What exactly is tested with Bartlett's sphericity test?

[Ad VanderVen]

TL;DR

What exactly is tested with Bartlett's sphericity test? Is it equality of variances in dependent samples or is it an identity matrix?

In SPSS with the command sequence:

Analysis / Dimension reduction / Factor / PRINT KMO

Bartlett's sphericity test can be calculated. Now I read on:

https://www.itl.nist.gov/div898/handbook/eda/section3/eda35a.htm

that this test is a test for equal variances in dependent samples. My question is whether that is indeed the case. Because on Youtube:



it is claimed that the test would also test for zero correlations in the correlation matrix. What exactly is the case now? Is both the case and how is that possible?

 

[Ad VanderVen]

A colleague of mine, Jules Ellis, told me that there are actually two different Bartlett tests: a sphericity test and a variance homogeneity test. He referred me to the site below:

https://www.statisticshowto.com/bartletts-test/