Page 203 - Intermediate Statistics for Dummies

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Part III: Comparing Many Means with ANOVA
Fisher 95% Individual Confidence Intervals
All Pairwise Comparisons
Simultaneous confidence level = 80.32%
Group 1 subtracted from:
Center
Upper –––––––––+–––––––––+–––––––––+–––––––––+
Lower
(*–)
Group 2 –436.97 –380.00 –323.03

(*–)
Group 3 –147.97 –91.00 –34.03
Group 4 –679.97 –623.00 –566.03 (*–)
–––––––––+–––––––––+–––––––––+–––––––––+
–350 0 350 700
Group 2 subtracted from:
Figure 10-3:
Center
Lower
Upper –––––––––+–––––––––+–––––––––+–––––––––+
Group 3
232.03
(*–)
345.97
289.00
Output
(–*–)
Group 4 –299.97 –243.00 –186.03
showing
–––––––––+–––––––––+–––––––––+–––––––––+
–350 0 350 700
Fisher’s LSD
applied to
Group 3 subtracted from:
Lower
Center
Upper –––––––––+–––––––––+–––––––––+–––––––––+
the cell-
Group 4 –588.97 –532.00 –475.03 (–*)
phone data.
–––––––––+–––––––––+–––––––––+–––––––––+
–350 0 350 700
Each subsequent row in the “Group 1 subtracted from” section of Figure 10-3
shows similar results. None of the confidence intervals contain 0, so you con-
clude that the mean cell-phone use for Group 1 isn’t equal to the mean cell-
phone use for any other group. Moreover, because all confidence intervals
are in negative territory, you can conclude that the mean cell-phone use time
for those 19 and under is greater than all the others. This process continues
as you move down through the output until all six pairs of means are com-
pared. Then you put them all together into one conclusion.
For example, in the second portion of the output, Group 2 is subtracted from
Groups 3 and 4. You see the confidence interval for the “Group 3” line is 232.03,
345.97; this gives possible values for Group 3’s mean minus Group 2’s mean.
The interval is entirely positive, so conclude that Group 3’s mean is greater
than Group 2’s mean (according to this data). On the next line, the interval for
Group 4 minus Group 2 is –299.97 to –186.03. All these numbers are negative, so
conclude Group 4’s mean is less than Group 2’s. Combine conclusions to say
that Group 3’s mean is greater than Group 2’s, which is greater than Group 4’s.
In the cell-phone example, none of the means are equal to each other, and
based on the signs of confidence intervals and the results of all the individual
pairwise comparisons, the following order of cell-phone mean usage prevails:
µ 1 > µ 3 > µ 2 > µ 4 . (Hypothetical data aside, it might be the case that 40- to
59-year-olds use a lot of cell phone time because of their jobs.)
Notice near the top of Figure 10-3 that you see “simultaneous confidence
level = 80.32 percent.” That means the overall error rate for this procedure
is 1 – 0.8032 = 0.1968, which is close to 20 percent.