# Inconsistency between global chi-square difference tests and t-tests

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George Richardson
Joined: 10/18/2018

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Hi,

I've specified a multivariate ACE model and found that the z/t-tests produce substantially different p-values than the chi-square difference test per parameter constrained to zero. My recollection is that these tests should produce equivalent results but I recall reading somewhere that at relatively small n (here, n = 260 pairs), the global test may have more power. Does anyone know if this is likely correct or if there are methods papers address it? Could the difference be due to correlations among the z/t-tests? Not sure what's going on here.

I've specified a multivariate ACE model and found that the z/t-tests produce substantially different p-values than the chi-square difference test per parameter constrained to zero. My recollection is that these tests should produce equivalent results but I recall reading somewhere that at relatively small n (here, n = 260 pairs), the global test may have more power. Does anyone know if this is likely correct or if there are methods papers address it? Could the difference be due to correlations among the z/t-tests? Not sure what's going on here.

Thanks in advance!

George

## asymptotics

Note that the Wald test is regarded as a poor choice for testing hypotheses about variance-covariance parameters in modest-sized samples, since the sampling distributions of such "second-order" parameters' estimates converge slowly to normality.

BTW, if you want to calculate a Wald test statistic for multiple parameters, you'll need to use the inverse of the repeated-sampling covariance matrix of those parameters' point estimates. See Wikipedia for details.

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In reply to asymptotics by AdminRobK

## Thanks you!

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