## Solomon's four group design

This paper (Braver MCW and Braver SL, 1988), gives an illustration (with a flow diagram) of a design specifically to assess the influence of a treatment at both baseline (pre-test) and post test. It involves six responses over four groups (G1, G2, G3, G4). Only two of the groups (G1 and G2) are tested at *both* baseline and post-test with G3 and G4 tested only at post-test ie the six responses are of form:

T1 G1 G2

T2 G1 G2 G3 G4

In addition two groups G1 and G3 are randomly given the treatment.

The aim is to assess treatment differences using analyses of variance firstly testing the difference in the four responses at post-test (time by treatment interaction). In particular if there is no time by treatment interaction, no main effect of treatment (ie ignoring time) using all six responses and then no treatment difference *both* using an ANCOVA to compare the two group scores between the two groups (G1 and G2) recorded at both baseline and post-test *and* between the two groups (G3 and G4) recorded only at post-test using an unpaired t-test then Stouffer's method (see also here) is used to give a combined treatment difference using the two p-values for treatment from the ANCOVA and the unpaired t-test.

Reference

Braver MCW and Braver SL (1988) Statistical treatment of the Solomon four-group design: a meta-analytic approach. *Psychological Bulletin* **104(1)** 150-154.