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# re: st: Statistical tests under heteroskedasticity

 From "Airey, David C" To "statalist@hsphsun2.harvard.edu" Subject re: st: Statistical tests under heteroskedasticity Date Mon, 14 May 2012 09:34:10 -0500

```.

I was just reviewing assumptions for linear regression (simple error structure).

independence -- needed for all types of inference
normally distributed coefficients -- needed for all types of inference
constant variance -- needed for all types of inference; can be relaxed by robust standard errors
correct mean model -- needed for group comparison and prediction
normal residuals -- needed for prediction; not fixed by robust standard errors

So we still want the correct mean model before doing tests between group means using robust standard errors. We may not have the correct mean model if important covariates are missing.

If we are not looking at group comparisons, but just the first order linear trend for a test of association (with a continuous or ordered X variable) using robust standard errors doesn't require the correct mean model.

Your hypothesis and what you want to conclude is important to communicate to the list.

You can see below the test command uses the robust standard error when called in the regression model, by running the same model without robust standard errors.

sysuse auto
ttest weight, by(foreign) welch
regress weight i.foreign, vce(robust)
test 1.foreign // square the regression t to get the F
regress weight i.foreign
test 1.foreign // square the regression t to get the F

I really like the -contrast- command in Stata 12 (an improved alternative to -test- in Stata 11).

-Dave

> Dear all,
>
> I use Stata 11.2 and I want to run several statistical tests to analyse my regression results. In my regression, I use the -robust- option but now I became aware, that heteroskedasticity invalidates my statistical tests such as hypothesis tests as well.
>
> Is there a way to run the -ttest- and -testparm- commands under heteroskedasticity without invalidating their results?
>
> Regards,
>
> Lukas
>
> #
> Lukas Borkowski

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