Pooled Standard Deviation Calculator

Your details

How many samples or groups you are combining.
Number of observations in group 1. Must be at least 2.
Sample standard deviation of group 1.
Number of observations in group 2. Must be at least 2.
Sample standard deviation of group 2.
Pooled standard deviation (Sp)
5.5169

Weighted average spread across all groups

Pooled variance (Sp²)30.4364
Degrees of freedom25
Total sample size (N)27
Pooled SD5.5169
Pooled Variance30.4364

Pooled SD = 5.5169 across 2 groups (N = 27)

  • The pooled standard deviation Sp = 5.5169 combines 2 groups with a total of 27 observations.
  • Individual group SDs range from 4.5000 to 6.2000. The pooled SD falls within this range, weighted by each group's degrees of freedom.
  • The pooled variance Sp² = 30.4364 and the total degrees of freedom = 25. These feed directly into two-sample or one-way ANOVA tests that assume equal variances.
  • Before pooling, verify the equal-variance assumption with Levene's test or an F-test. Pooling SDs from groups with very different spreads can produce a misleading combined estimate.

Next stepUse Sp in the standard error formula for a two-sample t-test: SE = Sp x sqrt(1/n1 + 1/n2), or as the error standard deviation in one-way ANOVA.

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