Getting the Big Picture
It is instructive to reflect on the big picture concerning your findings before proceeding to summarize them in text form. First, notice the bivariate correlations from Table 14.8. The correlations between commitment and rewards, between commitment and investment size, and between commitment and alternative value are each significant and in the predicted direction. Only the correlation between commitment and costs is nonsignificant. These findings provide partial support for the investment model.
A somewhat similar pattern of results can be seen in Table 14.9 which shows that the beta weights and uniqueness indices for investment size and alternative value are both significant and in the predicted direction. Unlike correlations, however, Table 14.9 shows that neither the beta weight nor the uniqueness index for rewards is statistically significant. This might come as a surprise because the correlation between commitment and rewards is moderately strong at .58. With such a strong correlation, how could the multiple regression coefficient and uniqueness index for rewards be nonsignificant?
A possible answer can be found in the correlations of Table 14.8. Notice that the correlation between Commitment and Rewards is somewhat weaker than the correlation between Commitment and either Investment size or Alternative value. In addition, it can be seen that the correlations between Rewards and both Investment size and Alternative value are fairly substantial at r = .57 and r = –.47, respectively. In short, REWARDS shares a great deal of variance in common with Investment size and Alternative value and is a poorer predictor of Commitment. In this situation, it is unlikely that a multiple regression equation that already contains Investment size and Alternative value would need a variable like REWARDS to improve the accuracy of prediction. In other words, any variance in commitment that is accounted for by REWARDS has probably already been accounted for by investment size and alternative value. As a result, the REWARDS variable is largely redundant and consequently displays a nonsignificant beta weight and uniqueness index.
Was this a real test of the investment model?It must be emphasized again that the results concerning the investment model presented here are entirely fictitious and should not be viewed as legitimate tests of that conceptual framework. Most published studies of the investment model are, in fact, very supportive of its predictions. For representative examples of this research, please refer to Rusbult (1980a, 1980b), Rusbult and Farrell (1983), and Rusbult, Johnson, and Morrow (1986). |
Formal Description of Results for a Paper
Again, there are several ways to summarize the results of these analyses within the text of the paper. The amount of detail provided when describing the analyses should be dictated by the statistical sophistication of your audience; less detail is needed if the audience is likely to be familiar with the use of multiple regression. The following format is fairly typical:
Results were analyzed using both bivariate correlations and multiple regression. Means, standard deviations, Pearson correlations, and Cronbach's alpha estimates appear in Table 14.8. The bivariate correlations revealed three predictor variables were significantly related to commitment: rewards (r = .58); investment size (r = .61); and alternative value (r = - .72). All of these correlations were significant at p < .01, and all were in the predicted direction. The correlation between costs and commitment, on the other hand, was nonsignificant as r = -.25.
Using multiple regression, commitment scores were then regressed on the linear combination of rewards, costs, investment size, and alternative value. The equation containing these four variables accounted for approximately 65% of observed variance in commitment, F(4, 43) = 19.60, p < .01, adjusted R2 = .61.
Beta weights (standardized multiple regression coefficients) and uniqueness indices were subsequently reviewed to assess the relative importance of the four variables in the prediction of commitment. The uniqueness index for a given predictor is the percentage of variance in the criterion accounted for by that predictor, beyond the variance accounted for by the other predictor variables. Beta weights and uniqueness indices are presented in Table 14.9.
The table shows that only investment size and alternative value displayed significant beta weights. Alternative value demonstrated somewhat larger beta weight at -.50 (p < .01), while the beta weight for investment size was .31 (p < .05). Both coefficients were in the predicted direction.
Findings regarding uniqueness indices correspond to those for beta weights in that only investment size and alternative value displayed significant indices. Alternative value accounted for approximately 18% of the variance in commitment, beyond the variance accounted for by the other three predictors, F(1, 43) = 21.51, p < .01. In contrast, investment size accounted for only 5% of the unique variance in commitment, F(1, 43) = 6.20, p < .05.
The preceding tables and text make reference to the degrees of freedom for the statistical tests that assessed the significance of the model R2 as well as the significance of the individual regression coefficients. It might be helpful to summarize how these degrees of freedom are calculated.
The second paragraph indicates that “The equation containing these four variables accounted for 65% of observed variance in commitment, F(4, 43) = 19.60, p < .01, adjusted R2 = .61.” The information from this passage is in the results of PROC REG using the STB option, which appeared as Output 14.2. The F value that tests the significance of the model R2 is in the analysis of variance section under “F Value.” The p value associated with this test appears to the right of the F value. The degrees of freedom for the test are in the second column, headed “DF.” Degrees of freedom for the numerator in the F ratio (4) can be found to the right of “Model”; the degrees of freedom for the denominator (43), is to the right of “Error.”
The beta weights and their corresponding t values are in the lower half of Output 14.2. The beta weights themselves appear under the heading “Standardized Estimate,” while the t values appear under “t Value.” The degrees of freedom for these t tests are equal to
N – KFull – 1
in which N = total sample size and KFull = number of predictor variables in the full equation. In this case, df = 48 – 4 – 1 = 43.