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.