What exactly is tested with Bartlett's sphericity test?

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In summary, Bartlett's sphericity test is a statistical test used to determine if the variances of multiple variables are equal. This test is commonly used in analysis of variance (ANOVA) to assess if the assumption of equal variances across groups is met. It takes into account the correlation between variables and adjusts for it in the calculation of the test statistic. Ultimately, Bartlett's sphericity test helps researchers determine if their data meets the necessary assumptions for further statistical analysis.
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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?
 
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Related to What exactly is tested with Bartlett's sphericity test?

1. What is Bartlett's sphericity test?

Bartlett's sphericity test is a statistical test used to determine whether the variances of multiple variables are equal. It is commonly used in multivariate analysis of variance (MANOVA) to assess the assumption of sphericity, which states that the variances of the differences between all pairs of variables are equal.

2. How does Bartlett's sphericity test work?

Bartlett's sphericity test calculates the ratio of the sum of squared differences between variables to the sum of squared differences within variables. This ratio is then compared to a chi-square distribution to determine if the differences between variables are significantly different from each other.

3. What is the purpose of Bartlett's sphericity test?

The purpose of Bartlett's sphericity test is to assess whether the assumption of sphericity is met in MANOVA. This is important because if the assumption is violated, the results of MANOVA may be inaccurate.

4. When should Bartlett's sphericity test be used?

Bartlett's sphericity test should be used when conducting MANOVA with multiple variables. It is important to check for sphericity to ensure the validity of the results.

5. What are the assumptions of Bartlett's sphericity test?

The assumptions of Bartlett's sphericity test are that the variables are normally distributed, the data is continuous, and the variances of the differences between all pairs of variables are equal. Violations of these assumptions can lead to inaccurate results.

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