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Test Statistic for Hypothesis Tests Concerning Differences Between Variances of Two Normally Distributed Populations
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\(F = \frac{s^{2}_{1}}{s^{2}_{2}}\)

  • \(F\) - f-statistic
  • \(s^{2}\) - sample variance

The F-test concerning the equality or inequality of variances of two populations makes use of the F-distribution. Like the chi-square distribution, the F-distribution is a family of asymmetrical distributions bounded from below by 0. Each F-distribution is defined by two values of degrees of freedom, called the numerator and denominator degrees of freedom. While conducting the F-test, we have to compute the sample variances for both populations.

For the F-test, put the greater variance in the numerator and the lower one in the denominator!