Data Analysis with Microsoft Excel: Updated for Office 2007

Chapter 10 Analysis of Variance 403

6 Click OK. Excel generates the output shown in Figure 10-9.

Figure 10-9

Pairwise

mean

difference

You can tell from the Pairwise Mean Difference table that the mean cost

for a single hotel room in Los Angeles is $27.25 less than the mean cost in

Chicago. The largest difference is between Denver and New York City, with

a single room in Denver hotels costing $300 less than a single room in New

York City hotels. Note that the output includes the mean squared error value

from the ANOVA table, 16,465.41, which is the estimate of the variance of

hotel prices.

Using the Bonferroni Correction Factor

You also requested in the dialog box a table of p values for these mean differ-

ences using the Bonferroni correction factor. Recall from Chapter 8 that the

Bonferroni procedure is a conservative method for calculating the probabili-

ties by multiplying the p value by the total number of comparisons. Because

the p values are much higher than you would see if you compared the cities

with t tests, it is harder to get signifi cant comparisons with the Bonferroni

procedure. However, the Bonferroni procedure has the advantage of giving

fewer false positives than t tests would give.

With the Bonferroni procedure, the chances of fi nding at least one signifi -

cant difference among the means is less than 5% if all of the four population

means are the same. On the other hand, if you do six t tests to compare the

four cities at the 5% level, there is much more than a 5% chance of get-

ting signifi cance in at least one of the six tests if all four population means