Effect size in regression analysis

In regression analysis, effect size refers to the strength or practical importance of the relationship between the predictor(s) and the outcome variable. Unlike t-tests, regression effect sizes focus on how much variance is explained or how much change in the dependent variable is associated with a change in predictors.

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📐 Common Effect Size Measures in Regression

✅ 1. R-squared (R²)

• Represents the proportion of variance in the dependent variable that is explained by the predictors.
• Ranges from 0 to 1:
  • 0 = model explains none of the variance
  • 1 = model explains all the variance

Interpretation (Cohen’s guidelines, very general):

• 0.01 = small
• 0.09 = medium
• 0.25 = large

📝 Note: R² increases with more predictors. Use Adjusted R² to correct for that.

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✅ 2. f² (Cohen’s f-squared)

Used to measure local effect size of individual predictors or for the model as a whole.

Formula: f_square=R_square/(1−R_square)​

Interpretation:

• 0.02 = small effect
• 0.15 = medium effect
• 0.35 = large effect

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✅ 3. Standardized Beta Coefficients (β)

• SPSS can give standardized coefficients, which show the relative effect size of each predictor.
• These coefficients are measured in standard deviations, making them easier to compare across variables.

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📊 Where to See This in SPSS

1. Linear regression path:
   • Go to: Analyze > Regression > Linear
   • Under Statistics, select:
     • R squared change
     • Descriptives
     • Part and partial correlations (for squared semi-partial correlation as another effect size)
2. Standardized Coefficients:
   • Automatically shown in the regression output under “Beta” if “Standardized coefficients” is selected.
3. f² Calculation:
   • Manually calculate using R² from the model: f² = R² / (1 - R²)

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✅ Final Tip

Use effect size in regression alongside p-values. A predictor might be statistically significant but still explain a tiny amount of variance, which effect sizes will reveal.