Pooled Variance - Statistics How To

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Statistics How To

Menu

• Home
• Tables
  • Binomial Distribution Table
  • F Table
  • Inverse T Distribution Table
  • PPMC Critical Values
  • T-Distribution Table (One Tail and Two-Tails)
  • Chi Squared Table (Right Tail)
  • Z-table (Right of Curve or Left)
• Probability and Statistics
  • Binomials
  • Chi-Square Statistic
  • Expected Value
  • Hypothesis Testing
  • Non Normal Distribution
  • Normal Distributions
  • Probability
  • Regression Analysis
  • Statistics Basics
  • T-Distribution
  • Multivariate Analysis & Independent Component
  • Sampling
• Calculators
  • Variance and Standard Deviation Calculator
  • Tdist Calculator
  • Permutation Calculator / Combination Calculator
  • Interquartile Range Calculator
  • Linear Regression Calculator
  • Expected Value Calculator
  • Binomial Distribution Calculator
• Matrices
• Experimental Design
• Calculus Based Statistics

Statistics Definitions >

Pooled variance (also called combined, composite, or overall variance) is a way to estimate common variance when you believe that different populations have the same variances.

The pooled sample variance formula is: Where:

• n = the sample size for the first sample,
• m = the sample size for the second sample,
• S2x = sample variance for sample 1,
• S2y = sample variance for sample 2.

It’s unlikely you’ll actually need to use the formula though. Most statistical software has an option for pooled variance, like R or SPSS. You can also try this online calculator for Pooling the Means, and Variances.

The square root of pooled variance is the pooled standard deviation.

When Can I Use Pooled Variance?

If you believe the population variances are the same, one way to check that you might be able to use pooled variance is to calculate a ratio of sample standard deviations: If this ratio is close to 1, then you can probably use pooled variance. This is a judgment call, but in general a ratio of 0.5 to 3 is a reasonable indication the variances are close enough (Penn State).

References

Penn State Eberly College of Science Department of Statistics. 7.3.1.1 – Pooled Variances. Retrieved February 25, 2020 from: https://online.stat.psu.edu/stat500/lesson/7/7.3/7.3.1/7.3.1.1

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