A social psychologist wants to determine if type of music has any effect on the number of beers consumed by people in tavern. Four taverns are selected that have different musical formats. Five people are randomly sampled in each tavern and their beer consumption monitored for three hours.

Complete the following one-factor ANOVA summary table using α=.05

Source SS df MS F Critical Value and Decision-

Between _ 7.52 5.01 _

Within _ _

Total _ _

There are four taverns and 5 subjects observed within each of the taverns. Therefore the total number of observations is 20 and the total df is 20-1 = 19.

There are four taverns and so the Between df is 4 - 1 = 3.

The Within df can be found by subtraction: 19 - 3 = 16.

The Between MS = Between SS/ between df.

Therefore, the Between SS = 7.52 x 3 = 22.56.

The F ratio is Between MS/ Within MS

Therefore the Within MS = 7.52/5.01 = 1.50.

The Within MS = Within SS/ Within df.

Therefore, the Within SS = 1.50 x 16 = 24.00.

To compute the Total SS we simply add up the Between and Within SS to get

22.56 + 24.00 = 46.56.

That completes the ANOVA table -- now it's decision time.

The observed value of the F ratio is 5.01 and the degrees of freedom are 3 and 16 -- and we are using alpha = 0.05.

Looking up the F tables, we find that the critical value is 3.24.

As the observed value of the F test statistic (5.01) is larger than 3.24 the decision is to reject the Null Hypothesis that the mean beer consumption is the same in all four taverns. We conclude that the mean beer consumption is not the same in all four taverns.

Source SS df MS F Critical Value and Decision-

Between 22.56 3 7.52 5.01 3.24 Reject the null hypothesis.

Within 24.00 16 1.50

Total 46.56 19