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Assessment Tools | Center for Teaching InnovationYou're teaching a class with students of varying abilities. How can you help each one succeed?Software Testing MethodologiesFour Phase Test at XUnitPatterns.comType III tests examine the significance of eachpartial effect, that is, the significance of aneffect with all the other effects in the model.They are computed by constructing a type IIIhypothesis matrix L and then computing statisticsassociated with the hypothesis L
= 0.Refer to the chapter titled "The Four Types of Estimable Functions," in theSAS/STAT User's Guidefor the construction of the matrix L.For linear models, the type III or partial sum of squares
- (Lb)' (L (X'X)-1 L')-1 (Lb)
= 0.The Type III Tests table for linear models,as illustrated by Figure 39.15,includes the following:- Source
- is the name for each effect.
- DF
- is the degrees of freedom associated with each effect.
- Sum of Squares
- is the partial sum of squares for each effect in the model.
- Mean Square
- is the sum of squares divided by its associated degrees of freedom.
- F Stat
- is the F statistic for testing the null hypothesis that the linear combinations of parameters described previously for the hypothesis matrix L are 0. This is formed by dividing the mean square for the hypothesis matrix L by the mean square for error from the complete model.
- Pr > F
- is the probability of obtaining a greater F statistic than that observed if the null hypothesis is true.
Figure 39.15: Type III Tests Table for Linear Models
For generalized linear models, either the Waldstatistic or the likelihood-ratio statistic canbe used to test the hypothesis L = 0.For the linear model, the two tests are equivalent.The Wald statistic is given by
is the estimatedcovariance matrix of the parameters.The likelihood-ratio statistic is computed as twicethe difference between the maximum log-likelihoodachievable under the unconstrained model and themaximum log-likelihood for the model under therestriction or constraint L = 0.Both the Wald statistic and the likelihood-ratio statistichave an asymptotic 
distribution.The Type III (Wald) Tests and Type III (LR) Teststables, as illustrated by Figure 39.16,include the following:- Source
- is the name for each effect.
- DF
- is the degrees of freedom associated with each effect.
- ChiSq
- is the Wald statistic for the Wald tests or the likelihood-ratio statistic for the LR tests of the null hypothesis that the parameters for the effect are 0. This has an asymptotic
distribution. - Pr > ChiSq
- is the probability of obtaining a greater statistic than that observed, if the null hypothesis is true.
Figure 39.16: Type III Tests Tables for Generalized Linear Models
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