a) Example of an Analysis of Variance (ANOVA) Result
Data were subjected to a 2 (gender of respondent: female vs. male) x 2 (coping mechanism: emotion-focused vs. problem-focused) Mixed Model Analysis of Variance (ANOVA), with the coping mechanism serving as a within-subjects factor and gender as a between-subjects factor. Findings revealed two main effects. Regardless of the coping mechanism, female respondents (M = 33.54) were more adept at coping with stress than did male respondents (M = 26.93), F (1, 967) = 85.78, p < .0001, partial h2 = .19, and overall, problem-focused coping strategies were used more (M = 78.65) than emotion-focused strategies (M = 66.56), F (1, 967) = 365.13, p < .0001, partial h2 = .38. This main effect of coping mechanism was qualified by an interaction between gender of respondent and coping mechanism, F (1, 967) = 256.72, p < .001, partial h2 = .28. Although the use of either emotion-focused or problem-focused coping did not differ for the female respondents, male participants tended to use problem-focused more than emotion-focused strategies, F (1, 967) = 157.92, p < .0001, partial h2 = .32 (see Table 1).
b) Example of a Discriminant Analysis (DDA) Result
Descriptive discriminant analysis (DDA) was used to discover differences between clinical patients and non-patients across the different psychological distress variables and dimensions. As a multivariate statistical procedure, DDA is sufficient to indicate that group differences exist and it can pinpoint exactly where the group differences are (Sherry, 2006). The discriminant analysis for the depression measure indicated one significant discriminant function, Wilk’s lambda = .975, c2 (3) = 20.22, p < .001. The canonical correlation was .43, indicating that 18.49% of the variability between patients and non-patients could be accounted for by the first linear combination of the depression measure dimensions. An examination of the standardized discriminant function coefficients and structure coefficients (see Table 2) indicated that the Suicidality dimension contributed most to discriminating between patients and non-patients. Patients had a higher centroid (2.03) than non-patients (-.11). This suggested that patients have a higher level of proneness to suicidality than non-patients.
c) Example of a Multiple Linear Regression Analysis Result
Multiple linear regression analysis was conducted to examine the contributions of the three leadership styles to the prediction of work productivity. According to Licht (2001), this analysis is used to test the utility of a set of independent variables (i.e., leadership styles) for predicting a criterion event or behavior (i.e., productivity). The regression analysis tested the hypothesis that leadership styles can jointly and uniquely predict work productivity. In the prediction of productivity, the model was significant, F(3, 301) = 59.47, p < .001; R2 = .372. Thus, it is concluded that the three leaderships styles of autocratic, democratic, and laissez faire jointly predicted and accounted for over 37% (i.e., a large effect size) of the variance in work productivity. The individual predictors were also examined to ascertain whether they have significant and meaningful unique contributions to the regression (see Table 7). Using the Bonferroni method (alpha’ = .0167), follow-up analyses revealed that democratic leadership style made a significant independent contribution to predicting work productivity, t = 10.86, p < .001. Moreover, autocratic leadership style also made a significant independent contribution to predicting work productivity, t = 5.04, p < .001. In contrast, a laissez faire leadership style did not make a significant independent contribution to the prediction of work productivity, t = -0.76, p = .447. Comparing the two leadership styles that have significant unique contributions to the regression, democratic leadership style accounted for 24.6% of unique variance in work productivity beyond that accounted for by the other leadership styles. On the other hand, autocratic leadership style accounted for 5.3% of unique variance in work productivity. Thus, it can be concluded that democratic leadership made the strongest unique contribution to the prediction of work productivity, over and beyond the unique contributions of the other two leadership styles.
d) Example of a Path Analysis Result
The trimmed model explained 29% of the variance in participants’ anxiety, 26% of the variance in participants’ depression, and 16% of the variance in participants’ adaptive functioning. The model and the resulting path coefficients, in the form of standardized regression weights represented by b, are shown in Figure 1. There was a significant negative direct effect of self-efficacy on depression, b = -.54, p < .001. The negative path coefficient can be interpreted to mean that the higher the perceived degree to which the participants believe that they are capable of attaining personal goals, the lesser the reported experience of depression. There was also a significant negative direct effect of impression management on anxiety, b = -.51, p < .001. This negative path coefficient can be interpreted to mean that the higher the perceived degree to which the participants feel that they are able to control the impressions that other people form of them, the lesser the reported experience of anxiety. To evaluate the fit of the trimmed model on the data, fit indexes cutoff levels as recommended by Hu and Bentler (1999) were used. In this study, the fit indexes obtained were the following: (a) CFI = .97; (b) RMSEA = .01; and (c) TLI = .98. All these indices indicate a good fit between the trimmed model and the observed data.
