Licensed therapists are mandated by law to report child abuse by their clients. This requires the therapist to breach confidentiality and possibly lose the client's trust. A national survey of licensed psychotherapists was conducted to investigate client's reactions to legally mandated child-abuse reports (American Journal of Orthopsychiatry, Jan. 1997). The sample consisted of 303 therapists who had filed a child-abuse report against one of their clients. The researchers were interested in finding the best predictors of a client's reaction (y) to the report, where y is measured on a 30-point scale. (The higher the value, the more favorable the client's response to the report.) The independent variables found to have the most predictive power are listed here.
x1 = Therapist's age (years)
x2 = Therapist's gender (1 if male, 0 if female)
x3 = Degree of therapist's role strain (25-point scale)
x4 = Strength of client-therapist relationship (40-point scale)
x5 = Type of case (1 if family, 0 if not)
x1x2 = Age × gender interaction
a. Hypothesize a first-order model relating y to each of the five independent variables.
b. Give the null hypothesis for testing the contribution of x4, strength of client-therapist relationship, to the model.
c. The test statistic for the test, part b, was t = 4.408 with an associated p-value of .001. Interpret this result.
d. The estimated β coefficient for the x1x2 interaction term was positive and highly significant (p < .001). According to the researchers, "This interaction suggests that ... as the age of the therapist increased. ... male therapists were less likely to get negative client reactions than were female therapists." Do you agree?
e. For this model, R2 = .2946. Interpret this value.