Ansari-Bradley Test

The Ansari-Bradley test is a rank-based test of whether two groups with a common median differ in dispersion, scoring observations by their distance from the ends of the pooled ordering.

Ansari-Bradley 검정은 중앙값이 같은 두 집단의 퍼짐(척도)이 다른지를 합친 자료의 양 끝에서 센 순위 점수로 검정하는 비모수 방법이다.

How can I test whether two groups differ in spread when the data are not normal?

정규분포가 아닌 두 집단의 퍼짐 정도가 다른지 어떻게 검정하나요?

The Ansari-Bradley test assigns each pooled observation a score equal to its smaller rank counted from either end and sums the scores for one group; a small sum means that group is concentrated in the tails. It uses an exact distribution for small samples without ties and a tie-corrected normal approximation otherwise.

When to use Ansari-Bradley Test

• You want to compare the spread of two independent groups.
• The data are not normally distributed.
• The two groups have similar medians.

When to use something else

• The medians differ noticeably; use the Fligner-Killeen or Brown-Forsythe test, or center each group first.
• More than two groups are compared; use the Fligner-Killeen test instead.

Assumptions and requirements

• Observations are independent.
• The two distributions have the same median and differ only in scale.
• The outcome is continuous so ties are rare.

What the analysis reports

• AB statistic
• Exact or normal-approximation p-value
• Group medians, IQRs and SDs
• Ratio of standard deviations

How to report it

An Ansari-Bradley test indicated that dispersion [differed/did not differ] between [group 1] (n = [value]) and [group 2] (n = [value]), AB = [value], p = [value].

Related methods

• Levene's Test
• Fligner-Killeen Test
• F Test for Equality of Two Variances

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