This problem is designed to help you see the effect of outliers can have on an ANOVA test.

Students enrolled in developmental mathematics classes at a community college are encouraged to go to the Math Tutoring Center (MTC) for help with their homework.  Some students schedule their time so that they go once or twice a week to focus on all of their math homework at once.  Some students even start forming study groups and meet at the MTC to work together.  The staff that run the MTC want to know if some classes are using their services more than others.  They collect data from 4 classes and 18 students per class that attend the session at least once in the term.  The dependent variable is the number of days a student visits the MTC during one academic term (about 12-13 weeks).

Group 1	Group 2	Group 3	Group 4
13	10	13	13
7	12	9	15
8	9	12	11
10	6	10	12
13	11	10	8
11	12	7	12
9	43	4	14
13	38	13	10
11	9	8	12
10	13	11	9
12	7	12	10
12	8	8	10
11	41	7	9
9	12	11	15
11	13	11	8
13	14	10	14
11	8	6	6
13	13	12	10

Conduct the one-factor fixed effect ANOVA with the data.  Report the requested sample statistics:
$\displaystyle {M}{S}_{{\text{between}}}=$
    (report answer accurate to 3 decimal places)
F-ratio =
    (report answer accurate to 3 decimal places)
P-value =     (report answer accurate to 4 decimal places)
What is the conclusion about groups, on average, using the MTC to equal amounts ($\displaystyle \alpha={0.05}$)?

As always, be sure to examine the data to confirm the assumptions.  In particular, check to see which groups (if any) have outliers.  From SPSS, you can use Graphs > Legacy Dialogs > Boxplot... > Simple > ... From this, which groups (if any) appear to have extreme outliers?

For any group with extreme outliers, delete these values and rerun the ANOVA.  Report the requested new sample statistics:
$\displaystyle {M}{S}_{{\text{between}}}=$
    (report answer accurate to 3 decimal places)
F-ratio =
    (report answer accurate to 3 decimal places)
P-value =     (report answer accurate to 4 decimal places)
What is the conclusion about groups, on average, using the MTC to equal amounts ($\displaystyle \alpha={0.05}$)?

Thought for reflection:  What values (statistics, results, or information from the ANOVA summary table) changed most noticeably with the inclusion of the outliers?

Do the presence of the outliers (if any) change how the MTC should interpret this data?