Effect Size Measures

Effect size measures help us understand the strength and practical significance of relationships in data. They go beyond p-values, offering insights into how meaningful findings are in real-world contexts, which is crucial for making informed decisions in statistical inference.

1. Cohen's d

   • Measures the standardized difference between two group means.
   • Commonly used in t-tests to assess the magnitude of treatment effects.
   • Values typically interpreted as small (0.2), medium (0.5), and large (0.8).
   • Helps in understanding the practical significance of results beyond p-values.

2. Pearson's correlation coefficient (r)

   • Quantifies the strength and direction of a linear relationship between two continuous variables.
   • Ranges from -1 to 1, where 0 indicates no correlation.
   • Positive values indicate a direct relationship, while negative values indicate an inverse relationship.
   • Important for assessing the degree of association in regression analyses.

3. Eta-squared (η²)

   • Represents the proportion of variance in the dependent variable explained by the independent variable(s).
   • Values range from 0 to 1, with higher values indicating a greater effect size.
   • Commonly used in ANOVA to assess the impact of categorical predictors.
   • Provides insight into the practical significance of group differences.

4. Odds ratio

   • Compares the odds of an event occurring in one group to the odds in another group.
   • Commonly used in case-control studies and logistic regression.
   • An odds ratio of 1 indicates no difference between groups, while values greater than 1 indicate increased odds in the first group.
   • Useful for understanding the strength of associations in categorical data.

5. Risk ratio (relative risk)

   • Compares the probability of an event occurring in the exposed group to the unexposed group.
   • Values greater than 1 indicate increased risk in the exposed group, while values less than 1 indicate decreased risk.
   • Commonly used in cohort studies and clinical trials.
   • Provides a clear interpretation of risk associated with exposure.

6. Standardized mean difference

   • A general term for effect size measures that standardize differences between group means.
   • Useful for comparing results across different studies with varying scales.
   • Includes measures like Cohen's d and Hedges' g.
   • Helps in meta-analysis to synthesize findings from multiple studies.

7. Glass's delta

   • Similar to Cohen's d but uses the standard deviation of the control group for standardization.
   • Particularly useful when the sample sizes of groups differ significantly.
   • Provides a measure of effect size that is less biased by the variability of the treatment group.
   • Helps in understanding the impact of interventions in experimental designs.

8. Hedges' g

   • A variation of Cohen's d that corrects for small sample sizes.
   • Provides a more accurate estimate of effect size when sample sizes are less than 20.
   • Values interpreted similarly to Cohen's d, aiding in the assessment of treatment effects.
   • Useful in meta-analyses to combine effect sizes from different studies.

9. R-squared (R²)

   • Represents the proportion of variance in the dependent variable explained by the independent variable(s) in regression models.
   • Ranges from 0 to 1, with higher values indicating better model fit.
   • Helps in assessing the explanatory power of the model.
   • Important for understanding the effectiveness of predictors in explaining outcomes.

10. Partial eta-squared

    • A measure of effect size that assesses the proportion of variance explained by a factor while controlling for other factors.
    • Commonly used in factorial ANOVA designs.
    • Values range from 0 to 1, with higher values indicating a stronger effect.
    • Provides insight into the unique contribution of each predictor in multivariate analyses.