http://www.explainxkcd.com/wiki/index.php?title=Special:RecentChangesLinked/Category:Statistics&feed=atom&target=Category%3AStatisticsexplain xkcd - Changes related to "Category:Statistics" [en]2014-07-28T10:26:35ZRelated changesMediaWiki 1.19.17http://www.explainxkcd.com/wiki/index.php?title=882:_Significant&diff=72341&oldid=68942882: Significant2014-07-26T10:58:57Z<p><span dir="auto"><span class="autocomment">Explanation: </span> removed duplicated word</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>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.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>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.</div></td></tr>
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<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>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 <del class="diffchange diffchange-inline">that </del>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'''.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>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'''.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>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 > 0.05) but then Megan and Cueball ask them to see if only one colour 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 highly 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)^20 = 35.85%. Probability of having ''no'' false positive in 21 tests (counting the test without color discrimination) is (0.95)^21 = 34.06%. In this case they find that green jelly beans do cause acne.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>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 > 0.05) but then Megan and Cueball ask them to see if only one colour 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 highly 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)^20 = 35.85%. Probability of having ''no'' false positive in 21 tests (counting the test without color discrimination) is (0.95)^21 = 34.06%. In this case they find that green jelly beans do cause acne.</div></td></tr>
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