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I am looking to compare two post-hoc analyses, one with the SNK test and the other with the Tukey. I have read that the SNK test is stronger but more likely to commit type 1 errors than the Tukey. Here is my question: if the Tukey test reports a significant difference with p<.001 between two populations, is it safe to conclude that the SNK test would also have p<.001? I ask because I have the p-value only for the Tukey, not for the SNK.

Many thanks, Greg

Greg Markowsky
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  • Greg, you will find pages 93-98 of this book helpful: https://books.google.ca/books?id=s1u4AwAAQBAJ&printsec=frontcover#v=onepage&q=Keuls&f=false. In particular, page 98 advises to "choose the post-hoc test before you perform the analysis for sound statistical reasons." Pages 93-94 indicate that Newman-Keuls is safe to use when comparing up to and including three group means but may be problematic when used for comparing four or five group means. For this reason, Tukey HSD should always be used if there are five or more groups to compare. – Isabella Ghement Apr 28 '20 at 02:32
  • Tukey HSD is more conservative than Student Newman-Keuls and as such it is less powerful. The critical values for Tukey HSD remain the same for each comparison of means, regardless of the total number of means to be compare. HSD stands for honestly significant difference. Tukey's Wholly Significant Difference uses critical values that are the average of those used in Tukey HSD and Student Newman-Keuls, being intermediate in conservatism between the two. – Isabella Ghement Apr 28 '20 at 02:46
  • See page 165 of https://books.google.ca/books?id=a34z_Ah2-LgC&pg=PA165&lpg=PA165&dq=newman-keuls+is+less+stringent&source=bl&ots=UI_Wo1a-2C&sig=ACfU3U2niurArU5mUYhQcwq8WEU9D6gLXw&hl=en&sa=X&ved=2ahUKEwjJ-_iMi4rpAhWaHTQIHapbC0QQ6AEwCnoECAUQAQ#v=onepage&q=newman-keuls%20is%20less%20stringent&f=false – Isabella Ghement Apr 28 '20 at 02:46
  • Thanks for your help, although I'm not able to view that book, for some reason. It does sound like, from what is said there, that the SNK test always returns values less than the Tukey one, which is what I want to conclude. As it happens, there are 3 group means in the data I was looking at, so I think the SNK is still sound here. Thanks! – Greg Markowsky Apr 28 '20 at 03:58
  • Some people advise against using SNK altogether - as seen for instance here: https://www.graphpad.com/support/faq/why-we-recommend-you-do-not-use-the-newman-keuls-multiple-comparison-test/. – Isabella Ghement Apr 28 '20 at 14:22

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