Talk:Welch's t-test

Formula v2
Welch's t-test formula should have absolute value in numerator as values are not defined for negative numbers, I would have edited it but am in hurry and can't figure out how to ad absolute value. — Preceding unsigned comment added by 147.229.93.14 (talk) 06:48, 6 August 2016 (UTC)

Formula
Is the formula for nu correct? It has highly counterintuitive behavior, e.g. it decreases as N increases. — Preceding unsigned comment added by 24.173.186.26 (talk) 14:55, 27 June 2013 (UTC)
 * OK, I followed through to the derivation, and it does seem to have been incorrectly copied here. So I changed it to match the derivation. — Preceding unsigned comment added by 24.173.186.26 (talk) 15:46, 27 June 2013 (UTC)
 * The formula is not correct. s_1^2 should be replaced by s_1^2/n_1 (and likewise for sample 2). 24.36.45.176 (talk) 21:58, 1 July 2013 (UTC)
 * Corrected according to NIST. Second formula removed. Alfie  ↑↓ © 15:52, 5 July 2013 (UTC)
 * Strange. Why does NIST's formula not match the original sources?  — Preceding unsigned comment added by 24.173.186.26 (talk) 21:39, 17 June 2014 (UTC)

Cheating!!!11eleven
From the "Advantages and limitations" section:

→"Note that performing a variety of tests and choosing one that gives the desired P-value is cheating!"

It seems kind of out of place, stylistically. Also, while I think the sentiment is good, is it appropriate in this context to give guidelines on how to do statistics? — Preceding unsigned comment added by 143.48.117.112 (talk) 16:02, 30 March 2015 (UTC)


 * Correct; I will remove this sentence. BTW, it makes sense to apply Welch's test routinely. If sample sizes are equal and variances are identical the result matches the conventional t-test. Therefore, in R by default Welch’s test is applied:
 * is equivalent to
 * is equivalent to

Alfie ↑↓ © 15:29, 31 March 2015 (UTC)
 * One has to state
 * to force R to apply the t-test.
 * to force R to apply the t-test.

Examples Section
OK - forget the below - it was indeed a funny 5 minutes - I saw s^2 and thought this was SD and not variance. Once I square root the s^2 it works (well, not exactly but rounding allowed). Happy for someone to delete this section in Talk - not sure how to do it myself. Cheers, Grant - Hi folks, I've just computed the examples in the table and none of them seem to give the right answer - Student t or Welch's t.

Take example 1. For N1=15, M1=20.8, SD1=7.9, N2=15, M2=23.0, SD2=3.8, I get:

Student's t = -0.97, df = 28 (correct), 2 tailed p = 0.34;

Welch's t = -0.97, df = 20.15, 2 tailed p = 0.34;

The rest are wrong by my calculations too. Can someone please check I'm not having a funny 5 minutes?

Many thanks, Grant Grant (talk) 13:06, 1 August 2017 (UTC)

I've added a tag for the Examples Section. There are no references, and it seems very likely that someone generated these examples for Wikipedia.

Who is B. L. Welch?
How does this guy not have a page about him? I've created a page Bernard Lewis Welch Wqwt (talk) 21:43, 5 April 2018 (UTC)

DF: to round or not?
The article says the approximate DF estimates needs to be rounded to integers in order to apply a statistical test. Is this a canonical part of Welch's method, or just a suggestion added by someone else? Both the t-distribution and the F-distribution are defined for non-integer values of the degrees of freedom! —DIV (120.17.79.121 (talk) 00:34, 22 January 2019 (UTC)) And why does the article insist on rounding DF down, rather than to the nearest integer? Could be to be more conservative, say, but needs at least a supporting reference, and a brief explanation/justification wouldn't hurt either. —DIV (120.17.79.121 (talk) 00:36, 22 January 2019 (UTC))


 * For me, specifically this part: "The approximate degrees of freedom are real numbers $$\left(\nu\in\mathbb{R}^+\right)$$ and used as such in statistics-oriented software, whereas they are rounded down to the nearest integer in spreadsheets." should have a reference, surely? Which spreadsheets? Why are DF rounded? So many questions! 31.121.27.210 (talk) 14:30, 11 August 2022 (UTC)

Formula for degrees of freedom
There was some prior discussion on this Talk page about the formula for df. The conclusion was that the formula stated by NIST was used.

However, I found that from January 2021 to April 2021 the formula for df mysteriously changed again, but without a clear explanation and without any citation.

The formula introduced in April 2021 seems to match neither the old formula in the article nor that in the NIST Handbook, nor that in other relevant WP articles (see Student's t-test and Welch–Satterthwaite_equation) nor various other websites (e.g. and ). It is also irritatingly stated needlessly as the reciprocal of the parameter of interest.

Conversely the reinstated formula from January 2021 agrees with all of the above-cited formulæ, in form and/or in substance.

—DIV (137.111.13.4 (talk) 05:54, 30 July 2021 (UTC))


 * I think I've figured out the logic of the 'incorrect' formula from April 2021. It appears to be wrong in general, but correct only under the special condition that $$N_1 = N_2$$.  I have therefore added this to the article.
 * I also removed the silly reciprocal.
 * —DIV (137.111.13.4 (talk) 06:03, 30 July 2021 (UTC))