explain xkcd - User contributions [en]

Talk:2701: Change in Slope

2022-11-21T21:28:56Z

162.158.142.176:

I am an occasional data scientist, and I can confirm this is why we have monitor stands that tilt. [[Special:Contributions/172.71.94.50|172.71.94.50]] 16:33, 21 November 2022 (UTC)

The third e in "neeed" in the title text seems to be a typo
[[User:Victor|Victor]] ([[User talk:Victor|talk]]) 16:41, 21 November 2022 (UTC)
:I think Randall may have added it to represent that the speaker prolongs the "e" sound for emphasis, although that's usually done with 4-5 e's. [[User:Barmar|Barmar]] ([[User talk:Barmar|talk]]) 16:53, 21 November 2022 (UTC)
::I had to double-check this, myself (presumed the 'Bot created the lage faithfully, but went straight to source to see if I needed to find a vandalism post to revert). May need a comment (to prevent hypercorrection, if not to note the implied emphisis) and certainly will if it turns out to be a typo and gets corrected (for which I'm sure a future checker will discover Randall's revisiting, but then worth a note to that effect). [[Special:Contributions/172.70.90.2|172.70.90.2]] 17:42, 21 November 2022 (UTC)
Bender Bot was one of the main characters in Futurama. [[User:Barmar|Barmar]] ([[User talk:Barmar|talk]]) 16:54, 21 November 2022 (UTC)

A couple(?) of authors used the word(s) "(point of) inflection", which is {{w|Inflection point|not really suitable}} for a join between two straight segments. Was tempted to talk about "discontinuity", but that really only applies to the meta-slope (derivatives, to one degree or other) where it suddenly jumps (at a point), or the derivative's derivative has jumps (as it enters and leaves the smoothly linking curve). Hope it works well enough how I left it, though. [[Special:Contributions/162.158.142.176|162.158.142.176]] 21:28, 21 November 2022 (UTC)

2701: Change in Slope

2022-11-21T21:21:50Z

162.158.142.176: /* Explanation */

{{comic
| number = 2701
| date = November 21, 2022
| title = Change in Slope
| image = change_in_slope_2x.png
| imagesize = 656x371px
| noexpand = true
| 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.
}}

==Explanation==
{{incomplete|Created by a SIDEWAYS STATISTIC - Confirm whether the rotated plot is accurate to the comic (i tilted my laptop screen to check this). Expand on statistical tools one could use to find the change in slope for a scatter plot. Do NOT delete this tag too soon.}}

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 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.

The other is the so-called 'expert' method, which involves 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 second panel is exaggerated for visual effect.

However, applying such an approach to data plots can run into errors £mdash; 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.

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==
{{incomplete transcript|Do NOT delete this tag too soon.}}

:How to detect a change in the slope of your data

:[First column, on the left]
:Novice method:
:[A graph, with dots forming a rough line, math formulas, and sub graphs]
:Do a bunch of statistics

:[Second column, on the right]
:Expert method:
:[Perspective view of the previous graph, with the legend "Hey look, it bends here" and an arrow pointing to the graph]
:Tip the graph sideways

{{comic discussion}}
[[Category:Scatter plots]]
[[Category:Bar charts]]
[[Category:Line graphs]]
[[Category:Statistics]]

2701: Change in Slope

2022-11-21T21:18:04Z

162.158.142.176: /* Explanation */ Needed links, got absorbed in sentences instead.

{{comic
| number = 2701
| date = November 21, 2022
| title = Change in Slope
| image = change_in_slope_2x.png
| imagesize = 656x371px
| noexpand = true
| 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.
}}

==Explanation==
{{incomplete|Created by a SIDEWAYS STATISTIC - Confirm whether the rotated plot is accurate to the comic (i tilted my laptop screen to check this). Expand on statistical tools one could use to find the change in slope for a scatter plot. Do NOT delete this tag too soon.}}

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 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 n, 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.

The other is the so-called 'expert' method, which involves 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, 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 second panel is exaggerated for visual effect.

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 misidentify or be unable to clearly find the point of inflection. It also does not reveal any data about the quantitative value of the change in slope, merely proving the existence of one.

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==
{{incomplete transcript|Do NOT delete this tag too soon.}}

:How to detect a change in the slope of your data

:[First column, on the left]
:Novice method:
:[A graph, with dots forming a rough line, math formulas, and sub graphs]
:Do a bunch of statistics

:[Second column, on the right]
:Expert method:
:[Perspective view of the previous graph, with the legend "Hey look, it bends here" and an arrow pointing to the graph]
:Tip the graph sideways

{{comic discussion}}
[[Category:Scatter plots]]
[[Category:Bar charts]]
[[Category:Line graphs]]
[[Category:Statistics]]