Testing the Global Null Hypothesis

The PHREG Procedure

Testing the Global Null Hypothesis

The following three likelihood statistics can be used to test the global null hypothesis $H_{0}\colon{{\beta}}=0$ . Under mild assumptions, each statistic has an asymptotic chi-squared distribution with p degrees of freedom given the null hypothesis. The value p is the dimension of ${\beta}$ .

Likelihood ratio test:

$\chi^2_{LR}=2 [ l (\hat{{\beta}}) - l(0) ]$

Wald's test:

$\chi^2_{W}=\hat{{\beta}}'[ \hat{V}(\hat{{\beta}})]^{-1}\hat{{\beta}}$

Score test:

$\chi^2_{S}= [ \frac { \partial l(0) }{ \partial {{\beta}} } ]' [ - \frac { \part... ...\partial {{\beta}}^2 } ]^{-1} [ \frac { \partial l (0) }{ \partial {{\beta}} } ]$

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