2533: Slope Hypothesis Testing - Revision history

FaviFake at 10:41, 28 July 2025

2025-07-28T10:41:41Z

FaviFake at 10:41, 28 July 2025

2025-07-28T10:41:30Z

42.book.addict: Undo revision 339425 by 172.70.162.38 (talk)

2024-04-12T01:13:42Z

Undo revision 339425 by 172.70.162.38 (talk)

172.70.162.38 at 00:24, 12 April 2024

2024-04-12T00:24:20Z

FaviFake: Fixed name

2023-07-08T08:52:04Z

Fixed name

Xurkitree10: /* Transcript */

2023-04-24T06:16:40Z

‎Transcript

Mushrooms at 10:00, 27 January 2023

2023-01-27T10:00:49Z

162.158.166.173: /* Explanation */ Tinnitus. The word you were looking for is tinnitus

2022-08-29T23:26:16Z

‎Explanation: Tinnitus. The word you were looking for is tinnitus

Natg19: /* Transcript */

2022-08-09T02:18:02Z

‎Transcript

Flekkie: /* Explanation */ added some examples of spurious correlation

2022-05-30T10:51:14Z

‎Explanation: added some examples of spurious correlation

@@ Line 49: / Line 49: @@
 [[Category:Charts]]
 [[Category:Scientific research]]
-[[Category:Note that this mnemonic is not accurate, especially outside the eastern united states where it was originally created]]
+[[Category:Comics featuring children]]

@@ Line 8: / Line 8: @@
 ==Explanation==
-"Slope hypothesis testing" is a method of testing the significance of a hypothesis involving a scatter plot.
+"Slope hypothesis testing" is a method of testing the significance of a hypothesis involving a scatter plot. In this comic, [[Cueball]] and [[Megan]] are performing a study comparing student exam grades to the volume of their screams. Student A has the worst grade and softest scream, but Student B has the ''best'' grades and Student C the ''loudest'' scream. A trendline has been plotted, indicating a positive correlation between grades and volume...but the p-value is extremely high, indicating little statistical significance to the trend. P-value is based on both how well the data fits the trendline and how many data points have been taken; the more data points and the better they fit, the lower the p-value and more significant the data.
 Megan complains about the insignificance of their results, so Cueball suggests having each student scream into the microphone a few more times. (The three students are still there as they can be seen behind them. The three students look like schoolkids; one of them is [[Jill]].)
@@ Line 20: / Line 18: @@
 Common statistical formulae assume the data points are statistically independent, that is, that the test score and volume measurement from one point don't reveal anything about those of the other points. By measuring each individual's scream multiple times, Cueball and Megan violate the independence assumption (a person's scream volume is unlikely to be independent from one scream to the next) and invalidate their significance calculation. This is an example of pseudoreplication. Furthermore, Megan and Cueball fail to obtain new test scores for each student, which would further limit their statistical options.
-Another strange aspect of their experiment is that the p-values obtained during a typical linear regression assume there is uncertainty in the y-values, but the x-values are fully known, whereas in this experiment, they are reducing uncertainty in the x-values of their data, while doing nothing to improve knowledge of the y-values.
+Another strange aspect of their experiment is that the p-values obtained during a typical linear regression assume there is uncertainty in the y-values, but the x-values are fully known, whereas in this experiment, they are reducing uncertainty in the x-values of their data, while doing nothing to improve knowledge of the y-values. Moreover, even if the new data were statistically independent, this still appears to be a classic example of "p-hacking", where new data is added until a statistically significant p-value is obtained. In current AI, there's a push toward "few-shot learning", where only a few data items are used to form conclusions, rather than the usual millions of them.  This comic displays danger associated with using such approaches without understanding them in depth. Additionally, a common theme in some research is the discovery of correlations that do not survive independent reproduction. This is because randomness with too few samples produces apparent correlations, and Randall has repeatedly made comics about this hopeful error (see [[111]], [[925]] and [[882]] among others).
 In the title text, Megan and Cueball are trying to yell over each other, asking each other to speak up so they can be heard; they are presumably suffering tinnitus or other hearing problems after listening to so much shouting.
@@ Line 57: / Line 49: @@
 [[Category:Charts]]
 [[Category:Scientific research]]
-[[Category:Kids]]
+[[Category:Note that this mnemonic is not accurate, especially outside the eastern united states where it was originally created]]

@@ Line 1: / Line 1: @@
-(Please kindly forward this to your CEO, because this is urgent. If you believe this has been sent to you in error, please ignore it. Thanks)
+{{comic
-Dear CEO,
+==Explanation==
-This email is from China domain name registration center, which mainly deal with the domain name registration in China. On 12-04-2024, we received an application from Hongqing Ltd requested the "explainxkcd" as their internet keyword and China (CN) domain names (explainxkcd.cn, explainxkcd.com.cn, explainxkcd.net.cn, explainxkcd.org.cn). But after checking it, we find this name conflict with your website name or company name. In order to deal with this matter better, it's necessary to send this message to your company and confirm whether this company is your distributor or business partner in China?
+In this comic, [[Cueball]] and [[Megan]] are performing a study comparing student exam grades to the volume of their screams. Student A has the worst grade and softest scream, but Student B has the ''best'' grades and Student C the ''loudest'' scream. A trendline has been plotted, indicating a positive correlation between grades and volume...but the p-value is extremely high, indicating little statistical significance to the trend. P-value is based on both how well the data fits the trendline and how many data points have been taken; the more data points and the better they fit, the lower the p-value and more significant the data.
-Best Regards
+Having the students scream again will not help though, because it only provides more data on the screaming without providing more data on its relation to exam scores and is a joke around poor statistical calculations likely made in the field today. The p-value is incorrectly recalculated based on the increased number of measurements without accounting for the fact that observations are nested within students. Each student has exactly the same test scores (probably referencing the same datum as before) and have vocal volume ranges that don't drift far either (each seems to have a range of scream that is fairly consistent and far from overlapping). Megan is pleased by these results, but Cueball belatedly realizes this technique may not be scientifically valid. Cueball is correct (presuming that they are using simple linear regression). A more appropriate technique would account for the non-independence of the data (that multiple data points come from each person). Examples of such techniques are multilevel modeling and Huber-White robust standard errors.
-Wade Liu | Service & Operations Manager
-China Registry (Head Office)
+Measuring data multiple times can be a way to increase its accuracy but does not increase the number of data points with regard to another metric, and the horizontally clustered points on the chart make this visually clear. A more effective and scientifically correct way of gathering data test would be to test other students and add their figures to the existing data, rather than repeatedly testing the same three students.
-Tel: +86-2161918696
-Fax: +86-2161918697
+Common statistical formulae assume the data points are statistically independent, that is, that the test score and volume measurement from one point don't reveal anything about those of the other points. By measuring each individual's scream multiple times, Cueball and Megan violate the independence assumption (a person's scream volume is unlikely to be independent from one scream to the next) and invalidate their significance calculation. This is an example of pseudoreplication. Furthermore, Megan and Cueball fail to obtain new test scores for each student, which would further limit their statistical options.
-Mob: +86-13816428671
-No.1780 Wuzhong Road, Shanghai 201103, China
+Another strange aspect of their experiment is that the p-values obtained during a typical linear regression assume there is uncertainty in the y-values, but the x-values are fully known, whereas in this experiment, they are reducing uncertainty in the x-values of their data, while doing nothing to improve knowledge of the y-values.

@@ Line 1: / Line 1: @@
-{{comic
+(Please kindly forward this to your CEO, because this is urgent. If you believe this has been sent to you in error, please ignore it. Thanks)
-==Explanation==
+Dear CEO,
-In this comic, [[Cueball]] and [[Megan]] are performing a study comparing student exam grades to the volume of their screams. Student A has the worst grade and softest scream, but Student B has the ''best'' grades and Student C the ''loudest'' scream. A trendline has been plotted, indicating a positive correlation between grades and volume...but the p-value is extremely high, indicating little statistical significance to the trend. P-value is based on both how well the data fits the trendline and how many data points have been taken; the more data points and the better they fit, the lower the p-value and more significant the data.
+This email is from China domain name registration center, which mainly deal with the domain name registration in China. On 12-04-2024, we received an application from Hongqing Ltd requested the "explainxkcd" as their internet keyword and China (CN) domain names (explainxkcd.cn, explainxkcd.com.cn, explainxkcd.net.cn, explainxkcd.org.cn). But after checking it, we find this name conflict with your website name or company name. In order to deal with this matter better, it's necessary to send this message to your company and confirm whether this company is your distributor or business partner in China?
-Having the students scream again will not help though, because it only provides more data on the screaming without providing more data on its relation to exam scores and is a joke around poor statistical calculations likely made in the field today. The p-value is incorrectly recalculated based on the increased number of measurements without accounting for the fact that observations are nested within students. Each student has exactly the same test scores (probably referencing the same datum as before) and have vocal volume ranges that don't drift far either (each seems to have a range of scream that is fairly consistent and far from overlapping). Megan is pleased by these results, but Cueball belatedly realizes this technique may not be scientifically valid. Cueball is correct (presuming that they are using simple linear regression). A more appropriate technique would account for the non-independence of the data (that multiple data points come from each person). Examples of such techniques are multilevel modeling and Huber-White robust standard errors.
+Best Regards
+Wade Liu | Service & Operations Manager
-Measuring data multiple times can be a way to increase its accuracy but does not increase the number of data points with regard to another metric, and the horizontally clustered points on the chart make this visually clear. A more effective and scientifically correct way of gathering data test would be to test other students and add their figures to the existing data, rather than repeatedly testing the same three students.
+China Registry (Head Office)
+Tel: +86-2161918696
-Common statistical formulae assume the data points are statistically independent, that is, that the test score and volume measurement from one point don't reveal anything about those of the other points. By measuring each individual's scream multiple times, Cueball and Megan violate the independence assumption (a person's scream volume is unlikely to be independent from one scream to the next) and invalidate their significance calculation. This is an example of pseudoreplication. Furthermore, Megan and Cueball fail to obtain new test scores for each student, which would further limit their statistical options.
+Fax: +86-2161918697
+Mob: +86-13816428671
-Another strange aspect of their experiment is that the p-values obtained during a typical linear regression assume there is uncertainty in the y-values, but the x-values are fully known, whereas in this experiment, they are reducing uncertainty in the x-values of their data, while doing nothing to improve knowledge of the y-values.
+No.1780 Wuzhong Road, Shanghai 201103, China

@@ Line 10: / Line 10: @@
 "Slope hypothesis testing" is a method of testing the significance of a hypothesis involving a scatter plot.
 In this comic, [[Cueball]] and [[Megan]] are performing a study comparing student exam grades to the volume of their screams. Student A has the worst grade and softest scream, but Student B has the ''best'' grades and Student C the ''loudest'' scream. A trendline has been plotted, indicating a positive correlation between grades and volume...but the p-value is extremely high, indicating little statistical significance to the trend. P-value is based on both how well the data fits the trendline and how many data points have been taken; the more data points and the better they fit, the lower the p-value and more significant the data.
-Megan complains about the insignificance of their results, so Cueball suggests having each student scream into the microphone a few more times. (The three students are still there as they can be seen behind them. The three students look like schoolkids; one of them is [[Science Girl]].)
+Megan complains about the insignificance of their results, so Cueball suggests having each student scream into the microphone a few more times. (The three students are still there as they can be seen behind them. The three students look like schoolkids; one of them is [[Jill]].)
-Having the students scream again will not help though, because it only provides more data on the screaming without providing more data on its relation to exam scores, and is a joke around poor statistical calculations likely made in the field today. The p-value is incorrectly recalculated based on the increased number of measurements without accounting for the fact that observations are nested within students. Each student has exactly the same test scores (probably referencing the same datum as before) and have vocal volume ranges that don't drift far either (each seems to have a range of scream that is fairly consistent and far from overlapping). Megan is pleased by these results, but Cueball belatedly realizes this technique may not be scientifically valid. Cueball is correct (presuming that they are using simple linear regression). A more appropriate technique would account for the non-independence of the data (that multiple data points come from each person). Examples of such techniques are multilevel modeling and Huber-White robust standard errors.
+Having the students scream again will not help though, because it only provides more data on the screaming without providing more data on its relation to exam scores and is a joke around poor statistical calculations likely made in the field today. The p-value is incorrectly recalculated based on the increased number of measurements without accounting for the fact that observations are nested within students. Each student has exactly the same test scores (probably referencing the same datum as before) and have vocal volume ranges that don't drift far either (each seems to have a range of scream that is fairly consistent and far from overlapping). Megan is pleased by these results, but Cueball belatedly realizes this technique may not be scientifically valid. Cueball is correct (presuming that they are using simple linear regression). A more appropriate technique would account for the non-independence of the data (that multiple data points come from each person). Examples of such techniques are multilevel modeling and Huber-White robust standard errors.
-Measuring data multiple times can be a way to increase its accuracy, but does not increase the number of data points with regard to another metric, and the horizontally clustered points on the chart make this visually clear. A more effective and scientifically correct way of gathering data test would be to test other students and add their figures to the existing data, rather than repeatedly testing the same three students.
+Measuring data multiple times can be a way to increase its accuracy but does not increase the number of data points with regard to another metric, and the horizontally clustered points on the chart make this visually clear. A more effective and scientifically correct way of gathering data test would be to test other students and add their figures to the existing data, rather than repeatedly testing the same three students.
 Common statistical formulae assume the data points are statistically independent, that is, that the test score and volume measurement from one point don't reveal anything about those of the other points. By measuring each individual's scream multiple times, Cueball and Megan violate the independence assumption (a person's scream volume is unlikely to be independent from one scream to the next) and invalidate their significance calculation. This is an example of pseudoreplication. Furthermore, Megan and Cueball fail to obtain new test scores for each student, which would further limit their statistical options.
-Another strange aspect of their experiment is that the p-values obtained during a typical linear regression assume there is uncertainty in the y-values but the x-values are fully known, whereas in this experiment, they are reducing uncertainty in the x-values of their data, while doing nothing to improve knowledge of the y-values.
+Another strange aspect of their experiment is that the p-values obtained during a typical linear regression assume there is uncertainty in the y-values, but the x-values are fully known, whereas in this experiment, they are reducing uncertainty in the x-values of their data, while doing nothing to improve knowledge of the y-values.
 Moreover, even if the new data were statistically independent, this still appears to be a classic example of "p-hacking", where new data is added until a statistically significant p-value is obtained.
@@ Line 53: / Line 53: @@
 [[Category:Comics featuring Megan]]
 [[Category:Comics featuring Cueball]]
-[[Category:Comics featuring Science Girl]] <!-- The other two kids are also, well, kids, and thus not Hairy or Megan -->
+[[Category:Comics featuring Jill]] <!-- The other two kids are also, well, kids, and thus not Hairy or Megan -->
 [[Category:Statistics]]
 [[Category:Charts]]
 [[Category:Scientific research]]
 [[Category:Kids]]

@@ Line 31: / Line 31: @@
 ==Transcript==
 :[Three points are labeled "Student A", "Student B" and "Student C" from left to right in a scatter plot with axes labeled "Stats exam grade" (60-100) and "Scream loudness (decibels)" (86-94) with a trend line. Student B has the highest exam grade, followed by Student C and then Student A.]
 :[A line goes from the trend line to a box containing the following:]

← Older revision		Revision as of 10:00, 27 January 2023
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	[[Category:Charts]]		[[Category:Charts]]
	[[Category:Scientific research]]		[[Category:Scientific research]]
		+	[[Category:Kids]]

← Older revision		Revision as of 02:18, 9 August 2022
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	[[Category:Statistics]]		[[Category:Statistics]]
	[[Category:Charts]]		[[Category:Charts]]
		+	[[Category:Scientific research]]

@@ Line 27: / Line 27: @@
 In current AI, there's a push toward "few-shot learning", where only a few data items are used to form conclusions, rather than the usual millions of them.  This comic displays danger associated with using such approaches without understanding them in depth.
-Additionally, a common theme in some research is the discovery of correlations that do not survive independent reproduction.  This is because randomness with too few samples produces apparent correlations, and Randall has repeatedly made comics about this hopeful error.
+Additionally, a common theme in some research is the discovery of correlations that do not survive independent reproduction.  This is because randomness with too few samples produces apparent correlations, and Randall has repeatedly made comics about this hopeful error (see [[111]], [[925]] and [[882]] among others).
 In the title text, Megan and Cueball are trying to yell over each other, asking each other to speak up so they can be heard, presumably because they are having trouble hearing from the yelling experiment.  Or possibly they have trouble speaking audibly because they score poorly on statistics exams.