Assuming there are three methods to kill bugs, and we want to know whether their performance differs. The Tukey's HSD test gives the following grouping results:

  trt means  M
1   1  1.96  a
2   3  1.88 ab
3   2  1.68  b

If we need suggest some methods to use, can we say method 1 and 3 can both be used as they are either better than or equal to method 2 (both have the grouping letter 'a')?

  • 1
    $\begingroup$ What is the actual scientific question here? What are you going to use the treatments for? $\endgroup$ – mdewey Aug 4 '17 at 15:23

You would not be able to say that.

Since treatment 3 shares a subscript with treatment 2, treatment 3 is not more than the expected standard error greater than treatment 2.

Basically, at an alpha of .05, we would expect a false positive 1 out of every 20 times we collect the data. Values that share a subscript mean this result would occur more than 1 out of every 20 times we collect the data.

You would be able to conclude, however, that treatment 1 is significantly greater than treatment 2.

| cite | improve this answer | |

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.