# Multiple Comparisons

## David C. Howell

The material in the section on the one-way analysis of variance generally offers good opportunities to look at multiple comparison techniques at the same time.

• I was asked a question about unequal sample sizes with multiple comparisons, and could not help writing a new web page. Most of that material is in the text, but it presented slightly differently here. The link is Unequal n's and mult. comp.
• A common question concerns the use of multiple comparison techniques when the variable in question is a repeated measures variable. I have addressed this problem in Multiple Comparison Procedures with Repeated Measures. I argue that in most cases you do not want something like a traditional Tukey test, although it is possible to accomplish that if it is really necessary.
• The Sethi & Seligman (1993) paper on optimism and religious fundamentalism involves both a one-way analysis of variance and multiple comparisons.
• Foa, Rothbaum, Riggs, & Murdock (1991) have investigated treatment of post traumatic stress disorder in rape cases, and their data illustrate several things about one-way analysis of variance.
• The example on the sampling distribution of F  allows you to change the means of the populations (and especially the spacing of those means within the range from lowest to highest) and note the effects on multiple comparison tests.
• An example of multiple comparison procedures with unequal n's and unequal variances can be found at SmokingPreg.html. It is based on a study by Solomon, Secker-Walker, Skelly, and Flynn (1996) on reducing smoking in pregnant women. It involves substantial hand calculation.
• An interesting example of a trend analysis is based on a modification of a study by Nolen-Hoeksema and Morrow (1991), and looks at stress as a function of time after a major earthquake.
• A great example about the practical implications of power analysis can be found at Utts-Salaries.html. Utts presents an example of a situation where, because of low power, an nonsignificant difference can still be important. I think that this example has something to say about multiple comparisons, but not necessarily in the way that we usually discuss such comparisons.

Send mail to: David.Howell@uvm.edu)

Last revised: 05/19/03