ANCOVA

(Modified from Gamst et al., 2008, p. 486, Q16.2)

Assume we are interested in the effect of treatment type (Factor A: a₁ = brief; a₂ = cognitive-behavioral, and a₃ = psychoanalytic) on community mental health clients (n = 5) global assessment of functioning (GAF) at the end of eight weeks of treatment (Time 2). The covariate for this study would be the clients GAF scores at the start of treatment (Time 1). The data are shown below.

Treatment type (A)
Brief			Cognitive-behavioral			Psychoanalytic
Time 1	Time 2		Time 1	Time 2		Time 1	Time 2
45.00	45.00		62.00	75.00		50.00	55.00
46.00	43.00		63.00	75.00		50.00	55.00
48.00	50.00		60.00	70.00		45.00	50.00
50.00	51.00		55.00	70.00		42.00	50.00
42.00	43.00		60.00	69.00		41.00	44.00

a) Conduct an ANCOVA with JASP, and attach the output. Extract and report the F ratio and degrees of freedom from the output. Based on the p values, determine whether the effect of treatment type on GAF (Time 2) adjusted for the covariate (i.e., GAF at Time 1) is significant at the .05 level.

b) If ANCOVA yields a significant result for the treatment effect, perform an appropriate multiple-comparison test (i.e., Brief versus Cognitive-behavioral, Brief versus Psychoanalytic, and Cognitive-behavioral versus Psychoanalytic) on GAF (Time 2), and conclude these results (i.e., significant or non-significant results).