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Effect Size Calculator

Created:October 23, 2024
Last Updated:March 18, 2025

This Effect Size Calculator helps you quantify the magnitude of differences between groups or relationships between variables. It calculates various effect size measures like Cohen's d, eta-squared, and proportion differences, helping you understand the practical significance of your statistical findings. For example, you can analyze the strength of treatment effects, differences between experimental groups, or the impact of interventions in your research.

Calculator

Parameters

Sample Size Calculation 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

Learn More

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).

Effect Size Formulas, Examples, and R Code

Formula:

d=Xˉ1−Xˉ2spooledd = \frac{\bar{X}_1 - \bar{X}_2}{s_{pooled}}
spooled=(n1−1)s12+(n2−1)s22n1+n2−2s_{pooled} = \sqrt{\frac{(n_1-1)s_1^2 + (n_2-1)s_2^2}{n_1 + n_2 - 2}}

Example Calculation:

Given:

  • Mean1=75.3,Mean2=70.1\text{Mean}_1 = 75.3, \text{Mean}_2 = 70.1
  • s1=12.4,s2=11.8s_1 = 12.4, s_2 = 11.8
  • n1=30,n2=32n_1 = 30, n_2 = 32
spooled=29(12.42)+31(11.82)60≈12.1s_{pooled} = \sqrt{\frac{29(12.4^2) + 31(11.8^2)}{60}} \approx 12.1
d=75.3−70.112.1≈0.43d = \frac{75.3 - 70.1}{12.1} \approx 0.43

Result: Small-to-medium effect size

R Code Example

R
library(effectsize)

group1 <- c(88.17, 69.04, 78.21, 80.88, 78.62, 73.57, 
           89.56, 73.69, 94.56, 74, 87.51, 97.21, 60.9, 
           71.87, 73.31, 80.91, 71.81, 48.38, 50.51, 
           87.67, 71.59, 57.02, 72.92, 86.62, 93.35, 
           70.37, 72.08, 57.2, 79.17, 68.3)
group2 <- c(82.38, 63.67, 72.64, 75.25, 73.04, 68.1, 
           83.74, 68.21, 88.64, 68.52, 81.74, 91.23, 
           55.7, 66.43, 67.84, 75.28, 66.38, 43.45, 
           45.54, 81.89, 66.16, 51.91, 67.47, 80.87, 
           87.45, 64.97, 66.64, 52.09, 73.58, 62.94, 73.53, 75.94)

print(str_glue("Group 1: Mean = {round(mean(group1), 2)}, 
               SD = {round(sd(group1), 2)}, 
               n = {length(group1)}"))
print(str_glue("Group 2: Mean = {round(mean(group2), 2)}, 
               SD = {round(sd(group2), 2)}, 
               n = {length(group2)}"))

result <- cohens_d(group1, group2)
print(result)

Output:

Group 1: Mean = 75.3, 
SD = 12.4, 
n = 30
========================
Group 2: Mean = 70.1, 
SD = 11.8, 
n = 32
========================
Cohen's d |        95% CI
-------------------------
0.43      | [-0.08, 0.93]

- Estimated using pooled SD.

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 & Power Analysis Calculator

Two Sample Paired T-Test Calculator

One-Way ANOVA Calculator

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StatsCalculators Team. (2025). Effect Size Calculator. StatsCalculators. Retrieved April 4, 2025 from https://www.statscalculators.com/calculators/hypothesis-testing/effect-size-calculator