Though not a favorite example, this problem is based on the sample demonstration problem used in the book.  The dependent variable is the number of times a student attends the statistics lab during one academic term.  The independent variable is the attractiveness of the lab instructor, with 1 for unattractive (ouch), 2 for slightly attractive, 3 for moderately attractive, and 4 for very attractive.  The researcher is exploring whether the attractiveness of the instructor influences student attendance at the statistics lab.  Students were randomly assigned to different groups at the start of the term.  There were 11 students in each group, and students could attend a maximum of 28 lab sessions.

Group 1: Unattractive	Group 2: Slightly	Group 3: Moderately	Group 4: Very Attractive
12	27	28	26
12	18	20	25
18	28	14	18
14	19	16	22
9	18	20	16
18	21	21	19
9	20	22	19
18	11	20	21
16	16	13	23
14	13	16	20
23	16	24	14

A 1-way fixed-effects ANOVA was run resulting in a statistically significant omnibus test:  $\displaystyle {F}={3.294}$, $\displaystyle {p}={0.0301}$.  The researcher planned specific contrasts for this study.  In particular, the main goal was to compare all groups to the very attractive (reference) group.  As such, the plan is to use Dunnett’s Method.  To assist in the calculations, the error variance from the ANOVA table was $\displaystyle {M}{S}_{{\text{within}}}={19.604545}$, and the sample means for each group are presented in the table below.

Level	Mean
Group 1: Unattractive	14.818
Group 2: Slightly	18.818
Group 3: Moderately	19.455
Group 4: Very Attractive	20.273

First, as this is a balanced design, the standard error for all of the contrasts will be the same (report to 3 decimal places):
$\displaystyle {s}_{\psi}=$

Using a significance level of $\displaystyle \alpha_{{\text{fw}}}={0.01}$, find the critical value from the table in the back of the book:
$\displaystyle {t}_{{\text{c.v.}}}=\pm$

Next, calculate the contrast for each comparison (report to 3 decimal places):
$\displaystyle \psi_{{{14}}}=$
$\displaystyle \psi_{{{24}}}=$
$\displaystyle \psi_{{{34}}}=$
With the contrasts, calculate the t-ratio for each contrast (report to 2 decimal places):
$\displaystyle {t}_{{{14}}}=$
$\displaystyle {t}_{{{24}}}=$
$\displaystyle {t}_{{{34}}}=$

Using the critical value and the t-ratios, which groups are statistically significantly different?