Pooled Standard Deviation Calculator
Enter sample sizes and standard deviations for two groups to compute the pooled standard deviation.
Group 1
Group 2
Pooled standard deviation
10.0091
Degrees of freedom: 56
How to Use This Calculator
- Enter sample size and standard deviation for each group.
- Ensure sample sizes are at least 2 to avoid division by zero.
- Review the pooled standard deviation and degrees of freedom.
- Use pooled SD in two-sample t-tests or effect size calculations under equal-variance assumptions.
Formula
sp = √[((n₁ − 1)·SD₁² + (n₂ − 1)·SD₂²) / (n₁ + n₂ − 2)]
Degrees of freedom = n₁ + n₂ − 2
Pooled standard deviation assumes both groups estimate the same population variance.
Full Description
Pooled standard deviation combines variability of two samples when variances are assumed equal. It is used in independent t-tests, ANOVA, and effect size calculations such as Cohen's d.
If group variances differ significantly, consider Welch's t-test or separate variance estimates instead.
Frequently Asked Questions
What if one sample size is 1?
Pooled SD requires both sample sizes ≥ 2 to estimate variance. Otherwise, the calculation is invalid.
Does pooled SD assume equal means?
No. It assumes equal variances only. Means may differ.
How does pooled SD relate to t-tests?
It is used in the two-sample t-test when equal variances are assumed, forming part of the t-statistic denominator.
Can I pool more than two groups?
Yes, by extending the numerator and denominator across all groups. This calculator focuses on two-group pooling.