Newman Keuls Test

TL;DR

A post-hoc method for comparing group means after a significant one-way or two-way ANOVA.
Performs pairwise comparisons to identify which group means differ.
Considered conservative: lower risk of Type I error but higher risk of Type II error and may be less powerful than Tukey or Bonferroni tests.

Definition

The Newman-Keuls test is a statistical procedure used to determine significant differences between means in a one-way or two-way analysis of variance (ANOVA). It is a post-hoc test, meaning it is used to make comparisons after the initial ANOVA has been conducted.

Explanation

After an ANOVA indicates that not all group means are equal, the Newman-Keuls test performs pairwise comparisons among group means to determine which specific means differ significantly. It can be applied following either one-way or two-way ANOVA. The test is described in the source as conservative: it has a lower risk of committing a Type I error (falsely rejecting the null hypothesis) and a higher risk of committing a Type II error (failing to reject the null hypothesis when it should be rejected). Because of this conservativeness, the Newman-Keuls test may be less powerful for detecting significant differences than other post-hoc tests such as the Tukey or Bonferroni tests.

Examples

Comparing test scores across three groups

One example is comparing the average scores of three different groups on a test. Group A consists of students who received extra tutoring, group B consists of students who received no extra help, and group C consists of students who received a different type of assistance. After administering the test, the mean scores for each group are calculated. The ANOVA is conducted to determine if there are significant differences between the means of the three groups. If the ANOVA shows that there are significant differences, the Newman-Keuls test can be used to determine which groups differ significantly from one another.

In this example, the Newman-Keuls test would compare the mean scores of group A to group B, group A to group C, and group B to group C. If the mean score for group A is significantly higher than the mean score for group B, it can be concluded that the extra tutoring provided to group A had a positive impact on their test scores. If the mean score for group C is significantly higher than the mean score for group B, it can be concluded that the type of assistance provided to group C had a positive impact on their test scores.

Comparing two therapies for anxiety

Another example is comparing the effectiveness of two different types of therapy in reducing anxiety in a group of individuals. Group A receives therapy type A, while group B receives therapy type B. After the therapy sessions are completed, the levels of anxiety are measured and the mean scores for each group are calculated. The ANOVA is conducted to determine if there are significant differences between the means of the two groups. If the ANOVA shows that there are significant differences, the Newman-Keuls test can be used to determine which group had a significantly lower level of anxiety.

In this example, the Newman-Keuls test would compare the mean anxiety scores of group A to group B. If the mean anxiety score for group A is significantly lower than the mean anxiety score for group B, it can be concluded that therapy type A was more effective in reducing anxiety levels.

Use cases

Making pairwise comparisons of group means after a one-way or two-way ANOVA.
Applied to situations such as comparing test scores or assessing the effectiveness of different therapies.

Notes or pitfalls

Considered conservative: lower risk of Type I error but higher risk of Type II error.
May be less powerful at detecting differences compared to other post-hoc tests such as Tukey or Bonferroni.

Analysis of variance (ANOVA)
Post-hoc test
Tukey test
Bonferroni test
Type I error
Type II error