Comparing more than two means: one factor ANOVA with independent samples. Multiple comparison testing with the Newman-Keuls test - Improving the User Experience through Practical Data Analytics - page 161

Also in this chapter, we have introduced the concept of multiple comparison test-
ing to determine when there are more than two means (e.g., designs, tasks, age-
groups, etc.) being compared, which means are different or the same as other means.
A multiple comparison test is typically analyzed after performing an ANOVA, and
when the F-test is signiicant. In this chapter, the ANOVA was a one-factor ANOVA.
In a subsequent chapter, we will discuss applying an ANOVA when two factors are
involved.
We also introduced the Newman-Keuls test, sometimes called the S-N-K test, as
the authors' choice of the best of several choices of multiple comparison tests. We
illustrated it using SPSS (basic Excel does not have the capability to perform the
S-N-K test) and discussed the results.
6.11 EXERCISES
1. Consider the case of the time it takes to perform a task and testing whether
the true average time it takes for each of four tasks (T1, T2, T3, and T4) is the
same. Each person performs only one of the four tasks, so that we have inde-
pendent samples. Data for the times for each task are in data iles in Excel (ile
name: Chapter 6.Exercise 1.data) and SPSS (ile name: Chapter 6..Exercise
1.data). The output in Excel is on sheet 2. In SPSS the output is in a ile (ile
name: Chapter 6..Exercise 1.output). All iles are on a Web site indicated in the
preface to the text.
Perform an ANOVA to test whether the (true) average times for the four tasks
are equal or not.
A Word ile (ile name: Chapter 6.Exercise 1.discussion) is also provided,
which discusses the results.
2. For the data in the SPSS ile, Chapter 6..Exercise 2.data, perform a Newman-
Keuls (S-N-K) test to examine what the differences are among the averages of
the four columns. The output will be in an SPSS ile named Chapter 6..Exercise
2.output. A discussion of the results will be in a Word ile called Chapter 6.
Exercise 2.discussion.
REFERENCES
Berger, Paul D., Maurer, Robert E., 2002. Experimental Design: With Applications in
Management, Engineering and the Sciences, second ed. Duxbury Press, Paciic Grove, CA.
Tversky, Amos, Kahneman, Daniel, 1974. Judgment under uncertainty: heuristics and biases.
Science 185 (4157), 1124-1131.