Editing 2701: Change in Slope
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− | | titletext = Squinting at a graph is fine for getting a rough idea of the answer, but if you want to pretend to know it exactly, you | + | | titletext = Squinting at a graph is fine for getting a rough idea of the answer, but if you want to pretend to know it exactly, you neeed statistics. |
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==Explanation== | ==Explanation== | ||
− | + | {{incomplete|Created by a SIDEWAYS STATISTIC. Do NOT delete this tag too soon.}} | |
− | The comic | + | The comic is a tip for detecting changes in slopes over a {{w|scatter plot}} of data. This is very prevalent in statistics while comparing trends — finding the cutoff where the slope changes may reveal valuable data about the data set. |
− | The | + | The comic compares two methods. Firstly, a novice method — by 'doing a bunch of statistics', applying various statistical tools to analyze the data and figure out the quantitative change in slope. This results in two equations for the trendlines above and below a given value, a box plot, a histogram and a line chart. It is unknown exactly what methods the novice used to figure out the change in slope in the data. Possibilities include calculating the [https://stackoverflow.com/a/45063636 derivatives] or the [https://stackoverflow.com/a/71744293 gradients], or using a [https://stackoverflow.com/a/47522444 Savitzky-Golay filter or piecewise linear smoothing spline fits]. |
− | + | The other is the so-called 'expert' method, which involves [https://cdn.discordapp.com/attachments/525939879805190154/1044395695525875712/xkcd_sideways.png tilting the page the graph is printed on to view changes in slope] better. For small changes in an underlying trend, similar to that apparently shown in the comic, direct visual inspection cannot always identify or even reveal the effect. The comic shows, however, that by taking the page and rotating it in just the right way, {{w|Perspective (graphical)|no longer flat on}} to the observer, a change in slope is more clearly visible to the naked eye. Ironically, tilting the comic to make the original' roughly resemble the perspective of the 'tilted' version graph shown in the comic shows that the right hand panel is slightly exaggerated for visual effect. | |
− | The title text then goes on to say that, while such a trick is useful to identify that there is some change in slope, in order to ''pretend'' to know it exactly one must revert to statistics (the "novice method") to obtain some form of information, defeating some of the premise of the comic. This at least produces a | + | However, applying such an approach to data plots can run into errors — the primary one being parallax error from the oblique viewing angle causing the observer to not necessariy identify or clearly find the point at which the slope changes. It also does not reveal any data about the quantitative value of the change in slope, merely proving the existence of one. |
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+ | The title text then goes on to say that, while such a trick is useful to identify that there is some change in slope, in order to ''pretend'' to know it exactly one must revert to statistics (the "novice method") to obtain some form of information, defeating some of the premise of the comic. This at least produces a semblence of statistical rigor although, once an answer appears obvious, data could be interpreted to reach an answer that you are now expecting rather than revealing something of more statistically useful significance. | ||
==Transcript== | ==Transcript== | ||
+ | {{incomplete transcript|Do NOT delete this tag too soon.}} | ||
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:How to detect a change in the slope of your data | :How to detect a change in the slope of your data | ||
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{{comic discussion}} | {{comic discussion}} | ||
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[[Category:Scatter plots]] | [[Category:Scatter plots]] | ||
[[Category:Bar charts]] | [[Category:Bar charts]] | ||
[[Category:Line graphs]] | [[Category:Line graphs]] | ||
[[Category:Statistics]] | [[Category:Statistics]] |