Pooled Standard Deviation Calculator
Pooled standard deviation combines two sample variability estimates when a common population variance is an appropriate assumption.
How to use this calculator
- Enter each sample size and its sample standard deviation.
- Confirm that all inputs use the stated units and the same population, period or scope.
- Change one assumption at a time when comparing scenarios.
Formula used by the pooled standard deviation calculator
sₚ=√(((n₁−1)s₁²+(n₂−1)s₂²)/(n₁+n₂−2))
- sₚ=√(((n₁−1)s₁²+(n₂−1)s₂²)/(n₁+n₂−2))
- Equal-variance pooling is not appropriate for every comparison; inspect the study design and assumptions.
- Inputs are validated against required ranges and outputs are rounded for readability.
Worked examples
Worked example
Sample sizes 20 and 25 with standard deviations 4 and 5.
The result weights each variance by its sample degrees of freedom.
The result weights each variance by its sample degrees of freedom.
Understanding the result
Pooled standard deviation combines two sample variability estimates when a common population variance is an appropriate assumption.
Equal-variance pooling is not appropriate for every comparison; inspect the study design and assumptions.
Important notes
Equal-variance pooling is not appropriate for every comparison; inspect the study design and assumptions.
Use the result as a calculation aid for the inputs supplied; confirm critical specifications independently.
Frequently asked questions
Why pool standard deviations?
It combines within-group variation under a shared-variance model.
Can I use it if group variances differ greatly?
A pooled estimate may mislead; consider methods that do not assume equal variance.
How do I use this calculator?
Enter each sample size and its sample standard deviation.
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Related explanations
Learn the method behind the number or compare the terminology before using the calculator.
- How to Calculate Standard Deviation — Learn what standard deviation measures, the population and sample formulas, and how to interpret the result.
- How to Calculate a Z-Score — Learn how a z-score shows how far a value is from the mean in standard-deviation units.
- Standard Deviation — Understand standard deviation as a measure of spread and the difference between population and sample standard deviation.
This page provides a calculation tool plus explanatory information so you can understand what the result means and when the underlying method may not fit your situation.