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Sample Variance Calculator

The average of the squared deviations from the mean for a sample.

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Sample Variance

Formula first

Overview

Sample variance is a measure of the dispersion or spread of data points around the mean within a specific subset of a population. In psychological research, it serves as an unbiased estimator of population variance by incorporating Bessel's correction, which uses degrees of freedom instead of the total count.

Symbols

Variables

s^2 = Sample Variance, SS = Sum of Squares, n = Sample Size

Sample Variance
Sum of Squares
Sample Size

Apply it well

When To Use

When to use: Use sample variance when you are analyzing a subset of a larger population and need to estimate the degree of individual differences. It is a fundamental requirement for inferential statistics such as t-tests and ANOVA, assuming the data is measured on an interval or ratio scale.

Why it matters: It allows psychologists to quantify how much scores vary from the average, which is crucial for determining if experimental effects are significant or due to chance. By using n - 1, the formula corrects for the systematic underestimation of variability that occurs when only a small group is studied.

Avoid these traps

Common Mistakes

  • Using N instead of n-1 for samples.

One free problem

Practice Problem

A clinical psychologist measures the anxiety scores of 10 patients. The Sum of Squares (ss) for these scores is calculated to be 180. What is the sample variance for this group?

Sum of Squares180
Sample Size10

Solve for:

Hint: Divide the Sum of Squares by the degrees of freedom, which is the sample size minus one.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Wikipedia: Sample variance
  2. Discovering Statistics Using IBM SPSS Statistics by Andy Field
  3. Statistics for Psychology by Arthur Aron, Elaine N. Aron, and Elliot J. Coups
  4. Wikipedia: Variance
  5. Statistical Methods for Psychology (David C. Howell)
  6. Discovering Statistics Using R (Andy Field)
  7. Gravetter, F. J., & Wallnau, L. B. (2017). Statistics for the Behavioral Sciences (10th ed.). Cengage Learning.
  8. Howell, D. C. (2013). Statistical Methods for Psychology (8th ed.). Wadsworth Cengage Learning.