# How to do Pairwise Comparisons in R? | R-bloggers

- Updated on: 2023-01-04
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How to do Pairwise Comparisons in R, To evaluate if there is a statistically significant difference between the means of three or more independent groups, a one-way ANOVA is utilized.

The following null and alternate hypotheses are used in a one-way ANOVA.

We reject the null hypothesis and come to the conclusion that not all of the group means are equal if the overall p-value of the ANOVA is less than a predetermined significance level (for example, =.05.

We can next conduct post hoc pairwise comparisons to determine which group means are different.

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Consider a teacher who is curious about whether or not the use of three different study methods affects pupils’ exam results.

She distributes ten students to each study method at random in order to test this, then she tracks their exam results.

To conduct a one-way ANOVA in R and check for variations in the mean exam scores among the three groups, use the following code:

Now we can perform one-way ANOVA

We will reject the null hypothesis that the mean exam score is the same for each studying method because the overall p-value of the ANOVA (.00626) is less than =.05.

We can now conduct posthoc pairwise comparisons to identify the groups with various means.

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When the sample sizes of each group are equal, the Tukey posthoc method performs the best.

The built-in TukeyHSD() function in R can be used to implement the Tukey posthoc method:

From the output, we can see that the only p-value (“p adj“) less than 0.05 those pairs are significantly different from each other.

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When comparing group means, the Scheffe technique yields the largest confidence intervals and is the most conservative posthoc pairwise comparison method.

To implement the Scheffe post-hoc approach in R, use the ScheffeTest() function from the DescTools package:

Now ready to perform the Scheffe post-hoc method

From the output we can see that the only p-value (“p adj“) less than 0.05 those pairs are significantly different from each other.

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When you want to make a set of pre-planned pairwise comparisons, the Bonferroni method is the best to apply.

To use the Bonferroni post-hoc procedure, we can use the R syntax shown below:

When you want to make a set of planned pairwise comparisons in advance, you can also use the Holm technique because it frequently has even higher power than the Bonferroni approach.

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The Holm post-hoc approach can be used in R using the syntax shown below:

Holm post-hoc approach should be used.

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