Use this calculation to reproduce a defined quantitative method when the observations, units, sampling process, and assumptions match the method shown here.

First sample variance

Required number.

First sample size

Required integer.

Second sample variance

Required number.

Second sample size

Required integer.

The cited overview of Statistics supplies background for the terminology and domain context used by this tool.^[1]

Calculate pooled sample standard deviation from two sample variances and sizes. Inputs are interpreted exactly in the displayed units and the calculation returns the following fields without presentation rounding.

Pooled standard deviation

Returned number.

• A numerical result does not by itself establish data quality, causation, representativeness, independence, distributional fit, or practical significance.
• First sample variance must be at least 0.
• First sample size must be at least 2.
• Second sample variance must be at least 0.
• Second sample size must be at least 2.
• Use finite inputs in the displayed units, preserve source measurements and assumptions, and independently verify consequential decisions.

Inspect the underlying data, visualize its distribution, report uncertainty and sample size, and compare the result with a robust or domain-specific method where appropriate.

• Pooled Variance Calculator

  Calculate pooled sample variance from two sample variances and sizes.

• Cohen's D Calculator

  Compute Cohen's d effect size between two independent samples using pooled standard deviation.

• Standard Error Calculator

  Calculate standard error from standard deviation and sample size.