate on the statistical theory behind this issue:&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;To elaborate on the statistical theory behind this issue:&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;If the probability that each trial gives a false positive result is 1 in 20, then by testing 20 different colors it is now likely that at least one jelly bean test will give a false positive. To be precise, the probability of having ''zero'' false positives in 20 tests is 0.95&amp;lt;sup&amp;gt;20&amp;lt;/sup&amp;gt; = 35.85% while the probability of having at least 1 false positive in 20 tests is 64.15% (the probability of having ''zero'' false positive in 21 tests (counting the test without color discrimination) is 0.95&amp;lt;sup&amp;gt;21&amp;lt;/sup&amp;gt; = 34.06%).&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;If the probability that each trial gives a false positive result is 1 in 20, then by testing 20 different colors it is now likely that at least one jelly bean test will give a false positive. To be precise, the probability of having ''zero'' false positives in 20 tests is 0.95&amp;lt;sup&amp;gt;20&amp;lt;/sup&amp;gt; = 35.85&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;amp;thinsp;&lt;/ins&gt;% while the probability of having at least 1 false positive in 20 tests is 64.15&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;amp;thinsp;&lt;/ins&gt;% (the probability of having ''zero'' false positive in 21 tests (counting the test without color discrimination) is 0.95&amp;lt;sup&amp;gt;21&amp;lt;/sup&amp;gt; = 34.06&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;amp;thinsp;&lt;/ins&gt;%).&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;In scientific fields that perform many simultaneous tests on large amounts of data it is therefore common to adjust for the effect of {{w|Multiple_comparisons_problem|multiple testing}}; typically by controlling the {{w|False_discovery_rate|False Discovery Rate}} which is the number of (expected) false positives compared to all positive results (here, it would be 1/1=1). For this, you bundle your tests into a single &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;&amp;quot;test &lt;/del&gt;of &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;tests&amp;quot; &lt;/del&gt;and adjust your single-test p-values such that the chance of your &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;''&amp;quot;test &lt;/del&gt;of &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;tests&amp;quot;'' &lt;/del&gt;reporting a significant result falls below a certain threshold. Typically, that threshold is 0.&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;05 - the &lt;/del&gt;same as the conventional p-value for a single test, and it can be interpreted the same way: that only 1 in 20 &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;&amp;quot;tests &lt;/del&gt;of &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;tests&amp;quot; &lt;/del&gt;would report a result at this level of significance even if the null hypothesis were true.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;In scientific fields that perform many simultaneous tests on large amounts of data it is therefore common to adjust for the effect of {{w|Multiple_comparisons_problem|multiple testing}}; typically by controlling the {{w|False_discovery_rate|False Discovery Rate}} which is the number of (expected) false positives compared to all positive results (here, it would be 1/1&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;amp;nbsp;&lt;/ins&gt;= 1). For this, you bundle your tests into a single &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;“test &lt;/ins&gt;of &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;tests” &lt;/ins&gt;and adjust your single-test p-values such that the chance of your &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;“test &lt;/ins&gt;of &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;tests” &lt;/ins&gt;reporting a significant result falls below a certain threshold. Typically, that threshold is 0.&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;05—the &lt;/ins&gt;same as the conventional p-value for a single test, and it can be interpreted the same way: that only 1 in 20 &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;“tests &lt;/ins&gt;of &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;tests” &lt;/ins&gt;would report a result at this level of significance even if the null hypothesis were true.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Applying the {{w|False_discovery_rate#Benjamini–Hochberg_procedure|Benjamini–Hochberg procedure}}, the lowest p-value of a set of 20 tests would need to be smaller than (1/20)&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;*&lt;/del&gt;0.05 = 0.0025 to be accepted as significant. Such an adjustment would likely have prevented the situation depicted in the comic.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Applying the {{w|False_discovery_rate#Benjamini–Hochberg_procedure|Benjamini–Hochberg procedure}}, the lowest p-value of a set of 20 tests would need to be smaller than (1/20)&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;amp;nbsp;× &lt;/ins&gt;0.05&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;amp;nbsp;&lt;/ins&gt;= 0.0025 to be accepted as significant. Such an adjustment would likely have prevented the situation depicted in the comic.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;This general situation is (sadly) often an issue with more serious matters than jelly beans and &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;acne – at &lt;/del&gt;any one time there are many studies about possible links between substances (e.g. red wine) and illness (e.g. cancer). Because only the positive results get reported, this limits the value any single study &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;has - especially &lt;/del&gt;if the mechanism linking the two things is not known.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;This general situation is (sadly) often an issue with more serious matters than jelly beans and &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;acne—at &lt;/ins&gt;any one time there are many studies about possible links between substances (e.&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;amp;thinsp;&lt;/ins&gt;g. red wine) and illness (e.&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;amp;thinsp;&lt;/ins&gt;g. cancer). Because only the positive results get reported, this limits the value any single study &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;has—especially &lt;/ins&gt;if the mechanism linking the two things is not known.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;=== p-hacking and bad news reporting in real life ===&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;=== p-hacking and bad news reporting in real life ===&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;In 2015 some journalists demonstrated the same problem: just how gullible other news outlets are with the same sort of flawed &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;&amp;quot;experimental design&amp;quot;&lt;/del&gt;: [http://www.washingtonpost.com/news/morning-mix/wp/2015/05/28/how-and-why-a-journalist-tricked-news-outlets-into-thinking-chocolate-makes-you-thin/?hpid=z5 How, and why, a journalist tricked news outlets into thinking chocolate makes you thin - The Washington Post]&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;In 2015 some journalists demonstrated the same problem: just how gullible other news outlets are with the same sort of flawed &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;“experimental design”&lt;/ins&gt;: [http://www.washingtonpost.com/news/morning-mix/wp/2015/05/28/how-and-why-a-journalist-tricked-news-outlets-into-thinking-chocolate-makes-you-thin/?hpid=z5 How, and why, a journalist tricked news outlets into thinking chocolate makes you thin - The Washington Post]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==Transcript==&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==Transcript==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>134.60.67.135</name></author>	</entry>

	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=882:_Significant&amp;diff=345111&amp;oldid=prev</id>
		<title>Elektrizikekswerk: /* Explanation */ Having such statements in the explanation of a comic about statistical evidence is rather ironic...</title>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=882:_Significant&amp;diff=345111&amp;oldid=prev"/>
				<updated>2024-06-26T09:57:31Z</updated>
		
		<summary type="html">&lt;p&gt;‎&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Explanation: &lt;/span&gt; Having such statements in the explanation of a comic about statistical evidence is rather ironic...&lt;/span&gt;&lt;/p&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 09:57, 26 June 2024&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l14&quot; &gt;Line 14:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 14:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Some people will suffer from acne whether they eat jelly beans or not, and some will never have acne even if they do eat jelly beans. There is an element of chance in how many people prone to acne are in each group. What if, purely by chance, all the group we selected to eat jelly beans would have had acne anyway while those who didn't eat jelly beans were the lucky sort of people who never get spots? Then, even if jelly beans did not cause acne, we would conclude that jelly beans did cause acne. Of course, it is very unlikely that all the acne prone people end up in one group by chance, especially if we have enough people in each group. However, to give more confidence in the result of this type of experiment, scientists use statistics to see how likely it is that the result they find is purely by chance. This is known as {{w|statistical hypothesis testing}}. Before we start the experiment, we choose a threshold known as the significance level. In the comic the scientists choose a threshold of 5%. If they find that more of the people who ate jelly beans had acne and the chance it was a purely random result is less than 1 in 20, they will say that jelly beans do cause acne. If, however, the chance that their result was purely by random chance is greater than 5%, they will say they have found no evidence of a link. The important point is this – '''there could still be a 1 in 20 chance that this result was purely a statistical fluke'''.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Some people will suffer from acne whether they eat jelly beans or not, and some will never have acne even if they do eat jelly beans. There is an element of chance in how many people prone to acne are in each group. What if, purely by chance, all the group we selected to eat jelly beans would have had acne anyway while those who didn't eat jelly beans were the lucky sort of people who never get spots? Then, even if jelly beans did not cause acne, we would conclude that jelly beans did cause acne. Of course, it is very unlikely that all the acne prone people end up in one group by chance, especially if we have enough people in each group. However, to give more confidence in the result of this type of experiment, scientists use statistics to see how likely it is that the result they find is purely by chance. This is known as {{w|statistical hypothesis testing}}. Before we start the experiment, we choose a threshold known as the significance level. In the comic the scientists choose a threshold of 5%. If they find that more of the people who ate jelly beans had acne and the chance it was a purely random result is less than 1 in 20, they will say that jelly beans do cause acne. If, however, the chance that their result was purely by random chance is greater than 5%, they will say they have found no evidence of a link. The important point is this – '''there could still be a 1 in 20 chance that this result was purely a statistical fluke'''.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;At first, the scientists do not want to stop playing &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;the addictive game &lt;/del&gt;''{{w|Minecraft}}'', but they do eventually start. Minecraft was previously referenced in [[861: Wisdom Teeth]].&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;At first, the scientists do not want to stop playing ''{{w|Minecraft}}'', but they do eventually start. Minecraft was previously referenced in [[861: Wisdom Teeth]].&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The scientists find no link between jelly beans and acne (the probability that the result is by chance is more than 5% i.e. ''p'' &amp;gt; 0.05), but then Megan and Cueball ask them to see if only one color of jelly beans is responsible. They test 20 different colors, each at a significance level of 5%. &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The scientists find no link between jelly beans and acne (the probability that the result is by chance is more than 5% i.e. ''p'' &amp;gt; 0.05), but then Megan and Cueball ask them to see if only one color of jelly beans is responsible. They test 20 different colors, each at a significance level of 5%. &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Elektrizikekswerk</name></author>	</entry>

	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=882:_Significant&amp;diff=315869&amp;oldid=prev</id>
		<title>Rebekka: Typo</title>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=882:_Significant&amp;diff=315869&amp;oldid=prev"/>
				<updated>2023-06-22T12:52:52Z</updated>
		
		<summary type="html">&lt;p&gt;Typo&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr style=&quot;vertical-align: top;&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 12:52, 22 June 2023&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l24&quot; &gt;Line 24:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 24:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;To elaborate on the statistical theory behind this issue:&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;To elaborate on the statistical theory behind this issue:&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;If the probability that each trial gives a false positive result is 1 in 20, then by testing 20 different colors it is now likely that at least one jelly bean test will give a false positive. To be precise, the probability of having ''zero'' false positives in 20 tests is 0.95&amp;lt;sup&amp;gt;20&amp;lt;/sup&amp;gt; = 35.85% while the probability of having at least 1 false positive in 20 tests is 64.15% (the probability of having ''zero'' false positive in 21 tests (counting the test without color discrimination) is 0.95&amp;lt;sup&amp;gt;21&amp;lt;/sup&amp;gt; = 34.06%).&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;If the probability that each trial gives a false positive result is 1 in 20, then by testing 20 different colors it is now likely that at least one jelly bean test will give a false positive. To be precise, the probability of having ''zero'' false positives in 20 tests is 0.95&amp;lt;sup&amp;gt;20&amp;lt;/sup&amp;gt; = 35.85% while the probability of having at least 1 false positive in 20 tests is 64.15% (the probability of having ''zero'' false positive in 21 tests (counting the test without color discrimination) is 0.95&amp;lt;sup&amp;gt;21&amp;lt;/sup&amp;gt; = 34.06%).&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;In fields &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;dealing &lt;/del&gt;that perform many simultaneous tests on large amounts of data it is therefore common to adjust for the effect of {{w|Multiple_comparisons_problem|multiple testing}}; typically by controlling the {{w|False_discovery_rate|False Discovery Rate}} which is the number of (expected) false positives compared to all positive results (here, it would be 1/1=1). For this, you bundle your tests into a single &amp;quot;test of tests&amp;quot; and adjust your single-test p-values such that the chance of your ''&amp;quot;test of tests&amp;quot;'' reporting a significant result falls below a certain threshold. Typically, that threshold is 0.05 - the same as the conventional p-value for a single test, and it can be interpreted the same way: that only 1 in 20 &amp;quot;tests of tests&amp;quot; would report a result at this level of significance even if the null hypothesis were true.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;In &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;scientific &lt;/ins&gt;fields that perform many simultaneous tests on large amounts of data it is therefore common to adjust for the effect of {{w|Multiple_comparisons_problem|multiple testing}}; typically by controlling the {{w|False_discovery_rate|False Discovery Rate}} which is the number of (expected) false positives compared to all positive results (here, it would be 1/1=1). For this, you bundle your tests into a single &amp;quot;test of tests&amp;quot; and adjust your single-test p-values such that the chance of your ''&amp;quot;test of tests&amp;quot;'' reporting a significant result falls below a certain threshold. Typically, that threshold is 0.05 - the same as the conventional p-value for a single test, and it can be interpreted the same way: that only 1 in 20 &amp;quot;tests of tests&amp;quot; would report a result at this level of significance even if the null hypothesis were true.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Applying the {{w|False_discovery_rate#Benjamini–Hochberg_procedure|Benjamini–Hochberg procedure}}, the lowest p-value of a set of 20 tests would need to be smaller than (1/20)*0.05 = 0.0025 to be accepted as significant. Such an adjustment would likely have prevented the situation depicted in the comic.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Applying the {{w|False_discovery_rate#Benjamini–Hochberg_procedure|Benjamini–Hochberg procedure}}, the lowest p-value of a set of 20 tests would need to be smaller than (1/20)*0.05 = 0.0025 to be accepted as significant. Such an adjustment would likely have prevented the situation depicted in the comic.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Rebekka</name></author>	</entry>

	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=882:_Significant&amp;diff=315867&amp;oldid=prev</id>
		<title>Rebekka: Added the subjects of multiple testing and false discovery rate to the statistcal part. Changed flow of paragraphs so that the stats theory is one single paragraph separate from the plot discription. Some minor additional changes of wording.</title>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=882:_Significant&amp;diff=315867&amp;oldid=prev"/>
				<updated>2023-06-22T12:50:39Z</updated>
		
		<summary type="html">&lt;p&gt;Added the subjects of multiple testing and false discovery rate to the statistcal part. Changed flow of paragraphs so that the stats theory is one single paragraph separate from the plot discription. Some minor additional changes of wording.&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 12:50, 22 June 2023&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l16&quot; &gt;Line 16:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 16:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;At first, the scientists do not want to stop playing the addictive game ''{{w|Minecraft}}'', but they do eventually start. Minecraft was previously referenced in [[861: Wisdom Teeth]].&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;At first, the scientists do not want to stop playing the addictive game ''{{w|Minecraft}}'', but they do eventually start. Minecraft was previously referenced in [[861: Wisdom Teeth]].&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The scientists find no link between jelly beans and acne (the probability that the result is by chance is more than 5% i.e. ''p'' &amp;gt; 0.05), but then Megan and Cueball ask them to see if only one color of jelly beans is responsible. They test 20 different colors, each at a significance level of 5&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;%. If the probability that each trial gives a false positive result is 1 in 20, then by testing 20 different colors it is now likely that at least one jelly bean test will give a false positive. To be precise, the probability of having ''no'' false positive in 20 tests is 0.95&amp;lt;sup&amp;gt;20&amp;lt;/sup&amp;gt; = 35.85%. Probability of having ''no'' false positive in 21 tests (counting the test without color discrimination) is 0.95&amp;lt;sup&amp;gt;21&amp;lt;/sup&amp;gt; = 34.06&lt;/del&gt;%. &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The scientists find no link between jelly beans and acne (the probability that the result is by chance is more than 5% i.e. ''p'' &amp;gt; 0.05), but then Megan and Cueball ask them to see if only one color of jelly beans is responsible. They test 20 different colors, each at a significance level of 5%. &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;This finding leads to a big newspaper headline saying '''Green Jelly Beans Linked To Acne''' where it is said that they have 95 percent confidence with only a 5% chance of a coincidence. &lt;del class=&quot;diffchange diffchange-inline&quot;&gt; &lt;/del&gt;Unfortunately, &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;although this number has been &lt;/del&gt;reported by the scientists&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;' stats package &lt;/del&gt;and would &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;be true &lt;/del&gt;if green jelly beans were the only ones tested&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;, it is also seriously misleading&lt;/del&gt;. &lt;del class=&quot;diffchange diffchange-inline&quot;&gt; If &lt;/del&gt;you &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;roll just one die, one time, &lt;/del&gt;you &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;aren't very likely to roll &lt;/del&gt;a &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;six... but if you roll &lt;/del&gt;it &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;20 times you are very &lt;/del&gt;likely &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;to have at least one six among them.&amp;#160; This means &lt;/del&gt;that you &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;cannot just ignore the other 19 experiments that failed. There are good methods for handling this problem, notably {{w|Bayesian_inference|Bayesian inference}}, but they can be difficult to use and explain, and complexity does not sell newspapers&lt;/del&gt;.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;This finding leads to a big newspaper headline saying '''Green Jelly Beans Linked To Acne''' where it is said that they have 95 percent confidence with only a 5% chance of a coincidence. Unfortunately, &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;while the p-values &lt;/ins&gt;reported by the scientists &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;are (presumably) mathematically correct, the wording in the newspaper is misleading &lt;/ins&gt;and would &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;only apply &lt;/ins&gt;if green jelly beans were the only ones tested. &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;Common sense should tell &lt;/ins&gt;you &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;that when &lt;/ins&gt;you &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;do &lt;/ins&gt;a &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;whole bunch of tests, &lt;/ins&gt;it &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;becomes much more &lt;/ins&gt;likely that you&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;'ll get a false positive result&lt;/ins&gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;In the title text, we find out that the scientists {{w|Reproducibility|repeated the experiment}} (another key part of the scientific method), but now they no longer find any evidence for the link between acne and green jelly beans. They try to tell the reporter something, maybe that it was probably a coincidence, but the reporters are not interested since that is not news. &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;So they do not listen to what the scientist has to say and instead uses the information &lt;/del&gt;they &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;have to &lt;/del&gt;make another major headline saying '''Research conflicted''' and recommend more study on the link&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;. But that was just &lt;/del&gt;what the scientist &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;already &lt;/del&gt;did.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;In the title text, we find out that the scientists {{w|Reproducibility|repeated the experiment}} (another key part of the scientific method), but now they no longer find any evidence for the link between acne and green jelly beans. They try to tell the reporter something, maybe that it was probably a coincidence, but the reporters are not interested since that is not news&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;, and refuse to listen&lt;/ins&gt;. &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;Instead, &lt;/ins&gt;they make another major headline &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;from the repeat study &lt;/ins&gt;saying '''Research conflicted''' &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;(which is not accurate, the scientists doubted their results and had their doubts ''confirmed'') &lt;/ins&gt;and recommend more study on the link &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;(which is &lt;/ins&gt;what the scientist &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;just &lt;/ins&gt;did&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;)&lt;/ins&gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;This is (sadly) often an issue with more serious matters than jelly beans and acne – at any one time there are many studies about possible links between substances (e.g. red wine) and illness (e.g. cancer). Because only the positive results get reported, this limits the value any single study has - especially if the mechanism linking the two things is not known.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;To elaborate on the statistical theory behind this issue:&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;If the probability that each trial gives a false positive result is 1 in 20, then by testing 20 different colors it is now likely that at least one jelly bean test will give a false positive. To be precise, the probability of having ''zero'' false positives in 20 tests is 0.95&amp;lt;sup&amp;gt;20&amp;lt;/sup&amp;gt; = 35.85% while the probability of having at least 1 false positive in 20 tests is 64.15% (the probability of having ''zero'' false positive in 21 tests (counting the test without color discrimination) is 0.95&amp;lt;sup&amp;gt;21&amp;lt;/sup&amp;gt; = 34.06%).&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;In fields dealing that perform many simultaneous tests on large amounts of data it is therefore common to adjust for the effect of {{w|Multiple_comparisons_problem|multiple testing}}; typically by controlling the {{w|False_discovery_rate|False Discovery Rate}} which is the number of (expected) false positives compared to all positive results (here, it would be 1/1=1). For this, you bundle your tests into a single &amp;quot;test of tests&amp;quot; and adjust your single-test p-values such that the chance of your ''&amp;quot;test of tests&amp;quot;'' reporting a significant result falls below a certain threshold. Typically, that threshold is 0.05 - the same as the conventional p-value for a single test, and it can be interpreted the same way: that only 1 in 20 &amp;quot;tests of tests&amp;quot; would report a result at this level of significance even if the null hypothesis were true.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;Applying the {{w|False_discovery_rate#Benjamini–Hochberg_procedure|Benjamini–Hochberg procedure}}, the lowest p-value of a set of 20 tests would need to be smaller than (1/20)*0.05 = 0.0025 to be accepted as significant. Such an adjustment would likely have prevented the situation depicted in the comic.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;This &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;general situation &lt;/ins&gt;is (sadly) often an issue with more serious matters than jelly beans and acne – at any one time there are many studies about possible links between substances (e.g. red wine) and illness (e.g. cancer). Because only the positive results get reported, this limits the value any single study has - especially if the mechanism linking the two things is not known.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;=== p-hacking and bad news reporting in real life ===&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;=== p-hacking and bad news reporting in real life ===&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Rebekka</name></author>	</entry>

	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=882:_Significant&amp;diff=305048&amp;oldid=prev</id>
		<title>108.162.221.42: /* Explanation */ minor grammatical and punctuation corrections</title>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=882:_Significant&amp;diff=305048&amp;oldid=prev"/>
				<updated>2023-01-20T07:59:02Z</updated>
		
		<summary type="html">&lt;p&gt;‎&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Explanation: &lt;/span&gt; minor grammatical and punctuation corrections&lt;/span&gt;&lt;/p&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 07:59, 20 January 2023&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l8&quot; &gt;Line 8:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 8:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==Explanation==&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==Explanation==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;This comic is about {{w|data dredging}} (aka ''p''-hacking), and the misrepresentation of science and statistics in the media. A girl with a black ponytail comes to [[Cueball]] with her claim that {{w|jelly beans}} cause {{w|acne}} and Cueball then &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;commission &lt;/del&gt;two scientists (a man with goggles and [[Megan]]) to do some research on the link between jelly beans and acne. They find no link, but in the end the real result of this research is bad news reporting!&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;This comic is about {{w|data dredging}} (aka ''p''-hacking), and the misrepresentation of science and statistics in the media. A girl with a black ponytail comes to [[Cueball]] with her claim that {{w|jelly beans}} cause {{w|acne}}&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;, &lt;/ins&gt;and Cueball then &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;commissions &lt;/ins&gt;two scientists (a man with goggles and [[Megan]]) to do some research on the link between jelly beans and acne. They find no link, but in the end the real result of this research is bad news reporting!&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;First some basic statistical theory. Let's imagine you are trying to find out if jelly beans cause acne. To do this you could find a group of people and randomly split them into two groups - one group who you get to eat lots of jelly beans and a second group who are banned from eating jelly beans. After some time you compare whether the group that eat jelly beans have more acne than those who do not. If more people in the group that eat jelly beans have acne then you might think that jelly beans cause acne. However, there is a problem.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;First&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;, &lt;/ins&gt;some basic statistical theory. Let's imagine you are trying to find out if jelly beans cause acne. To do this you could find a group of people and randomly split them into two groups - one group who you get to eat lots of jelly beans and a second group who are banned from eating jelly beans. After some time you compare whether the group that eat jelly beans have more acne than those who do not. If more people in the group that eat jelly beans have acne&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;, &lt;/ins&gt;then you might think that jelly beans cause acne. However, there is a problem.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Some people will suffer from acne whether they eat jelly beans or not and some will never have acne even if they do eat jelly beans. There is an element of chance in how many people prone to acne are in each group. What if, purely by chance, all the group we selected to eat jelly beans would have had acne anyway while those who didn't eat jelly beans were the lucky sort of people who never get spots? Then, even if jelly beans did not cause acne, we would conclude that jelly beans did cause acne. Of course it is very unlikely that all the acne prone people end up in one group by chance, especially if we have enough people in each group. However, to give more confidence in the result of this type of experiment, scientists use statistics to see how likely it is that the result they find is purely by chance. This is known as {{w|statistical hypothesis testing}}. Before we start the experiment, we choose a threshold known as the significance level. In the comic the scientists choose a threshold of 5%. If they find that more of the people who ate jelly beans had acne and the chance it was a purely random result is less than 1 in 20, they will say that jelly beans do cause acne. If however, the chance that their result was purely by random chance is greater than 5% they will say they have found no evidence of a link. The important point is this – '''there could still be a 1 in 20 chance that this result was purely a statistical fluke'''.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Some people will suffer from acne whether they eat jelly beans or not&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;, &lt;/ins&gt;and some will never have acne even if they do eat jelly beans. There is an element of chance in how many people prone to acne are in each group. What if, purely by chance, all the group we selected to eat jelly beans would have had acne anyway while those who didn't eat jelly beans were the lucky sort of people who never get spots? Then, even if jelly beans did not cause acne, we would conclude that jelly beans did cause acne. Of course&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;, &lt;/ins&gt;it is very unlikely that all the acne prone people end up in one group by chance, especially if we have enough people in each group. However, to give more confidence in the result of this type of experiment, scientists use statistics to see how likely it is that the result they find is purely by chance. This is known as {{w|statistical hypothesis testing}}. Before we start the experiment, we choose a threshold known as the significance level. In the comic the scientists choose a threshold of 5%. If they find that more of the people who ate jelly beans had acne and the chance it was a purely random result is less than 1 in 20, they will say that jelly beans do cause acne. If&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;, &lt;/ins&gt;however, the chance that their result was purely by random chance is greater than 5%&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;, &lt;/ins&gt;they will say they have found no evidence of a link. The important point is this – '''there could still be a 1 in 20 chance that this result was purely a statistical fluke'''.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;At first the scientists do not want to stop playing the addictive game ''{{w|Minecraft}}'', but they do eventually start. Minecraft was previously referenced in [[861: Wisdom Teeth]].&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;At first&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;, &lt;/ins&gt;the scientists do not want to stop playing the addictive game ''{{w|Minecraft}}'', but they do eventually start. Minecraft was previously referenced in [[861: Wisdom Teeth]].&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The scientists find no link between jelly beans and acne (the probability that the result is by chance is more than 5% i.e. ''p'' &amp;gt; 0.05) but then Megan and Cueball ask them to see if only one color of jelly beans is responsible. They test 20 different colors each at a significance level of 5%. If the probability that each trial gives a false positive result is 1 in 20, then by testing 20 different colors it is now likely that at least one jelly bean test will give a false positive. To be precise, the probability of having ''no'' false positive in 20 tests is 0.95&amp;lt;sup&amp;gt;20&amp;lt;/sup&amp;gt; = 35.85%. Probability of having ''no'' false positive in 21 tests (counting the test without color discrimination) is 0.95&amp;lt;sup&amp;gt;21&amp;lt;/sup&amp;gt; = 34.06%. &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The scientists find no link between jelly beans and acne (the probability that the result is by chance is more than 5% i.e. ''p'' &amp;gt; 0.05)&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;, &lt;/ins&gt;but then Megan and Cueball ask them to see if only one color of jelly beans is responsible. They test 20 different colors&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;, &lt;/ins&gt;each at a significance level of 5%. If the probability that each trial gives a false positive result is 1 in 20, then by testing 20 different colors it is now likely that at least one jelly bean test will give a false positive. To be precise, the probability of having ''no'' false positive in 20 tests is 0.95&amp;lt;sup&amp;gt;20&amp;lt;/sup&amp;gt; = 35.85%. Probability of having ''no'' false positive in 21 tests (counting the test without color discrimination) is 0.95&amp;lt;sup&amp;gt;21&amp;lt;/sup&amp;gt; = 34.06%. &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;This leads to a big newspaper headline saying '''Green Jelly Beans Linked To Acne''' where it is said that they have 95 percent confidence with only a 5% chance of a coincidence.&amp;#160; Unfortunately, although this number has been reported by the scientists' stats package and would be true if green jelly beans were the only ones tested, it is also seriously misleading.&amp;#160; If you roll just one die, one time, you aren't very likely to roll a six... but if you roll it 20 times you are very likely to have at least one six among them.&amp;#160; This means that you cannot just ignore the other 19 experiments that failed.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;This &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;finding &lt;/ins&gt;leads to a big newspaper headline saying '''Green Jelly Beans Linked To Acne''' where it is said that they have 95 percent confidence with only a 5% chance of a coincidence.&amp;#160; Unfortunately, although this number has been reported by the scientists' stats package and would be true if green jelly beans were the only ones tested, it is also seriously misleading.&amp;#160; If you roll just one die, one time, you aren't very likely to roll a six... but if you roll it 20 times you are very likely to have at least one six among them.&amp;#160; This means that you cannot just ignore the other 19 experiments that failed&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;. There are good methods for handling this problem, notably {{w|Bayesian_inference|Bayesian inference}}, but they can be difficult to use and explain, and complexity does not sell newspapers&lt;/ins&gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;There are good methods for handling this problem, notably {{w|Bayesian_inference|Bayesian inference}}, but they can be difficult to use and explain, and complexity does not sell newspapers.&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;In the title text&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;, &lt;/ins&gt;we find out that the scientists {{w|Reproducibility|repeated the experiment}} (another key part of the scientific method), but now they no longer find any evidence for the link between acne and green jelly beans. They try to tell the reporter something, maybe that it was probably a coincidence, but the reporters are not interested since that is not news. So they do not listen to what the scientist has to say and instead uses the information they have to make another major headline saying '''Research conflicted''' and recommend more study on the link. But that was just what the scientist already did.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;In the title text we find out that the scientists {{w|Reproducibility|repeated the experiment}} (another key part of the scientific method), but now they no longer find any evidence for the link between acne and green jelly beans. They try to tell the reporter something, maybe that it was probably a coincidence, but the reporters are not interested since that is not news. So they do not listen to what the scientist has to say and instead uses the information they have to make another major headline saying '''Research conflicted''' and recommend more study on the link. But that was just what the scientist already did.&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;This is (sadly) often an issue with more serious matters than jelly beans and acne – at any one time there are many studies about possible links between substances (e.g. red wine) and illness (e.g. cancer). Because only the positive results get reported, this limits the value any single study has - especially if the mechanism linking the two things is not known.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;This is (sadly) often an issue with more serious matters than jelly beans and acne – at any one time there are many studies about possible links between substances (e.g. red wine) and illness (e.g. cancer). Because only the positive results get reported, this limits the value any single study has - especially if the mechanism linking the two things is not known.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>108.162.221.42</name></author>	</entry>

	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=882:_Significant&amp;diff=298792&amp;oldid=prev</id>
		<title>172.70.131.161: /* Transcript */</title>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=882:_Significant&amp;diff=298792&amp;oldid=prev"/>
				<updated>2022-11-16T20:07:27Z</updated>
		
		<summary type="html">&lt;p&gt;‎&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Transcript&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
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				&lt;tr style=&quot;vertical-align: top;&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 20:07, 16 November 2022&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l32&quot; &gt;Line 32:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 32:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:Girl with black ponytail: Jelly beans cause acne!&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:Girl with black ponytail: Jelly beans cause acne!&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:Cueball: Scientists! Investigate!&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:Cueball: Scientists! Investigate!&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:Scientist (off &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;screen&lt;/del&gt;): But we're playing Minecraft! &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:Scientist (off &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;panel&lt;/ins&gt;): But we're playing Minecraft! &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:Scientist (off &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;screen&lt;/del&gt;): ...Fine.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:Scientist (off &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;panel&lt;/ins&gt;): ...Fine.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:[Two scientists. The man has safety goggles on, Megan has a sheet of notes.]&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:[Two scientists. The man has safety goggles on, Megan has a sheet of notes.]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l44&quot; &gt;Line 44:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 44:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:Scientist (off screen): But Miiiinecraft!&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:Scientist (off screen): But Miiiinecraft!&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:[20 identical small panels follow, 4 rows 5 columns. The exact same picture as in panel 2 above. The scientist with goggles &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;are stating &lt;/del&gt;the results and Megan holds some notes in her hand. The only difference from panel to panel is the color and then in the 14th panel where the result is positive and there is an exclamation from off &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;screen&lt;/del&gt;.]&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:[20 identical small panels follow, &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;in &lt;/ins&gt;4 rows &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;of &lt;/ins&gt;5 columns. The exact same picture as in panel 2 above. The scientist with goggles &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;states &lt;/ins&gt;the results and Megan holds some notes in her hand. The only difference from panel to panel is the color and then in the 14th panel where the result is positive and there is an exclamation from off&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;-panel&lt;/ins&gt;.]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:Scientist with goggles: We found no link between purple jelly beans and acne (p &amp;gt; 0.05).&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:Scientist with goggles: We found no link between purple jelly beans and acne (p &amp;gt; 0.05).&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l72&quot; &gt;Line 72:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 72:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:Scientist with goggles: We found a link between green jelly beans and acne (p &amp;lt; 0.05).&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:Scientist with goggles: We found a link between green jelly beans and acne (p &amp;lt; 0.05).&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:Voice (off &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;screen&lt;/del&gt;): ''Whoa!''&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:Voice (off &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;panel&lt;/ins&gt;): ''Whoa!''&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:Scientist with goggles: We found no link between mauve jelly beans and acne (p &amp;gt; 0.05).&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:Scientist with goggles: We found no link between mauve jelly beans and acne (p &amp;gt; 0.05).&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l92&quot; &gt;Line 92:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 92:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:Only 5% chance of coincidence!&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:Only 5% chance of coincidence!&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:Scientists...&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:Scientists...&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{{comic discussion}}&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{{comic discussion}}&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>172.70.131.161</name></author>	</entry>

	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=882:_Significant&amp;diff=297308&amp;oldid=prev</id>
		<title>JLZ0kTC5 at 15:17, 21 October 2022</title>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=882:_Significant&amp;diff=297308&amp;oldid=prev"/>
				<updated>2022-10-21T15:17:20Z</updated>
		
		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr style=&quot;vertical-align: top;&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 15:17, 21 October 2022&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l16&quot; &gt;Line 16:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 16:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;At first the scientists do not want to stop playing the addictive game ''{{w|Minecraft}}'', but they do eventually start. Minecraft was previously referenced in [[861: Wisdom Teeth]].&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;At first the scientists do not want to stop playing the addictive game ''{{w|Minecraft}}'', but they do eventually start. Minecraft was previously referenced in [[861: Wisdom Teeth]].&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The scientists find no link between jelly beans and acne (the probability that the result is by chance is more than 5% i.e. ''p'' &amp;gt; 0.05) but then Megan and Cueball ask them to see if only one &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;colour &lt;/del&gt;of jelly beans is responsible. They test 20 different colors each at a significance level of 5%. If the probability that each trial gives a false positive result is 1 in 20, then by testing 20 different colors it is now likely that at least one jelly bean test will give a false positive. To be precise, the probability of having ''no'' false positive in 20 tests is 0.95&amp;lt;sup&amp;gt;20&amp;lt;/sup&amp;gt; = 35.85%. Probability of having ''no'' false positive in 21 tests (counting the test without color discrimination) is 0.95&amp;lt;sup&amp;gt;21&amp;lt;/sup&amp;gt; = 34.06%. &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The scientists find no link between jelly beans and acne (the probability that the result is by chance is more than 5% i.e. ''p'' &amp;gt; 0.05) but then Megan and Cueball ask them to see if only one &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;color &lt;/ins&gt;of jelly beans is responsible. They test 20 different colors each at a significance level of 5%. If the probability that each trial gives a false positive result is 1 in 20, then by testing 20 different colors it is now likely that at least one jelly bean test will give a false positive. To be precise, the probability of having ''no'' false positive in 20 tests is 0.95&amp;lt;sup&amp;gt;20&amp;lt;/sup&amp;gt; = 35.85%. Probability of having ''no'' false positive in 21 tests (counting the test without color discrimination) is 0.95&amp;lt;sup&amp;gt;21&amp;lt;/sup&amp;gt; = 34.06%. &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;This leads to a big newspaper headline saying '''Green Jelly Beans Linked To Acne''' where it is said that they have 95 percent confidence with only a 5% chance of a coincidence.&amp;#160; Unfortunately, although this number has been reported by the scientists' stats package and would be true if green jelly beans were the only ones tested, it is also seriously misleading.&amp;#160; If you roll just one die, one time, you aren't very likely to roll a six... but if you roll it 20 times you are very likely to have at least one six among them.&amp;#160; This means that you cannot just ignore the other 19 experiments that failed.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;This leads to a big newspaper headline saying '''Green Jelly Beans Linked To Acne''' where it is said that they have 95 percent confidence with only a 5% chance of a coincidence.&amp;#160; Unfortunately, although this number has been reported by the scientists' stats package and would be true if green jelly beans were the only ones tested, it is also seriously misleading.&amp;#160; If you roll just one die, one time, you aren't very likely to roll a six... but if you roll it 20 times you are very likely to have at least one six among them.&amp;#160; This means that you cannot just ignore the other 19 experiments that failed.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>JLZ0kTC5</name></author>	</entry>

	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=882:_Significant&amp;diff=292208&amp;oldid=prev</id>
		<title>Natg19: /* Transcript */</title>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=882:_Significant&amp;diff=292208&amp;oldid=prev"/>
				<updated>2022-08-09T01:41:56Z</updated>
		
		<summary type="html">&lt;p&gt;‎&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Transcript&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr style=&quot;vertical-align: top;&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 01:41, 9 August 2022&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l99&quot; &gt;Line 99:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 99:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Category:Comics featuring Megan]]&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Category:Comics featuring Megan]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Category:Statistics]]&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Category:Statistics]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Category:&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;Research Papers&lt;/del&gt;]]&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Category:&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;Scientific research&lt;/ins&gt;]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Category:Minecraft]]&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Category:Minecraft]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Natg19</name></author>	</entry>

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