Test for Equality of Coefficients of Variation

The Feltz-Miller test checks whether k groups share the same coefficient of variation using an asymptotic chi-square statistic built from the deviations of each group CV from the pooled CV.

Feltz-Miller 검정은 집단별 변동계수가 합동 변동계수에서 벗어난 정도로 만든 점근 카이제곱 통계량으로 k 집단의 변동계수가 같은지 검정하는 방법입니다.

Two assays have very different means; is one relatively more variable than the other once scale is taken into account?

두 분석법의 평균이 크게 다른데, 규모를 감안하면 한쪽이 상대적으로 더 들쭉날쭉한가요?

Compute each group's coefficient of variation, pool them weighted by n - 1 and compare the weighted squared deviations with a chi-square distribution on k - 1 degrees of freedom. A small p indicates that relative variability differs between groups.

When to use Test for Equality of Coefficients of Variation

• Groups have different means and you want to compare relative rather than absolute variability.
• The outcome is on a positive ratio scale, such as concentrations or durations.
• Each group has a reasonable sample size (about 10 or more).

When to use something else

• You want to compare absolute variances; use Levene's or Bartlett's test instead.
• Values can be negative or the mean is near zero, which makes the CV unstable; compare variances on a log scale instead.

Assumptions and requirements

• Independent samples from approximately normal populations.
• Positive values with positive group means.
• Large enough samples for the asymptotic chi-square.

What the analysis reports

• Feltz-Miller statistic D'AD with df = k - 1 and p-value
• Pooled coefficient of variation
• Group n, mean, SD and CV

How to report it

The Feltz-Miller test indicated that the coefficients of variation differed across the [value] groups, chi-square([value]) = [value], p = [value] (pooled CV = [value]).

Related methods

• Levene's Test
• Bartlett's Test
• F Test for Equality of Two Variances

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