Van der Waerden Normal Scores Test

The Van der Waerden test compares k independent groups by replacing pooled ranks with normal scores and testing whether the group mean scores differ with a chi-square statistic.

Van der Waerden 검정은 합동 순위를 정규점수로 바꾸고 집단별 평균 점수의 차이를 카이제곱 통계량으로 검정해 k 개 독립 집단을 비교하는 방법입니다.

Is there a rank-based alternative to Kruskal-Wallis that keeps more power when my data are close to normal?

자료가 정규분포에 가까울 때 Kruskal-Wallis 보다 검정력이 더 좋은 순위 검정이 있나요?

Rank all observations together, convert each rank R to the normal score Phi^-1(R/(N + 1)) and compute T = (N - 1) sum n_j Abar_j^2 / sum A^2, which follows a chi-square distribution with k - 1 degrees of freedom. It tests the same hypothesis as Kruskal-Wallis but is more efficient for near-normal data.

When to use Van der Waerden Normal Scores Test

• You compare three or more independent groups and normality is doubtful.
• The data are roughly normal but you want protection against outliers.
• You want a rank test with efficiency close to one-way ANOVA.

When to use something else

• Observations are repeated on the same subjects; use the Friedman test instead.
• You need pairwise follow-up comparisons; this implementation reports only the omnibus test, so use Dunn's test for pairs.

Assumptions and requirements

• Independent observations.
• Continuous outcome; ties receive average ranks.
• Groups have similarly shaped distributions if the result is read as a location difference.

What the analysis reports

• T statistic with df = k - 1 and p-value
• Mean normal score and mean rank per group
• Group sizes and medians

How to report it

A Van der Waerden normal scores test indicated differences among the [value] groups, T([value]) = [value], p = [value], N = [value].

Related methods

• Kruskal-Wallis Test
• One-Way ANOVA
• Fligner-Killeen Test

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