Thanks to all who replied to my query, which was:
In the past, I have been asked by publishers to review three different proposals for introductory statistics textbooks which contained this idea. "We should not do t tests for samples with fewer than six observations but should always use rank methods." This is the reverse of my own view, as the Wilcoxon, Sign, Spearman, Kendall, and Mann-Whitney methods cannot produce two-tailed P values less than 0.05 for any data, all orderings arising in more than 5% of possible samples. I did not discover where this misleading idea came from, because none of these authors gave a reference and as it was confidential I could not ask them. Does anybody know of a published work which contains this idea?
Brian Faragher supplied the answer. He tells me that on page 32 of Sydney Siegel's widely used text on Nonparametric Statistics (which in my experience often has biblical properties attached to it), he states: "If sample sizes as small as N = 6 are used, there is no alternative to using a nonparametric statistical test unless the nature of the population distribution is known exactly" (Siegel puts the last two words in italics for emphasis). This would not be the first example of a statement being expanded and, in the process, having its exact meaning changed.
Adrian Baddeley provided a recent paper where the very same mistake is made.
M.B. Havnes, A. Mollerlokken and A.O. Brubakk The effect of two consecutive dives on bubble formation and endothelial function in rats. Diving and Hyperbaric Medicine 38 #1 (2008) 29-32
On page 30: "Nonparametric statistical methods were used due to the small number of animals in each group".
The study is a controlled experiment with 4 groups each containing 7 or 8 animals. They found no significant effects at 0.05.
He says that he practically choked on his coffee, seeing this paper only 10 minutes after reading my email to Allstat. Apologies for any adverse health effects of my words.
Thanks to everyone else who commented,
Martin
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J. Martin Bland
Prof. of Health Statistics
Dept. of Health Sciences
Seebohm Rowntree Building Area 2
University of York
Heslington
York YO10 5DD
Email: [log in to unmask]
Phone: 01904 321334 Fax: 01904 321382
Web site: http://martinbland.co.uk/
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--
***************************************************
J. Martin Bland
Prof. of Health Statistics
Dept. of Health Sciences
Seebohm Rowntree Building Area 2
University of York
Heslington
York YO10 5DD
Email: [log in to unmask]
Phone: 01904 321334 Fax: 01904 321382
Web site: http://martinbland.co.uk/
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