Pooled standard deviation calculator
Combine the variability of two independent groups by weighting their variances by degrees of freedom.
How do I use this page?
- Paste at least two observations in each group.
- Compare the two group standard deviations.
- Read sₚ and the degrees of freedom.
What this page does not do: The calculation assumes independent samples and a defensible common variance. Paired data or clearly unequal variances require a method suited to that design.
Further reading
Theory — how is pooled standard deviation calculated?
Pooled standard deviation estimates the shared spread of two independent populations from two separate samples. Each variance enters the calculation weighted by its degrees of freedom, n−1, so a larger sample has a stronger influence on the final result. The square root is taken only after the weighted variances have been combined; simply averaging two standard deviations is not valid. The measure is used, among other things, in the classic two-sample t-test.
Frequently asked questions
Can I average the two standard deviations?
Must the groups have equal size?
See also
A/B test calculator
Compare two proportions in an A/B test. Calculate conversion rates, difference, uplift, z score, p value and c
A/B test planning — sample size, MDE and duration
Plan a two-proportion experiment, estimate detectable effect and traffic duration.
ACF and PACF autocorrelation calculator
Calculate ACF and PACF across time-series lags. Review the chart, reference bounds and coefficient table.