# Interpreting a Tukey - Kramer Confidence Interval Plot

In order to see if any statistically significant differences in the means of 4 particular diets exist, a post-hoc test is conducted i.e. Tukey – Kramer.

Could someone please explain to me the plot which is attached below?

Note: Tukey - Kramer is being used here as there is not equal observations between diets. • What don't you understand? – user2974951 Feb 15 '19 at 10:28
• The plot in general. I'm unsure about how to interpret it. – asasas Feb 15 '19 at 10:30

There are 4 diets - which gives 6 possible pairwise comparisons between them: 1-2, 1-3, 1-4, 2-3, 2-4, and 3-4 (2-1 would be the same as 1-2, so we don't count it twice).

The plot has all these comparisons displayed at different heights with the label on the left y axis side.

The x-axis represent the mean differences that were found between those pairs. So for example the comparison 2-1 had a mean difference of 20.

The extended lines show the 95% confidence intervals. In this case if the confidence interval crosses the 0 point - the difference would not be statistically significant. In the plot colors seem to indicate this significance: red lines do not cross the 0 so the differences in their means were found to be statistically significant.

Based on this we could reason that diet No. 1 was different from the rest as all the pairwise comparisons that included diet 1 were statistically significant (red in the plot) while all the other comparisons were not.

On the y-axis you have all the tested contrasts, that is 2 vs 1, 3 vs 1, ... 4 vs 2. On the x-axis you have the mean differences (the points) for that particular contrast. The lines represent the 95 % confidence interval.

So for ex. the contrast on the bottom, 2 vs 1, says that there is a mean difference of 20 between 2 and 1, and the 95 % CI is in the range of 0 to 40.