Comparing more than two means: one factor ANOVA with independent samples. Multiple comparison testing with the Newman-Keuls test - Improving the User Experience through Practical Data Analytics - page 158

SIDEBAR: WHY CAN'T I SKIP THE ANOVA STEP?—cont'd

differ in mean height? There have to be two states that have the extreme values of the means, but,
assuming all states have the same mean, it is random which ones, and it would almost surely be
different for different samples of men. Generalizing that Louisiana and Idaho men differ in mean
height, based on this t-test, is ridiculous. If you did conclude that, you'd be guilty of bias (and per-
haps stupidity). But that kind of bias can creep into your analysis when you simply eyeball different
means, and perform t-tests only on the pairs of means that “look” different, or have large enough
differences in sample means that you suspect it to be so.
Performing an ANOVA and doing all the pairwise comparisons (or a subset of comparisons that
are chosen to be analyzed before you see the results) eliminates that bias—i.e., it eliminates the
increased chance of committing at least one type I error.

6.9 MEANWHILE, BACK AT MADEMOISELLE LA LA …
You'll remember that Cinny Bittle, your new texting-mad marketing manager, got
her hand on a Forrester report that claimed older boomers (ages 56-66 years) spend
the most online of all generations. Since Bittle was worried that your new home
page design was not considered sophisticated by this age bracket, you offered to
slice and dice the survey data by age. You were trying to determine if there were dif-
ferent perceptions of sophistication by age, and perhaps appease Bittle. Or at least
get her to stop texting on her cell phone for 10 seconds by delivering the results of
your analysis.
To refresh your memory, you sorted the data by youngest to oldest, using these
age brackets:
1. Gen Z, 18-25 years
2. Gen Y, 26-35 years
3. Gen X, 36-45 years
4. Younger boomers, 46-55 years
5. Older boomers, 56-66 years

Then you calculated the mean for each age bracket, as displayed below in
Table 6.2 .

Table 6.2 A Refresher on Our Age-Groups and Their Means

Age Bracket 1 Age Bracket 2 Age Bracket 3 Age Bracket 4 Age Bracket 5

18-25
Gen Z

26-35
Gen Y

36-45
Gen X

46-55
Younger
boomers

56-66
Older boomers

Mean = 2.25
n = 28

4.38
26

4.50
26

3.04
23

2.74
23

Agreement with statement: “This page makes Mademoiselle seem sophisticated.”
1 = Strongly disagree, 5 = strongly agree.