Ajit kumar Roy

Dear Tomasz,

Check the links below, stating reference for the same;

1. https://www.graphpad.com/support/faqid/1568/

2. https://en.wikipedia.org/wiki/Welch%27s_t-test

You may refer this paper also,

The unequal variance t-test is an underused alternative to Student's t-test and the Mann–Whitney U test

Graeme D. RuxtonDivision of Environmental and Evolutionary Biology, Institute of Biomedical and Life Sciences, Graham Kerr Building, University of Glasgow

Dear Praheli Dhar Chowdhuri - how Your answer is related to my question? I mean - I asked a completely different question... :(

Dear Tomasz,

If you kindly go through the references shared, you will find that its Welch Test that is used to measure non equal variance in t test. The first 2 links are to give you some insight and the 2nd one is more advanced and if you want to quote it somewhere.

Dear Praheli Dhar Chowdhuri - thank You for Your answer, but my question was about what is calculated in IBM SPSS statistical software, not what is recomended, or supposed. :P

Both the Welch test and the Cochran-Cox test are used as the equivalent of the student's t-test for unequal variances. Their similarity is large and their results often differ only in their degrees of freedom and even with some results they are practically imperceptible.

Now the question is - which one is calculated by IBM SPSS? They are not signed, and in various places, eg on the Internet, information is contradictory.

Although Wikipedia (a link from you) says that it is a Welch test, none of the pages quoted, for example, given in the Wiki link and others - https://www.ibm.com/support/knowledgecenter/SSLVMB_24.0.0/spss/base/syn_t-test_overview.html - does not confirm or deny this information.

To sum up - I am looking for confirmation that the SPSS test is one or the other indicated.

Once again thank You.

Dear Tomasz,

If its how spss does it, they use a combination. Check this link if helps;

https://www-01.ibm.com/support/docview.wss?uid=swg21497421

Dear Tomasz,

I had that same questioning, if you find the answer, please let me know. Good luck! :)

Tomasz,

As it is documented in the algorithms manual of SPSS 24, it is Welch's test.

Dear Praheli Dhar Chowdhuri - at link You send there is no information about it; and there is no answer eiter. :/

Dear Jorge Ortiz Pinilla - I've downloaded IBM SPSS Statistics 24 Algorithms pdf file, which is available on ftp://public.dhe.ibm.com/software/analytics/spss/documentation/statistics/24.0/en/client/Manuals/IBM_SPSS_Statistics_Algorithms.pdf already. On page 735 there is Welch Test, but for Non Homogeneous Anova (with Brown-Forsythe also), but i dont see that in student's test section. Can You show me exact page? Thank You. :)

Dear Tomasz,

The formulas in page 954 for separate variances are those of Welch's statistics.

Dear Jorge Ortiz Pinilla - Thank you very much for this tip. Indeed, on page 954 are all patterns, in general from page 953 are all patterns for t-student tests. :) This is the answer I was looking for! Thank you!

Dearn Zongman Qiu

Interesting, really, thank You. The modification date is present in this article. This mentioned article is something like a Q&A blog and I don't know who or how it provides information there. Technical documentation however, indicates that these are templates and formulas for Welch's statistics. It is difficult to tell who to believe in this case. :)

Just adding a little to the other answers. It's the Welch's correction. You can corroborate it in SPSS. Run a one-way ANOVA with Welch's correction and Homogeneity of variances test for your two independent samples comparison. You'll find the resulting p-values are the same as observed in independent samples t-test.

Dear all,

Don't worry if there isn't a Welch test name registration date. Today it is widely recognized as such, although it should be more fairly called the Welch-Satterthwaite test. In the article published in 2011, we (Ortiz & Moreno) make a brief review of the background of this test.

Ortiz, J.; Moreno E., Is the Student's t-test needed for two independent samples assuming equal variances? Communications in Statistics December 2011, Vol. 4, No. 2 (sorry, it is written in Spanish)

In summary, Welch (1938), Welch (1947) and Satterthwaite (1946) proposed approaches that are considered satisfactory for practical use. Satterthwaite (1946) defines a complex estimator of variance as a linear combination of independent mean squares. Welch (1938) had previously shown that the distribution of this type of estimator can be approximated with the Chi-square distribution. In our article we summarize the algebra of Satterthwaite's (1946) approximation for two independent samples and believe that it is easily understood. The differences with the Student statistic are great: Student has degrees of freedom n1 + n2 - 2 and assumes equality of unknown variances, while Welch's is not based on this assumption and its degrees of freedom are random. The distribution of T is known and parameterized by the degrees of freedom, while that of W is unknown (only known in some particular cases) but it is well approximated by the Student distribution. Thus, it is not a Student test with unequal variances, as stated, but the Welch-Satterthwaite test, designed for unknown variances, without assuming either equality or inequality. History claims for name it “Welch’s Statistic” and “Welch´s test”, or, better, “Welch- Satterthwaite's Statistic” 😊

Welch, B. L. (1938), The significance of the difference between two means when the population variances are unequal, Biometrika 28 (3/4), 350–362.

Welch, B. L. (1947), The generalization of Student’s problem when several different population variances are involved, Biometrika 34 (1/2), 28–35.

Satterthwaite, F. E. (1946), An Approximate Distribution of Estimates of Variance Components, Biometrics Bulletin 2 (6), 110–114.