# How do you write up Tukey post-hoc findings?

What is the proper way to write a Tukey post-hoc result?

There are several examples with different results?

Say you have North, South, East and West.

North N=50 Mean=2.45  SD=3.9 std error=.577 LB=1.29 UB=3.62
South N=40 Mean=2.54  SD=3.8 std error=.576 LB=1.29 UB=3.63
East  N=55 Mean=3.45  SD=3.7 std error=.575 LB=1.29 UB=3.64
West  N=45 Mean=3.54  SD=3.6 std error=.574 LB=1.29 UB=3.65


North is statistically significant with East (sig=.009) and West(sig= .040) but not South (sig=.450). East is statistically significant with South(.049).

• Did you get homogenous subsets? Personally, I think that's the easiest way to report true differentiation of means by a measure (in your case, region). It's also "client friendly" if letters are the same means are the same. – Brandon Bertelsen Sep 2 '11 at 0:30
• yes, the groups were similar – Sue Sep 2 '11 at 0:36
• Just so we're clear if one subset contains any letter of the next or previous subset there are no real differences in mean. – Brandon Bertelsen Sep 2 '11 at 0:38

### General strategy of article deconstruction

A general strategy for learning how to write up results involves finding and deconstructing an example publication. I like to call this article deconstruction. A simple way of doing this involves searching Google Scholar to find a few examples. You may want to limit your search to good journals in your area (e.g., "tukey post hoc social psychology"). Then extract a few writing principles.

### Example write up of post-hoc test

Here's one example of a write-up of a post-hoc test from a social psychology context:

The article includes a table of means and standard deviations for each condition for a set of dependent variables. In the text it has the following:

An analysis of variance (ANOVA) on these scores again yielded significant variation among conditions, F(2, 37) = 4.29, p < .03. A post hoc Tukey test showed that the future alone and future belonging groups differed significantly at p < .05; the misfortune control group was not significantly different from the other two groups, lying somewhere in the middle.

--- Baumeister RF, Twenge JM, Nuss CK. (2002). Effects of social exclusion on cognitive processes: anticipated aloneness reduces intelligent thought. Journal of Personality and Social Psychology, 83, 817-27.

### Extract writing principles

• Present a table of means and standard deviations
• First report overall ANOVA
• Then report which pairs were significantly different at a given alpha level
• Then report which pairs were not significantly different.

Of course, a post-hoc test could be written up in other ways; for example, you could use a graph of means rather than a table; or you could incorporate post-hoc test results into a table using the $a \le b<c$ style notation ($a,b,c,...$ correspond to groups); but at least by taking a good example, you have a starting point.

It's a tough one to visualize, especially considering the potential audience. But you should also show the homogenous subsets so it's easy to identify those elements that are truly differentiated from each other. Depending on the audience, I don't even bother showing SE or L/U B nor p-values. I had to cut the row labels from the left hand because it's real data, but you can see the presentation below:

Plotting the subsets helps the user "see" which means are truely different from each other. Depending on your audience, adding a p-value could also be useful.

• Oh, I just realized that you said "write" not "report". My bad. – Brandon Bertelsen Sep 2 '11 at 0:42
• Thanks, I think that I am just going to use the p-value. – Sue Sep 2 '11 at 0:54