F Test for Equality of Two Variances

The F test for equality of two variances compares the ratio of two independent sample variances with an F distribution to test whether two normal populations have the same variance.

두 분산의 동일성 F 검정은 두 독립 표본분산의 비를 F 분포와 비교해, 두 정규 모집단의 분산이 같은지 검정한다.

How do I test whether two groups have the same variance?

두 집단의 분산이 같은지 어떻게 검정하나요?

The F test divides the variance of the first sample by that of the second and refers the ratio to an F distribution with n1 − 1 and n2 − 1 degrees of freedom. It also yields a confidence interval for the ratio of population variances, but it is very sensitive to non-normality.

When to use F Test for Equality of Two Variances

• Two independent samples are compared on spread.
• The outcome is approximately normally distributed in both groups.
• A confidence interval for the variance ratio is needed, for example in measurement precision studies.

When to use something else

• The data are skewed or contain outliers; use Levene's test or the Fligner-Killeen test.
• More than two groups are compared; use Bartlett's test or Levene's test.

Assumptions and requirements

• Both samples are independent random samples.
• The outcome is normally distributed in each population.

What the analysis reports

• F ratio
• Numerator and denominator degrees of freedom
• Two-sided p value
• Confidence interval for the variance ratio
• Group variances

How to report it

An F test indicated that the variance of group 1 (s² = [var1]) differed from that of group 2 (s² = [var2]), F([df1], [df2]) = [F], p = [p], 95% CI [[lower], [upper]].

Related methods

• Levene's Test
• Fligner-Killeen Test
• Bartlett's Test

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