Tukey’s Honest Significant Difference (HSD) test is a post hoc test commonly used to assess the significance of differences between pairs of group means. Tukey HSD is often a follow up to one-way ANOVA, when the F-test has revealed the existence of a significant difference between some of the tested groups. Running the test in R involves using the function TukeyHSD() which does not require any additional package installation.

The null hypothesis H0 for the test states that the means of the tested groups are equal.

We will reuse the example introduced here (one-way ANOVA). To create the corresponding dataframe, use the following code:

# response variable
size <- c(25,22,28,24,26,24,22,21,23,25,26,30,25,24,21,27,28,23,25,24,20,22,24,23,22,24,20,19,21,22)

# predictor variable
location <- as.factor(c(rep("ForestA",10), rep("ForestB",10), rep("ForestC",10)))

# dataframe
my.dataframe <- data.frame(size,location)


The assumptions are:

NB: these are indeed the same assumptions as for one-way ANOVA; in other words, if you were allowed (or if you allowed yourself) to conduct an ANOVA test, then it is ok to run Tukey’s test.

Running the test with TukeyHSD()

The syntax is TukeyHSD(aov(response ~ predictor), conf.level) where response is the response variable, predictor is the predictor variable, and conf.level is the confidence level that you want to define (usually fixed at 0.95). Let’s apply it to our example:

TukeyHSD(aov(size ~ location), conf.level=0.95)
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## Fit: aov(formula = size ~ location)
## $location
##                 diff       lwr         upr     p adj
## ForestB-ForestA  1.3 -1.097245  3.69724537 0.3835917
## ForestC-ForestA -2.3 -4.697245  0.09724537 0.0619108
## ForestC-ForestB -3.6 -5.997245 -1.20275463 0.0025530

The output displays the results of all pairwise comparisons among the tested groups (here three groups: ForestA, ForestB and ForestC, thus 3 comparisons). You’ll find the actual difference between the means under diff and the adjusted p-value (p adj) for each pairwise comparison. Looking at the last column, the only significant difference to be reported in the present test is between the means of the groups ForestB and ForestC.