Analysis of Variance with PROC GLM

Analysis of variance (ANOVA) tests whether the mean of a numeric outcome differs between groups. PROC GLM (general linear models) fits ANOVA, regression, and mixtures of both, with categorical predictors in a CLASS statement.

Do boys and girls in SASHELP.CLASS differ in average weight?

proc glm data=sashelp.class;
   class sex;
   model weight = sex;
   means sex;
run;
quit;

Output (abridged):

                      The GLM Procedure

Dependent Variable: Weight

                             Sum of
Source             DF       Squares   Mean Square   F Value   Pr > F

Model               1   1681.122953   1681.122953      3.73   0.0702
Error              17   7654.613889    450.271405
Corrected Total    18   9335.736842

R-Square     Coeff Var      Root MSE    Weight Mean

0.180074      21.21402      21.21960       100.0263

Source             DF     Type III SS   Mean Square   F Value   Pr > F

Sex                 1     1681.122953   1681.122953      3.73   0.0702


Level of          --------Weight--------
Sex         N         Mean         Std Dev

F           9     90.111111      19.383914
M          10    108.950000      22.727186

How to read it:

• The boys are about 18.8 pounds heavier on average.
• Pr > F = 0.0702 — above the usual 0.05 threshold, so with only 19 students this difference isn't statistically significant.
• R-Square 0.18 — sex alone explains 18% of the variation in weight (compare 77% for height in the previous lesson).
• With one factor, the Type I and Type III tables (the full output shows both) are identical. With several factors and unequal group sizes they differ; Type III is usually the one to report.

For two groups, this F test is equivalent to a two-sample t test (PROC TTEST): F equals t squared.

More factors and comparisons

proc glm data=sashelp.class;
   class sex;
   model weight = sex height / solution;
   lsmeans sex / pdiff cl;
run;
quit;

• model weight = sex height mixes a factor and a numeric covariate (analysis of covariance) — the sex difference adjusted for height.
• a*b in a MODEL adds an interaction.
• lsmeans ... / pdiff compares adjusted group means; add adjust=tukey for many groups.
• solution prints the parameter estimates.

Beyond GLM

• PROC MIXED and PROC GLIMMIX — random effects and repeated measures (common in clinical trials).
• PROC NPAR1WAY — non-parametric tests (Wilcoxon, Kruskal-Wallis).
• PROC ANOVA — older, for balanced designs only; prefer GLM.