I am looking at someone else’s published data where they report treatment means and then a single standard error value across treatment means.
I want to know if certain treatments are significantly different from each other. For example, I’ve highlighted a comparison I am interested in in green.
I am thinking that I might be able to use the Tukey HSD test, but I am not sure because I am not sure how standard error is defined and used in the Tukey HSD.
I am looking at an example from the following textbook by Robert O. Kuehl: “Design of Experiments: Statistical Principles of Research Design and Analysis. 2nd Edition.”
In the example (p. 107-109), you calculate the HSD by multiplying the Studentized range statistic (q) by the standard error.
Here’s my confusion. On page 107 it says the standard error is “the standard error of a treatment mean” which, to me, evokes the idea of a unique standard error for each treatment mean calculated from that treatments individual replications.
That understanding of it doesn’t reconcile well with the idea that the HSD is going to be the same across treatments comparisons. On page 109 there’s an actual numeric example, and the standard error used is constant no matter what means are being compared. That suggests that the standard error is calculated from all the treatments, but I am not sure how.
What does the standard error used in the Tukey HSD calculation refer to and how is it calculated?
Also, is it safe to assume that the standard error reported in the table above (highlighted in blue) is the standard error you would use in a Tukey HSD calculation? There's no additional information in the text of the article further defining what is meant by SE in the table.