A researcher runs a hierarchical multiple regression in SPSS to predict first-year university GPA. Step 1 includes SAT score. Step 2 adds weekly Study Hours. SPSS output shows:
Model Summary
- Model 1 (SAT): R = .500, R Square = .250, Adjusted R Square = .242
- Model 2 (SAT + StudyHours): R = .574, R Square = .330, Adjusted R Square = .316
Change Statistics (Model 2)
- R Square Change = .080
- F Change = 11.94, df1 = 1, df2 = 98, Sig. F Change = .001
Which statement is the most accurate interpretation of the effect size of adding Study Hours (beyond SAT) in Step 2?
(Use Cohen’s f² for the incremental effect: f²_change = (R²_full − R²_reduced) / (1 − R²_full). Cohen’s benchmarks: .02 small, .15 medium, .35 large.)
The incremental effect size is f²_change ≈ 0.12, which is a small-to-approaching-medium effect; Study Hours adds a practically meaningful amount of variance beyond SAT.
The incremental effect size is f²_change ≈ 0.32, which is a medium effect; this comes directly from ΔR² = .080 by converting it to a percentage (8%) and multiplying by 4.
The incremental effect size is f²_change ≈ 0.11, which is computed as ΔR² / (1 − R²_reduced) = .080 / (1 − .250); this is the standard definition in hierarchical regression.
Because Sig. F Change = .001, the effect size is large; statistical significance implies a large effect.