I have a 2x2 design.   To make it simple, here’s a small data set with two factors, A and B, each with 2 levels and a DV ,Y. The design is perfectly balanced: The results from the ANOVA portion of proc glm produce different findings than the solution, which doesn’t make sense. The solution option in the model statement provides regression estimates of  effects of the dummy-coded variables. Given that both IVs are only 2 levels, each estimable effect corresponds to the effects in the design (i.e., A, B and A*B). Therefore the p-values for the F-tests should be identical to those of the parameter estimates from the regression solution, correct? data exp;       input A $ B $ Y @@;       datalines;    A1 B1 12 A1 B1 14     A1 B2 11 A1 B2 9    A1 B1 13 A1 B1 12     A1 B2 10 A1 B2 8    A2 B1 20 A2 B1 18     A2 B2 17 A2 B2 10    A2 B1 22 A2 B1 20     A2 B2 19 A2 B2 11 ;    proc glm data=exp;       class A B;       model Y=A B A*B/SOLUTION; run; Dependent Variable: Y Sum of        Source                      DF         Squares     Mean Square    F Value Pr > F        Model                        3     231.2500000      77.0833333      12.42 0.0005        Error                       12      74.5000000       6.2083333        Corrected Total             15     305.7500000 R-Square     Coeff Var      Root MSE        Y Mean 0.756337      17.64002      2.491653      14.12500        Source                      DF       Type I SS     Mean Square    F Value Pr > F        A                            1     144.0000000     144.0000000      23.19 0.0004        B                            1      81.0000000      81.0000000      13.05 0.0036        A*B                          1       6.2500000       6.2500000       1.01 0.3355        Source                      DF     Type III SS     Mean Square    F Value Pr > F        A                            1     144.0000000     144.0000000      23.19 0.0004        B                            1      81.0000000      81.0000000      13.05 0.0036        A*B                          1       6.2500000       6.2500000       1.01 0.3355 Standard Parameter Estimate             Error    t Value Pr > |t| Intercept            14.25000000 B      1.24582637      11.44 <.0001             A         A1         -4.75000000 B      1.76186454      -2.70 0.0195             A         A2          0.00000000 B       . .         .             B         B1          5.75000000 B      1.76186454       3.26 0.0068             B         B2          0.00000000 B       .                .         .             A*B       A1 B1      -2.50000000 B      2.49165273      -1.00 0.3355             A*B       A1 B2       0.00000000 B       .                .         .             A*B       A2 B1       0.00000000 B       .                .         .             A*B       A2 B2       0.00000000 B       .                .         . NOTE: The X'X matrix has been found to be singular, and a generalized inverse was used to solve       the normal equations.  Terms whose estimates are followed by the letter 'B' are not       uniquely estimable.   Shouldn’t the p-value for the effect of B in the type III SS  F-test  (p=.0036) be equal to p-value for the parameter B B (p=.0068)? ... View more