# 13.4 - Testing the Significance of the Carry-over Effect

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To test for the overall significance of carry-over effects, we can drop the carry-over covariates (x1 and x2 in our example) and re-run the ANOVA.  Because the reduced model is a subset of the full model that includes the covariates, we can construct a likelihood ratio test.

$\Delta G^2=(-2logL_{Reduced})-(-2logL_{Full})$

with $df_{Reduced}-df_{Full}$ degrees of freedom

The -2logL values are provided in the SAS Fit Statistics output for each model.  For our example, the SAS output for the Full model with carry-over covarates is:

and for the reduced model without the carry-over covariates is:

So,

$\Delta G^2 =136.5-122.5=14$

and with

$\chi^2_{.05, 2}=5.991$

we conclude that there are significant carry-over effects.