## Wald test and SE of variances

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tjsduq64
Posts: 31
Joined: Mon Jul 15, 2019 10:04 pm

### Wald test and SE of variances

I ran a complex level-1 model for two groups, let's say group 1 and group 2. I now have variance estimate for each group and its standard error (SE). I see if the two variances are significantly different from each other by adding and subtracting 1.96*SE to each estimate and check if they overlap. Shouldn't this method give the same result as using "Intervals and Tests" tab on MLwiN to do a chi-square wald test on random effects (variances) by inserting 1 for group 1 and -1 for group 2? The two methods do not give the same results... could anyone explain this please? Thank you.

Sun
billb
Posts: 140
Joined: Fri May 21, 2010 1:21 pm

### Re: Wald test and SE of variances

Hi Sun,
the Wald test is only an approximate test for variance parameters as they do not have a normal distribution. That withstanding the test will form the difference of the 2 variances and then work out the SE for this difference to test for significance. This SE is made up of the SE for each parameter but also the covariance between the parameters which will explain why it is different from your slightly more ad hoc approach.
Best wishes,
Bill.
tjsduq64
Posts: 31
Joined: Mon Jul 15, 2019 10:04 pm

### Re: Wald test and SE of variances

billb wrote: Wed Aug 07, 2019 1:11 pm Hi Sun,
the Wald test is only an approximate test for variance parameters as they do not have a normal distribution. That withstanding the test will form the difference of the 2 variances and then work out the SE for this difference to test for significance. This SE is made up of the SE for each parameter but also the covariance between the parameters which will explain why it is different from your slightly more ad hoc approach.
Best wishes,
Bill.
Thank you!