variance ratio test result

[parastou amirifar]

Hi.I did the variance ratio test after two samples using groups t test and the result is as seen in the photo. Can one reject the zero hypothesis and state that the variances are not equal? Or, in other words, is the only one of the p-values can reject the zero hypothesis?

[Clyde Schechter]

Well, if you were going to make a decision about the usability of your t-test based on a significance test of the variance ratio, the relevant null hypothesis is the one in the middle: Ha: ratio != 1. For that, the p-value is 0.0553, so if you are also going to make a fetish out of the magic number 0.05, the result is not statistically significant.

That said, this is not the right approach to take in the first place. t-tests have a certain degree of robustness to inequality of variance (heteroskedasticity). In general, if the variance ratio is between 0.25 and 4.0, results of a ttest can still be valid. Some people prefer a stricter criterion and require a variance ratio between 0.5 and 2.0 to accept the ttest. Either way, you can clearly see from your output that the variance ratio here is (0.074114/0.0204451)^2 = 13.140807 is quite large. So in this situation you should have some doubts about your ttest. I would lean towards using a heteroskedasticity-robust estimator of the standard errors instead. The -ttest- command does not provide that, but you can do an equivalent analysis with regress:

regress efficiency i.unit, vce(robust)

If you are not familiar with robust variance estimation, you can learn more about it in the PDF documentation that comes with your Stata installation. Assuming you are using up-to-date Stata version 15.1, you will find it in the User's Guide [U] volume, section 20.22.

[parastou amirifar]

Thank's Clyde for your response. So, I wanted to make sure my t test is correct, assuming that the variances are equal.
But I have the same problem with the result of the ttest. For example, in this picture, as you said, should only consider the middle result, or zero hypothesis can be rejected with regard to p-value = 0.04, and state that there is a significant difference

between means?