See real interpretations, not screenshots

Prior to conducting the primary analyses, a series of assumption tests were performed at a significance level of α = .05. Normality was assessed for all four variables using both the Shapiro-Wilk and Kolmogorov-Smirnov tests. Both tests indicated statistically significant departures from normality for all variables: LS_Mean, IQ_Mean, TU_Mean, and PI_Mean all returned p < .05 on both tests (see Table 1). However, inspection of skewness and kurtosis values revealed that all variables fell within the acceptable range of ±1, and visual examination of Q-Q plots suggested approximate normality in the distributions. Furthermore, given the large sample size (N = 400), the Shapiro-Wilk and Kolmogorov-Smirnov tests are known to be highly sensitive to even trivial deviations from normality. In accordance with the Central Limit Theorem, parametric tests remained appropriate and robust to these violations (Pallant, 2020; Field, 2018). The assumption of homogeneity of variance was assessed using Levene's test based on the mean. The result was non-significant, F(3, 396) = 0.623, p = .601, indicating that equal variances across Year groups for LS_Mean could be assumed. This assumption was met.

For the multiple regression model, three additional diagnostic assumptions were examined. Independence of residuals was assessed using the Durbin-Watson statistic, which yielded a value of 1.979, falling within the acceptable range of 1.5–2.5 and indicating no problematic autocorrelation among residuals. Multicollinearity was evaluated using Tolerance and Variance Inflation Factor (VIF) values for each predictor (see Table 2). All VIF values were well below the threshold of 5, and all Tolerance values were well above 0.10, indicating no multicollinearity concerns among the four predictors in the model. Outliers were assessed through inspection of standardized residuals. The maximum absolute standardized residual observed was 3.024, which is marginally beyond the ±3.0 guideline but remains within the more conservative ±3.29 threshold for extreme outliers (Field, 2018). Cook's Distance and leverage values were not available in the output; however, based on the standardized residual inspection, no severe outlier concern was identified. Overall, the assumptions for parametric testing and multiple regression were considered sufficiently met, and the planned analyses proceeded accordingly.

Table 1: Normality Test Results

Note. S-W = Shapiro-Wilk; K-S = Kolmogorov-Smirnov. df = 400 for all variables. All variables showed statistically significant departures from normality; however, parametric tests remained appropriate due to the large sample size (N = 400) and the Central Limit Theorem (Pallant, 2020; Field, 2018). Skewness and kurtosis values for all variables fell within ±1, and Q-Q plot inspection suggested approximate normality.

Table 2: Collinearity Statistics

Note. VIF values < 5 indicate no multicollinearity concern (Hair et al., 2019). Tolerance values > .10 further confirm the absence of multicollinearity among predictors.

References

Field, A. (2018). Discovering statistics using IBM SPSS Statistics (5th ed.). SAGE Publications.

Hair, J. F., Babin, B. J., Anderson, R. E., & Black, W. C. (2019). Multivariate data analysis (8th ed.). Cengage Learning.

Pallant, J. (2020). SPSS survival manual: A step-by-step guide to data analysis using IBM SPSS (7th ed.). McGraw-Hill Education.