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:

sas output

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

sas output

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.