Statistical Power Calculator

Estimate statistical power for one-sample mean or proportion tests using sample size, alpha, and expected effect

Example Results

1 examples

Estimate power for a one-sample mean test

Estimate power for detecting a 5-point mean difference with standard deviation 15 and sample size 64

{
  "result": {
    "power": 0.7601,
    "powerPercent": 76.0126,
    "effectSize": 0.3333
  }
}
View input parameters
{ "testType": "mean", "alternative": "two-sided", "alpha": 0.05, "sampleSize": 64, "nullMean": 100, "alternativeMean": 105, "standardDeviation": 15, "nullProportion": 0.5, "alternativeProportion": 0.6, "decimalPlaces": 4 }

Key Facts

Category
Math, Date & Finance
Input Types
select, number
Output Type
json
Sample Coverage
4
API Ready
Yes

Overview

The Statistical Power Calculator estimates the probability of correctly rejecting a false null hypothesis for one-sample mean or proportion tests. By inputting your sample size, significance level (alpha), and expected effect size parameters, you can quickly determine the statistical power of your study design and ensure your experiments yield reliable results.

When to Use

  • When planning a study and needing to verify if a predetermined sample size provides sufficient power to detect an expected effect.
  • When evaluating the feasibility of a one-sample mean or proportion test before collecting data.
  • When conducting post-hoc analysis to understand the statistical power of a completed experiment given the observed sample size.

How It Works

  • Select the test type (Mean Difference or Proportion Difference) and the alternative hypothesis direction (two-sided, greater, or less).
  • Enter your study parameters, including the significance level (alpha), sample size, and the null and alternative values.
  • Provide the standard deviation for mean tests, or adjust the proportion values for proportion tests.
  • The calculator computes the effect size and returns the estimated statistical power as both a probability and a percentage.

Use Cases

Academic researchers verifying study designs to ensure adequate power before submitting grant proposals.
Data analysts evaluating whether a fixed sample size in an A/B test is sufficient to detect a specific conversion rate change.
Quality control engineers determining if a sample batch size is large enough to detect deviations from a target manufacturing mean.

Examples

1. Evaluating Power for a Manufacturing Quality Test

Quality Control Engineer
Background
A factory produces widgets with a target weight of 100g and a historical standard deviation of 15g. The engineer can only sample 64 widgets per batch due to resource constraints.
Problem
Determine if a sample size of 64 is powerful enough to detect a 5g shift in the mean weight.
How to Use
Select 'Mean Difference', set sample size to 64, null mean to 100, alternative mean to 105, and standard deviation to 15.
Example Config
{
  "testType": "mean",
  "alternative": "two-sided",
  "alpha": 0.05,
  "sampleSize": 64,
  "nullMean": 100,
  "alternativeMean": 105,
  "standardDeviation": 15
}
Outcome
The calculator reveals a statistical power of 76.01%, indicating a moderate chance of detecting the 5g difference with the current sample size.

2. Assessing Power for a Marketing Campaign

Marketing Analyst
Background
A marketing team expects a new email template to increase the click-through rate from a baseline of 50% to 60%. They plan to test it on a small segment of 100 users.
Problem
Check if testing 100 users provides enough statistical power to confidently detect this 10% increase in proportion.
How to Use
Select 'Proportion Difference', set the alternative hypothesis to 'Greater Than', sample size to 100, null proportion to 0.5, and alternative proportion to 0.6.
Example Config
{
  "testType": "proportion",
  "alternative": "greater",
  "alpha": 0.05,
  "sampleSize": 100,
  "nullProportion": 0.5,
  "alternativeProportion": 0.6
}
Outcome
The tool calculates the effect size and outputs the statistical power, helping the analyst decide whether to increase the sample size before launching the test to reach the 80% power threshold.

Try with Samples

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Related Hubs

FAQ

What is statistical power?

Statistical power is the probability that a hypothesis test will correctly reject a false null hypothesis, effectively avoiding a Type II error.

What is considered a good statistical power level?

A common standard in many scientific and business fields is 0.80 (or 80%), meaning there is an 80% chance of detecting an effect if one genuinely exists.

How does sample size affect statistical power?

Generally, increasing the sample size increases statistical power, making it easier to detect a true effect because it reduces the standard error.

What is the difference between a one-sided and two-sided test?

A two-sided test checks for differences in both directions (greater or less than the null), while a one-sided test only looks for a difference in one specific direction.

Can I calculate power for proportions?

Yes, select 'Proportion Difference' as the test type and input your null and alternative proportions to calculate the power.

API Documentation

Request Endpoint

POST /en/api/tools/statistical-power-calculator

Request Parameters

Parameter Name Type Required Description
testType select No -
alternative select No -
alpha number No -
sampleSize number No -
nullMean number No -
alternativeMean number No -
standardDeviation number No -
nullProportion number No -
alternativeProportion 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-statistical-power-calculator": {
      "name": "statistical-power-calculator",
      "description": "Estimate statistical power for one-sample mean or proportion tests using sample size, alpha, and expected effect",
      "baseUrl": "https://elysiatools.com/mcp/sse?toolId=statistical-power-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]