Talk:2533: Slope Hypothesis Testing - Revision history

172.68.50.218 at 11:56, 21 March 2023

2023-03-21T11:56:50Z

Flekkie at 10:52, 30 May 2022

2022-05-30T10:52:06Z

172.70.34.165 at 19:42, 27 October 2021

2021-10-27T19:42:25Z

172.70.134.131 at 19:40, 27 October 2021

2021-10-27T19:40:32Z

172.70.91.50 at 15:19, 27 October 2021

2021-10-27T15:19:04Z

GreatWyrmGold at 14:30, 27 October 2021

2021-10-27T14:30:09Z

172.70.162.173 at 11:50, 27 October 2021

2021-10-27T11:50:44Z

Hkmaly at 23:06, 26 October 2021

2021-10-26T23:06:56Z

172.70.85.185 at 15:57, 26 October 2021

2021-10-26T15:57:26Z

172.70.45.243: made a comment

2021-10-26T14:50:55Z

made a comment

← Older revision		Revision as of 11:56, 21 March 2023
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	: * - though there are doubtless many different direct calculation/reformulation methods that don't require progressive iterations towards a better solution. And identify where multiple minima might lie in the numeric landscape.		: * - though there are doubtless many different direct calculation/reformulation methods that don't require progressive iterations towards a better solution. And identify where multiple minima might lie in the numeric landscape.
	: (Summary, indeed! This is why I didn't myself feel the need to try to do anything with the Explanation. It just seems like a typical Munrovian mash up of {{w\|Statistical Hypothesis Testing}} and working with a slope. If I was ever taught this Slope-specific one (other than assessment by inspection, to preface or afterwards sanity-check loads of Sigma-based mathematics/etc that one can easily mess up by hand, or GIGO when plugged into a computer wrongly) then I've forgotten its name.) [[Special:Contributions/172.70.91.50\|172.70.91.50]] 15:19, 27 October 2021 (UTC)		: (Summary, indeed! This is why I didn't myself feel the need to try to do anything with the Explanation. It just seems like a typical Munrovian mash up of {{w\|Statistical Hypothesis Testing}} and working with a slope. If I was ever taught this Slope-specific one (other than assessment by inspection, to preface or afterwards sanity-check loads of Sigma-based mathematics/etc that one can easily mess up by hand, or GIGO when plugged into a computer wrongly) then I've forgotten its name.) [[Special:Contributions/172.70.91.50\|172.70.91.50]] 15:19, 27 October 2021 (UTC)
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		+	What makes the graph even worse is that both axis don't start at zero.[[Special:Contributions/172.68.50.218\|172.68.50.218]]

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 :Definitely, otherwise it would not be very useful. --[[Special:Contributions/162.158.203.54|162.158.203.54]] 13:10, 26 October 2021 (UTC)
 :hi, I added the line.  <thinking-out-loud removed in copyediting>.  I think there was one where article titles that blatantly used poor statistical techniques were listed, not sure. [[Special:Contributions/172.70.114.3|172.70.114.3]] 14:40, 26 October 2021 (UTC)
 I love it. [[User:Fwacer|Fwacer]] ([[User talk:Fwacer|talk]]) 02:52, 26 October 2021 (UTC)

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 :: You seem to be the only person so far who's learned in academia why this is wrong.  Is the current state of the article correct? [[Special:Contributions/172.70.114.3|172.70.114.3]] 14:31, 26 October 2021 (UTC)
 : The scientific error isn't quite what people are saying it is. The issue here is not "reusing a single test score" or an issue with non-normality of errors, the issue is that the data are *nested* within participants and that isn't being accounted for. There are fairly standard ways of managing this, at least in the social science literature (and these ways are statistically valid), most commonly the use of multilevel modeling (also known as hierarchical linear modeling). This accounts for the correlated nature of the errors. Now, even using the right method they're not going to attain statistical significance, but at least they aren't making a statistical mistake.
-:: You can look at it in different ways. Obviously the error they made in their research was sampling the same people repeatedly and assuming that could increase the significance of their result. But mathematically, the analysis fails because the errors are not normally distributed. The math doesn't care about how you gather data. If the random variables ε is normally distributed, you can calculate confidence intervals for the parameters and for predictions exactly. Even if it isn't normally distributed, the central limit theorem guarantees that the sum of squared residuals will have a chi square distribution. In particular, this means the estimator for beta will be normally distributed, and therefore the standard error in the point estimator will have a (scaled and translated) t distribution. Knowing this, you can use the CDF for the t distribution to compute the p-value exactly. To explain what's wrong with this, we need to spot which assumption was in error. Here, the false assumption was the normality of ε. Even if ε is not normally distributed, as long as it has finite mean and variance, the mean of n independent samples will converge in distribution to z as n goes to infinity. But here, the samples are not independent. So even if you sampled these same kids infinitely many times, the distribution of errors will not converge to the normal distribution, so the assumption of normality remains false. (BTW, this is the same IP as before, just from my phone this time.) [[Special:Contributions/172.70.134.131|172.70.134.131]] 19:40, 27 October 2021 (UTC)
+:: You can look at it in different ways. Obviously the error they made in their research was sampling the same people repeatedly and assuming that could increase the significance of their result. But mathematically, the analysis fails because the errors are not normally distributed. The math doesn't care about how you gather data. If the random variables ε is normally distributed, you can calculate confidence intervals for the parameters and for predictions exactly. The sum of squared residuals will have a chi square distribution. In particular, this means the estimator for beta will be normally distributed, and therefore the standard error in the point estimator will have a (scaled and translated) t distribution. Knowing this, you can use the CDF for the t distribution to compute the p-value exactly. To explain what's wrong with this, we need to spot which assumption was in error. Here, the false assumption was the normality of ε. Even if ε is not normally distributed, as long as it has finite mean and variance, the mean of n independent samples will converge in distribution to z as n goes to infinity. But here, the samples are not independent. So even if you sampled these same kids infinitely many times, the distribution of errors will not converge to the normal distribution, so the assumption of normality remains false. (BTW, this is the same IP as before, just from my phone this time.) [[Special:Contributions/172.70.134.131|172.70.134.131]] 19:40, 27 October 2021 (UTC)
 I don't think the title text speakers are unidentified, I'm pretty sure it's a direct continuation of the dialogue in the last panel. [[User:Esogalt|Esogalt]] ([[User talk:Esogalt|talk]]) 04:11, 26 October 2021 (UTC)

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 :: You seem to be the only person so far who's learned in academia why this is wrong.  Is the current state of the article correct? [[Special:Contributions/172.70.114.3|172.70.114.3]] 14:31, 26 October 2021 (UTC)
 : The scientific error isn't quite what people are saying it is. The issue here is not "reusing a single test score" or an issue with non-normality of errors, the issue is that the data are *nested* within participants and that isn't being accounted for. There are fairly standard ways of managing this, at least in the social science literature (and these ways are statistically valid), most commonly the use of multilevel modeling (also known as hierarchical linear modeling). This accounts for the correlated nature of the errors. Now, even using the right method they're not going to attain statistical significance, but at least they aren't making a statistical mistake.
 I don't think the title text speakers are unidentified, I'm pretty sure it's a direct continuation of the dialogue in the last panel. [[User:Esogalt|Esogalt]] ([[User talk:Esogalt|talk]]) 04:11, 26 October 2021 (UTC)

← Older revision		Revision as of 15:19, 27 October 2021
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	Speaking as the person who wrote the explanation for "slope hypothesis testing," we need someone to write a better explanation for it. It's just a placeholder meant to patch a gap until someone who knows what they're talking about (or what to google) can write a better one. [[User:GreatWyrmGold\|GreatWyrmGold]] ([[User talk:GreatWyrmGold\|talk]]) 14:30, 27 October 2021 (UTC)		Speaking as the person who wrote the explanation for "slope hypothesis testing," we need someone to write a better explanation for it. It's just a placeholder meant to patch a gap until someone who knows what they're talking about (or what to google) can write a better one. [[User:GreatWyrmGold\|GreatWyrmGold]] ([[User talk:GreatWyrmGold\|talk]]) 14:30, 27 October 2021 (UTC)
		+	:My (armchair) summary(!) would be that a general proposition is that there is a simple linear relationship between two factors (or their logs/powers/whatevers, reformulated as necessary) so those are plotted and their conformity to a gradient(±offset) is evaluated.
		+	:The slope is defined by just two values which can, if necessary*, be emperically tested against the 'wrongness' of the points against the line (including error allowances) to find that line which is itself therefore minimally 'wrong', and that remaining wrongness (including how much of the possible error may need to be accepted) conveys the conformity or otherwise and you have also tied down the possibly unknown relationships - as best you are allowed to.
		+	: * - though there are doubtless many different direct calculation/reformulation methods that don't require progressive iterations towards a better solution. And identify where multiple minima might lie in the numeric landscape.
		+	: (Summary, indeed! This is why I didn't myself feel the need to try to do anything with the Explanation. It just seems like a typical Munrovian mash up of {{w\|Statistical Hypothesis Testing}} and working with a slope. If I was ever taught this Slope-specific one (other than assessment by inspection, to preface or afterwards sanity-check loads of Sigma-based mathematics/etc that one can easily mess up by hand, or GIGO when plugged into a computer wrongly) then I've forgotten its name.) [[Special:Contributions/172.70.91.50\|172.70.91.50]] 15:19, 27 October 2021 (UTC)

← Older revision		Revision as of 14:30, 27 October 2021
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	:Also, infinite number of polynomials which fits this data exactly. -- [[User:Hkmaly\|Hkmaly]] ([[User talk:Hkmaly\|talk]]) 23:06, 26 October 2021 (UTC)		:Also, infinite number of polynomials which fits this data exactly. -- [[User:Hkmaly\|Hkmaly]] ([[User talk:Hkmaly\|talk]]) 23:06, 26 October 2021 (UTC)
	::But ''exactly one'' circle (assuming all mutually different, and not already upon a line), in an {{w\|Circumscribed_circle#Triangles\|elegantly obvious}} manner. Therefore clearly the more individually significant statistical match for three datum points. :P [[Special:Contributions/172.70.162.173\|172.70.162.173]] 11:50, 27 October 2021 (UTC)		::But ''exactly one'' circle (assuming all mutually different, and not already upon a line), in an {{w\|Circumscribed_circle#Triangles\|elegantly obvious}} manner. Therefore clearly the more individually significant statistical match for three datum points. :P [[Special:Contributions/172.70.162.173\|172.70.162.173]] 11:50, 27 October 2021 (UTC)
		+
		+	Speaking as the person who wrote the explanation for "slope hypothesis testing," we need someone to write a better explanation for it. It's just a placeholder meant to patch a gap until someone who knows what they're talking about (or what to google) can write a better one. [[User:GreatWyrmGold\|GreatWyrmGold]] ([[User talk:GreatWyrmGold\|talk]]) 14:30, 27 October 2021 (UTC)

← Older revision		Revision as of 11:50, 27 October 2021
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	:Given three points, there's a ''circle'' that exactly fits them... ;) [[Special:Contributions/172.70.85.185\|172.70.85.185]] 15:57, 26 October 2021 (UTC)		:Given three points, there's a ''circle'' that exactly fits them... ;) [[Special:Contributions/172.70.85.185\|172.70.85.185]] 15:57, 26 October 2021 (UTC)
	:Also, infinite number of polynomials which fits this data exactly. -- [[User:Hkmaly\|Hkmaly]] ([[User talk:Hkmaly\|talk]]) 23:06, 26 October 2021 (UTC)		:Also, infinite number of polynomials which fits this data exactly. -- [[User:Hkmaly\|Hkmaly]] ([[User talk:Hkmaly\|talk]]) 23:06, 26 October 2021 (UTC)
		+	::But ''exactly one'' circle (assuming all mutually different, and not already upon a line), in an {{w\|Circumscribed_circle#Triangles\|elegantly obvious}} manner. Therefore clearly the more individually significant statistical match for three datum points. :P [[Special:Contributions/172.70.162.173\|172.70.162.173]] 11:50, 27 October 2021 (UTC)

← Older revision		Revision as of 23:06, 26 October 2021
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	Is there a polynomial that better fits this data? [[Special:Contributions/108.162.241.143\|108.162.241.143]] 14:29, 26 October 2021 (UTC)		Is there a polynomial that better fits this data? [[Special:Contributions/108.162.241.143\|108.162.241.143]] 14:29, 26 October 2021 (UTC)
	:Given three points, there's a ''circle'' that exactly fits them... ;) [[Special:Contributions/172.70.85.185\|172.70.85.185]] 15:57, 26 October 2021 (UTC)		:Given three points, there's a ''circle'' that exactly fits them... ;) [[Special:Contributions/172.70.85.185\|172.70.85.185]] 15:57, 26 October 2021 (UTC)
		+	:Also, infinite number of polynomials which fits this data exactly. -- [[User:Hkmaly\|Hkmaly]] ([[User talk:Hkmaly\|talk]]) 23:06, 26 October 2021 (UTC)

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 :What they have here is a 1D distribution of scream-ability/tendency (which was originally a single datum), arbitrarily set against test scores. (Could as easily have been against shoe-size, father's income-before-tax, a single dice-roll, etc.)
 ::I initially assumed that the participants are screaming in response to learning their scores, so the relationship is not arbitrary -- the students with good scores sceam loudly with joy. [[User:Barmar|Barmar]] ([[User talk:Barmar|talk]]) 14:45, 26 October 2021 (UTC)
 :Whether there ''was'' an original theory that grades correlated with intensity of vocalisation is perhaps a valid speculation, but clearly the design of the test is wrong. Too few datum points, in the first instance, and the wrong way to increase them when they find out their original failing.
 : The true solution is to recruit more subject. (And justify properly if it's intensity of spontaneous result-prompted evocations or merely general ability to be loud that is the quality the wish to measure. Either could be valid, but it's not obvious that the latter is indeed the one that they meant to measure.) [[Special:Contributions/141.101.77.54|141.101.77.54]] 04:21, 26 October 2021 (UTC)
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 Is there a polynomial that better fits this data? [[Special:Contributions/108.162.241.143|108.162.241.143]] 14:29, 26 October 2021 (UTC)