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

To test for the overall significance of carry-over effects, we can drop the carry-over covariates (*x*_{1} and *x*_{2} 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 -2*logL* 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.