Editing 2701: Change in Slope
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The comic is a tip for detecting changes in slopes over a {{w|scatter plot}} of data. This is a common requirement in exploratory statistics for comparing trends in a series — finding the cutoff where the slope changes may reveal valuable information about the data. | The comic is a tip for detecting changes in slopes over a {{w|scatter plot}} of data. This is a common requirement in exploratory statistics for comparing trends in a series — finding the cutoff where the slope changes may reveal valuable information about the data. | ||
| β | The comic compares two methods. Firstly, a novice method — by 'doing a bunch of statistics'- i.e, 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] (which probably won't work well on noisy data such as shown), or [https://stackoverflow.com/a/71744293 gradients], or using a [https://stackoverflow.com/a/47522444 Savitzky-Golay filter or piecewise linear smoothing spline fits]. [[Randall]]'s light gray figures may be suggesting [https://colab.research.google.com/drive/ | + | The comic compares two methods. Firstly, a novice method — by 'doing a bunch of statistics'- i.e, 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] (which probably won't work well on noisy data such as shown), or [https://stackoverflow.com/a/71744293 gradients], or using a [https://stackoverflow.com/a/47522444 Savitzky-Golay filter or piecewise linear smoothing spline fits]. [[Randall]]'s light gray figures may be suggesting [https://colab.research.google.com/drive/1Ru90DAxHO9zzXrx-_4P28UJ_8MaHT0RL this method.] |
The other is the so-called 'expert' method, which involves [https://web.archive.org/web/20221122041345/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, the foreshortened perspective can make certain details much more apparent, allowing the 'expert' to see at a glance that there is a change in the slope. 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 use of {{w|Perspective (graphical)|perspective}} to make information pop into the audience's view has been used by artists for {{w|The_Ambassadors_(Holbein)|centuries}}. | The other is the so-called 'expert' method, which involves [https://web.archive.org/web/20221122041345/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, the foreshortened perspective can make certain details much more apparent, allowing the 'expert' to see at a glance that there is a change in the slope. 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 use of {{w|Perspective (graphical)|perspective}} to make information pop into the audience's view has been used by artists for {{w|The_Ambassadors_(Holbein)|centuries}}. | ||
