A professor has a class with four recitation sections.Each section has 11 students (rare, but there are exactly the same number in each class...how convenient for our purposes, yes?).At first glance, the professor has no reason to assume that these exam scores from the first test would not be independent and normally distributed with equal variance.However, the question is whether or not the section choice (different TAs and different days of the week) has any relationship with how students performed on the test.

Group-1Group-2Group-3Group-493.681.847.5857887.163.179.470.877.572.173.883.287.371.8819099.268.482.778.88085.451.478.39388.392.983.690.267.684.298.777.265.686.88979.672.580.188.982.882.795.8

First, run an ANOVA with this data and fill in the summary table.(ReportP-values accurate to 4 decimal places and all other values accurate to 3 decimal places.

SourceSSdfMSF-ratioP-valueBetweenWithin

To follow-up, the professor decides to use the Tukey-Kramer method to test all possible pairwise contrasts.

What is the Q critical value for the Tukey-Kramer critical range (alpha=0.01)?

Use the website link in your notes (http://davidmlane.com/hyperstat/sr_table.html) to locate the Q critical value to 4 decimal places.

Q =

Using the critical value above, compute the critical range and then determine which pairwise comparisons are statistically significant?

• group 1 vs. group 2
• group 1 vs. group 3
• group 1 vs. group 4
• group 2 vs. group 3
• group 2 vs. group 4
• group 3 vs. group 4
• none of the groups are statistically significantly different

List of: 3.340491405927 , 4.5703855590805 , 4.6569107758852 , 1.2298941531535 , 1.3164193699583 , 0.086525216804767