Effect Size
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Parameters
Results
Notes:
- Effect size measures the magnitude of an effect independent of sample size
- Different types of tests use different effect size measures
- Effect sizes help in planning sample sizes for future studies
- Guidelines for effect sizes are field-dependent
- Consider practical significance alongside statistical significance
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Understanding Effect Size Measures
What is Effect Size?
Effect size quantifies the magnitude of differences or relationships between groups. It helps researchers understand the practical significance of their findings beyond statistical significance (p-values).
Why Effect Size Matters
Unlike p-values, effect sizes are independent of sample size and provide a standardized way to compare results across studies.
Effect Size Formulas and Examples
Formula:
Example Calculation:
Given:
Result: Small-to-medium effect size
Available Effect Size Measures
Mean Difference (Cohen's d)
- Small effect: 0.2
- Medium effect: 0.5
- Large effect: 0.8
- Used for comparing two independent groups
Paired Difference (Cohen's d)
- Uses same scale as regular Cohen's d
- Accounts for correlation between measures
- Typically larger than independent d
- Used for before-after or matched pairs
Proportions Difference
- Small effect: 0.1
- Medium effect: 0.3
- Large effect: 0.5
- Used for comparing success rates between groups
ANOVA (Eta-squared)
- Small effect: 0.01
- Medium effect: 0.06
- Large effect: 0.14
- Used for comparing multiple groups
Calculation Examples
Independent Groups Example
Treatment vs Control Group:
- • Treatment: Mean = 75, SD = 10, n = 30
- • Control: Mean = 70, SD = 10, n = 30
- • Cohen's d = 0.5 (Medium effect)
- • Interpretation: Moderate treatment effectiveness
Paired Design Example
Before vs After Intervention:
- • Before: Mean = 20, SD = 5
- • After: Mean = 25, SD = 5
- • Correlation = 0.7, n = 25
- • Cohen's d = 1.2 (Large effect)
Proportions Example
Success Rates Comparison:
- • Group 1: 40 successes out of 100
- • Group 2: 60 successes out of 100
- • Effect size = 0.4 (Medium-large)
- • Substantial difference in success rates
ANOVA Example
Comparing Multiple Groups:
- • F-value = 10.5
- • df between = 2, df total = 100
- • η² = 0.17 (Large effect)
- • Strong evidence of group differences
Interpretation Guidelines
Important Considerations:
- Effect sizes should be interpreted within your field's context
- Small effects can be meaningful in some research areas
- Consider practical implications alongside numerical values
- Use effect sizes to plan sample sizes for future studies
- Report effect sizes alongside confidence intervals when possible
Related Calculators
Sample Size Calculator
Power Analysis Calculator
Two Sample Paired T-Test Calculator
One-Way ANOVA Calculator
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