Statistics & Probability

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Pooled Standard Deviation Calculator.

Calculate the equal-variance pooled standard deviation for two independent samples.

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pooledStandardDeviation: 9.535023

pooledStandardDeviation

9.535023
degreesOfFreedom: 36

degreesOfFreedom

36.000000

Uses the unbiased pooled estimator with two entered sample SDs and sample sizes n₁,n₂ ≥ 2; equal-variance suitability is not tested.

Results update automatically as you type.

Use Cases

Combine variability from two groups

When you have two independent samples with similar variances, the pooled standard deviation provides a single measure of variability for the combined data, useful for further statistical analysis.

Example: Comparing test scores from two classes to get an overall standard deviation.

Prepare for t-test calculations

The pooled standard deviation is a key component in the two-sample t-test formula when assuming equal variances, helping to determine if group means differ significantly.

Example: Calculating the t-statistic for a clinical trial comparing two treatments.

Frequently Asked Questions

What is the pooled standard deviation?
The pooled standard deviation is a single estimate of the common standard deviation of two independent samples, assuming they have equal population variances. It combines the sample standard deviations (s₁ and s₂) weighted by their sample sizes (n₁ and n₂).
How is the pooled standard deviation calculated?
The formula uses the sample standard deviations and sizes: sqrt(((n₁-1)*s₁² + (n₂-1)*s₂²) / (n₁ + n₂ - 2)). This gives a weighted average of the variances, then takes the square root.
When should I use the pooled standard deviation?
Use it when comparing two independent samples and you assume they come from populations with equal variances. It's commonly used in t-tests and ANOVA to estimate the common standard deviation.

Tips & Common Mistakes

Tips

  • Ensure your sample standard deviations are calculated from the same units to get a meaningful pooled result.
  • The pooled standard deviation is only appropriate when the two samples have similar variances; check with an F-test if unsure.
  • Use the sample sizes (n₁ and n₂) as the number of observations in each group, not the degrees of freedom.
  • Double-check that your sample sizes are at least 2, as the formula requires n-1 in the numerator.

Common Mistakes to Avoid

  • Using the population standard deviation formula instead of the sample standard deviation (dividing by n instead of n-1).
  • Forgetting to square the standard deviations before weighting them by sample sizes.
  • Assuming the pooled standard deviation is the simple average of the two standard deviations, which is incorrect.

Last updated: August 13, 2026