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Chapter 10: Pairing Things Down with Multiple Comparisons
You could help lower the error rate for Fisher’s test if you lower the value of
α for each test from 0.05 to, say, 0.01. However, doing so makes it harder to
reject Ho for each pair of means. A lower value of α also doesn’t solve the
error-rate problem; it just slows it down for a bit, until the number of tests
gets larger, and the error rate goes back up again.
If you want or need to know how I arrived at the number 26.50 percent as
the overall error rate in that last example, here it goes: The probability of
making a Type I error for each test is 0.05. The chance of making at least one
error in six tests equals one minus the probability of making no errors in six
tests. The chance of not making an error in one test is 1 – α = 0.95. The chance
6
of no error in six tests is this quantity times itself six times, or (0.95) , which
equals 0.735. Now take one minus this quantity to get 1 – 0.735 = 0.2650 or
26.50 percent.
To conduct Fisher’s LSD, go to Stat>ANOVA>One-way or One-way unstacked.
(If your data appear in two columns with Column 1 representing the popula-
tion number and Column 2 representing the response, just click One-way 181
because your data is stacked. If your data is shown in k columns, one for
each of the k populations, click One-way unstacked.) In either case, the next
step is to highlight the data for the groups you’re comparing and click Select.
Then click on Comparisons. Click on Fisher’s. The individual error rate is
listed at 5 (percent), which is typical. If you want to change it, type in the
desired error rate (between 0.5 and 0.001) and click OK. You may type in
your error rate as a decimal, 0.05, or as a number greater than one, such as 5.
Numbers greater than one are interpreted as a percentage.
Applying Fisher’s LSD to cell phones
An ANOVA procedure was done on the cell-phone data presented in Table 10-1
to compare the mean number of minutes used for four age groups. Looking at
Figure 10-2, you see Ho (all the populations means are equal) was rejected.
The next step is to conduct multiple comparisons by using Fisher’s LSD to see
which population means differ. Figure 10-3 shows the Minitab output.
The first block of results shows “Group 1 subtracted from” where Group 1 = age
19 and under. Each line after that represents the other age groups (Group 2 =
20- to 39-year-olds, Group 3 = 40- to 59-year-olds, and Group 4 = 60 and over).
Each line shows the results of comparing the mean for the other group minus
the mean for Group 1. For example, the first line shows Group 2 being com-
pared with Group 1.
Moving to the right in that same row, you see the confidence interval for
the difference in these two means, which turns out to be –436.97 to –323.03.
Because 0 isn’t contained in this interval, you conclude that these two means
are different in the populations also. You can also say, because this difference
µ 2 – µ 1 is negative, that µ 2 is less than µ 1 . Or, a better way to think of it may
be that µ 1 is greater than µ 2 . That is, Group 1’s mean is greater than Group 2’s
mean.