Spirituality Studies 147 Muhammad Japar et al. 2.7 Data Analysis The data were analyzed using IBM SPSS Statistics Version 24.0. As noted in Section 2.2, group membership (Module A vs. Module B) was not included as an analytical variable given the complementary rather than comparative nature of the two modules and the sample size constraints of this pilot study. All analyses were therefore conducted on the full sample (N = 50) with gender as the sole between-subjects factor, preceding hypothesis testing, the data were checked for missing values, outliers, and data entry mistakes. For all the variables, descriptive statistics were determined (means, standard deviations, and frequencies). Assumption testing. The One-Sample Kolmogorov-Smirnov test was used to review the normality of the distributions. Levene’s test was used to evaluate the homogeneity of the variance across groups. Box’s M test was used to assess the homogeneity of the covariance matrices. These results are shown in the results section. Primary analyses. A repeated measures multivariate analysis of variance (MANOVA) was used to test the hypotheses with time (pre-test, post-test, and follow-up) as the within-subject factors and gender as the between-subjects factor. For the self-oriented meaning and other-oriented meaning dimensions, separate MANOVAs were performed. Bonferroni correction was applied to adjust for Type I error inflation in follow-up pairwise comparisons. For all statistical tests, the alpha level was set to.05. Effect sizes were calculated for all primary analyses. Partial eta-squared (η²) was used as the effect size index for MANOVA and between-subjects effects, interpreted following Cohen’s (1988) conventions as small (η² =.01), medium (η² =.06), or large (η² =.14). Effect sizes are reported throughout the Results section alongside F-statistics and significance values to provide a more complete picture of practical significance, particularly given the subcritical sample size (N = 50). It is acknowledged that a sample of N = 50 is subcritical for MANOVA procedures, which typically require larger samples to achieve adequate statistical power (Cohen 1988). A formal a priori power analysis was not conducted prior to data collection, which increases the risk of Type II errors. Findings are therefore interpreted with appropriate caution. 2.7.1 Post-Hoc Statistical Power Analysis Given the subcritical sample size (N = 50) and the absence of a formal a priori power analysis, post-hoc achieved statistical power was computed for all primary effects using G*Power 3.1 (α =.05, two groups, three measurement points, inter-measurement correlation =.50). Observed partial η² values were converted to Cohen’s f using the formula f = √(η² / (1 − η²)). Results are presented in Table 3. Power for detecting gender effects on both SOM (1−β =.97) and OOM (1−β =.98) substantially exceeded the conventional threshold of .80 (Cohen 1988), indicating that the present sample was adequate for detecting the gender differences reported. The risk of Type II error for these effects is therefore low (approximately 2–3%). In contrast, power for detecting the main effect of Time was only .58, falling below the .80 threshold. This indicates that the study was underpowered for detecting change across measurement points. The non-significant Time effect (p =.082) should therefore be interpreted with caution, as it may reflect insufficient statistical power rather than a true absence of change. Based on G*Power projections, a sample of approximately N = 85–90 would be required to achieve power of .80 for detecting a time effect of similar magnitude in a two-group repeated-measures design. Future randomized controlled trials should incorporate this estimate into a priori power calculations, with an additional 10–20% to account for attrition.
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