Commentaries: Use of the correlation coefficient with normal probability plots

Stephen W. Looney, Thomas R. Gulledge

Research output: Contribution to journalComment/debatepeer-review

136 Scopus citations


The use of the correlation coefficient is suggested as a technique for summarizing and objectively evaluating the information contained in probability plots. Goodness-of-fit tests are constructed using this technique for several commonly used plotting positions for the normal distribution. Empirical sampling methods are used to construct the null distribution for these tests, which are then compared on the basis of power against certain nonnormal alternatives. Commonly used regression tests of fit are also included in the comparisons. The results indicate that use of the plotting position pi = (i – .375)/(n + .25) yields a competitive regression test of fit for normality.

Original languageEnglish (US)
Pages (from-to)75-79
Number of pages5
JournalAmerican Statistician
Issue number1
StatePublished - Feb 1985
Externally publishedYes


  • Empirical power comparison
  • Filliben test
  • Plotting position
  • Regression tests of fit
  • Shapiro-Francia test
  • Shapiro-Wilk test

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty


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