WARNING: 1. One standard deviation below the mean for Housing Contacts or -.095 is below its minimum value of .000. MODERATION MODEL The causal variable is Treatment, a dichotomy, 42.2% Controls and 57.8% Experimentals. the outcome variable is Days Housed, and the moderator variable is Housing Contacts. The causal model is as follows: The variable Treatment is presumed to cause Days Housed linearly whose causal effect is presumed to be altered linearly by Housing Contacts. RESULTS Descriptives There are a total of 109 cases. The power of the test of moderation assuming that f squared is .02 (a small effect size, but optimistic according to Aguinis (2004)) is .11, and the power of the test of moderation assuming that f squared is .15 (a moderate effect size) is .52. The means and standard deviations are presented in Table 1. The unexplained standard deviation in Days Housed is equal to 11.711, and the multiple correlation for the regression equation is .473. Effects of Treatment and Housing Contacts The results of the moderated regression analysis are summarized in Table 2. The overall effect of Treatment on Days Housed, when Housing Contacts is equal to zero, is 2.482 (p = .441), with a small effect size (d = .212). The overall effect of Housing Contacts on Days Housed, when Treatment is equal to zero, is 4.792 (p = .005), with a small effect size (r = .269). The mean of Days Housed for the Controls is equal to 9.563 and the mean of Days Housed for the Experimentals is equal to 12.045. Interaction Effects The interaction between Treatment and Housing Contacts is equal to 1.666 and is not statistically significant (p = .492), with a less than small effect size (f squared = .0045). As the Housing Contacts increases, the causal effect of Treatment, though not statistically significant, is amplified or strengthened. The effect of Treatment for persons who are one standard deviation below the mean on Housing Contacts (-.095) is equal to 2.323 (p = .492) with a less than small effect size (d = .198); the effect of Treatment for persons who are one standard deviation above the mean on Housing Contacts (1.826) is equal to 5.524 (p = .089), with a small effect size (d = .472). (See Table 3 and the graph or table as the end of the SPSS output.) Test of Nonlinearity The test of nonlinearity is as follows: The quadratic interaction effect of Housing Contacts with Treatment is -3.041 and is not statistically significant (p = .084). Regions of Statistical Significance Considered here are regions of Housing Contacts in which the effect of Treatment on Days Housed are statistically significant (Aiken & West, 1991). The effect of Treatment is not statistically significant at all in the range of possible values of Housing Contacts. Table 1: Descriptive Statistics Variable Mean Standard Deviation --------------------------------------------------------- Treatment .422 .496 Housing Contacts .865 .961 Days Housed 15.552 13.107 Table 2: Moderated Regression Coefficients Predictor Estimate Effect Size p -------------------------------------------------------------------- Intercept 9.563 <.001 Treatment 2.482 .212 .441 Housing Contacts 4.792 .269 .005 Treatment x Housing Contacts 1.666 .0045 .492 (Note that the effect size measure in Table 2 is d for Treatment, r for Housing Contacts, and f squared for the interaction.) Table 3: Predicted Means for the Causal Variable and the Moderator (+1 and -1 sd) Housing Contacts Treatment -.095 1.826 ------------------------------------------------- Controls 9.106 18.314 Experimentals 11.428 23.839 References Aguinis, H. (2004). Moderated regression. New York: Guilford. Aiken, L. S., & West, S. G. (1991). Multiple regression: Testing and interpreting interactions. Thousand Oaks, CA: Sage. Baron, R. M., & Kenny, D. A. (1986). The moderator-mediator variable distinction in social psychological research: Conceptual, strategic and statistical considerations. Journal of Personality and Social Psychology, 51, 1173-1182.