4

I apologize for this easy/basic question. Please forgive me if this is a duplicate question.

I've been researching the Shapiro-Wilk test (1965) of normality for a project. In doing so, I found an article by Royston (1982), which allows for a sample size up to n=2000 (providing a way to calculate p-values up to n=2000).

Further research has now lead me to Shapiro-Francia (1972), which reads exactly like Royston's Extension. (I guess it read to me exactly like Royston's Extension.)

Can someone please explain the difference between the Shapiro-Wilk and Shapiro-Francia tests of Normality?

References
Royston, J. P. (1982). An extension of Shapiro and Wilk's W test for normality to large samples. Applied Statistics, 115-124.

Shapiro, S. S. and Francia, R. S. (1972). An approximate analysis of variance test for normality. Journal of the American Statistical Association, 67(1):215–216.

Shapiro, S. S. and Wilk, M. B. (1965). An analysis of variance test for normality (complete samples). Biometrika, 52(3 and 4):591–611.

Anthony
  • 1,564
  • 12
  • 24
Macromika
  • 141
  • 5
  • Can someone please add the tags: "Shapiro-Wilks" or "Shapiro-Francia"? Or "Test-for-Normality"? – Macromika Sep 26 '18 at 17:23
  • These are tests *of* not tests *for* normality: the null hypothesis is that the data are normally distributed. The tests provide evidence/fail to provide evidence that the data *are not* normally distributed. – Alexis Sep 26 '18 at 17:36
  • I apologize. The various articles I've been reading refer to the tests both ways: "tests OF Normality" and "tests FOR Normality". – Macromika Sep 26 '18 at 19:49
  • Frequentist hypothesis tests either reject or fail to reject a null, and they only provide evidence for, or fail to provide evidence for the alternate. And no apology needed! :) – Alexis Sep 26 '18 at 20:09

0 Answers0