The F statistic in the two-way layout with rank–score transformed data

Stephen C. Hora, W. J. Conover

Research output: Contribution to journalArticlepeer-review

75 Scopus citations


The limiting null distribution of the usual F statistic for main effects in the two-way layout is shown to have the same limiting distribution when applied to ranks and scores based on ranks as when applied to normal data. The limit is taken as the cell size N increases without bound. The denominator of the F statistic times (J − 1)/J is shown to provide an unbiased and consistent estimator of the limit (as N → ∞) of N−1 times the variance of the treatment sum of scores when the null hypothesis is true. The test based on the scores statistic is demonstrated to be consistent for a wide class of fixed alternative hypotheses.

Original languageEnglish
Pages (from-to)668-673
Number of pages6
JournalJournal of the American Statistical Association
Issue number387
StatePublished - Sep 1984


  • Analysis of variance
  • Rank statistics
  • Rank transform
  • Scores


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