Effect Size Calculator

Calculate Cohen d, Hedges g, Cohen h for proportions, or correlation r effect sizes from summary statistics

Example Results

1 examples

Calculate Cohen d from two group summaries

Compare two group means using pooled standard deviation to estimate standardized effect size

{
  "result": {
    "effectSize": 0.3333,
    "magnitude": "small",
    "metric": "Cohen d"
  }
}
View input parameters
{ "effectType": "cohen-d", "group1Mean": 105, "group2Mean": 100, "group1Sd": 15, "group2Sd": 15, "group1Size": 30, "group2Size": 30, "proportion1": 0.6, "proportion2": 0.5, "correlation": 0.3, "decimalPlaces": 4 }

Key Facts

Category
Math, Date & Finance
Input Types
select, number
Output Type
json
Sample Coverage
2
API Ready
Yes

Overview

The Effect Size Calculator is a statistical utility designed to compute standardized effect sizes directly from summary statistics. Whether you need to calculate Cohen's d or Hedges' g for mean differences, Cohen's h for proportions, or evaluate correlation r, this tool provides precise effect size values and qualitative magnitude interpretations to help you understand the practical significance of your data.

When to Use

  • •When comparing the means of two independent groups to determine the standardized difference.
  • •When evaluating the practical significance of a difference between two proportions in A/B testing or survey results.
  • •When converting summary statistics into standardized effect sizes for meta-analyses or academic research reports.

How It Works

  • •Select your desired effect type: Cohen's d, Hedges' g, Proportion h, or Correlation r.
  • •Input the required summary statistics, such as group means, standard deviations, sample sizes, or proportions.
  • •Specify the number of decimal places for your desired output precision.
  • •The calculator instantly computes the effect size and provides a qualitative magnitude interpretation (e.g., small, medium, or large).

Use Cases

Academic researchers reporting the practical significance of experimental results in peer-reviewed journals.
Data analysts conducting meta-analyses to standardize and compare results across multiple independent studies.
A/B testing practitioners evaluating whether a statistically significant difference in conversion rates is practically meaningful.

Examples

1. Evaluating a New Teaching Method

Educational Researcher
Background
A researcher is comparing test scores between a control group and an experimental group using a new teaching method.
Problem
Needs to determine the standardized effect size of the new method to report in a journal, having only the summary statistics.
How to Use
Select 'Cohen d', input Group 1 Mean (105), Group 2 Mean (100), both standard deviations (15), and sample sizes (30).
Example Config
Effect Type: Cohen d, Group 1 Mean: 105, Group 2 Mean: 100, Group 1 SD: 15, Group 2 SD: 15, Group 1 Size: 30, Group 2 Size: 30
Outcome
Calculates an effect size of 0.3333, indicating a 'small' magnitude of difference between the two teaching methods.

2. Analyzing A/B Test Conversion Rates

Marketing Analyst
Background
An analyst ran an A/B test on a landing page. Variant A had a 60% conversion rate, while Variant B had a 50% conversion rate.
Problem
Wants to know the standardized effect size of the conversion rate difference to see if it warrants a permanent design change.
How to Use
Select 'Proportion h' as the effect type and input Proportion 1 (0.6) and Proportion 2 (0.5).
Example Config
Effect Type: Proportion h, Proportion 1: 0.6, Proportion 2: 0.5
Outcome
Outputs the Cohen's h effect size along with its magnitude, helping the analyst confirm the practical impact of the new landing page.

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FAQ

What is the difference between Cohen's d and Hedges' g?

Cohen's d calculates the standardized mean difference, while Hedges' g applies a correction factor that provides a less biased estimate for small sample sizes (typically under 20).

How do I interpret the magnitude of the effect size?

The tool automatically provides a magnitude label based on standard statistical conventions, such as 0.2 for small, 0.5 for medium, and 0.8 for large effects in Cohen's d.

Can I calculate effect sizes without raw data?

Yes, this calculator is specifically designed to work with summary statistics like means, standard deviations, and sample sizes, requiring no raw dataset.

What is Cohen's h used for?

Cohen's h is used to measure the effect size between two independent proportions, helping to determine if the difference between two rates or percentages is practically meaningful.

How many decimal places can I calculate?

You can configure the output precision from 0 up to 10 decimal places using the decimal places setting.

API Documentation

Request Endpoint

POST /en/api/tools/effect-size-calculator

Request Parameters

Parameter Name Type Required Description
effectType select No -
group1Mean number No -
group2Mean number No -
group1Sd number No -
group2Sd number No -
group1Size number No -
group2Size number No -
proportion1 number No -
proportion2 number No -
correlation number No -
decimalPlaces number No -

Response Format

{
  "key": {...},
  "metadata": {
    "key": "value"
  },
  "error": "Error message (optional)",
  "message": "Notification message (optional)"
}
JSON Data: JSON Data

AI MCP Documentation

Add this tool to your MCP server configuration: 

{
  "mcpServers": {
    "elysiatools-effect-size-calculator": {
      "name": "effect-size-calculator",
      "description": "Calculate Cohen d, Hedges g, Cohen h for proportions, or correlation r effect sizes from summary statistics",
      "baseUrl": "https://elysiatools.com/mcp/sse?toolId=effect-size-calculator",
      "command": "",
      "args": [],
      "env": {},
      "isActive": true,
      "type": "sse"
    }
  }
}

You can chain multiple tools, e.g.: `https://elysiatools.com/mcp/sse?toolId=png-to-webp,jpg-to-webp,gif-to-webp`, max 20 tools.

If you encounter any issues, please contact us at [email protected]