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
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.
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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.