STATISTICS
• categorical independent variable
– e.g., men versus women, control vs.
experimental groups
• continuous dependent variable
– e.g, # times purchased, $ spent
• comparisons of means
– men 4.0, women 5.0
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Basic strategy:
• You have two groups
and a mean (average) for each
– e.g., men = 4.0,
– women = 5.0
• How do you determine the strength
of the covariation?
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Examples
Situation #1
Situation #2
M W
W W
M W
M W
M W
M M MW
1 2 3 4 5 6 7 8
1 2 3 4
5 6 7 8
Mean: M = 4, W = 5 Means: C = 4, W = 5
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Comparison of means
How do you test the covariation?
1. “inter-ocular” test
– does it “hit you between the eyes?”
– does it look big?
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Comparison of means
2. t-test
– use the numbers in the sample
– scale by the “spread” [variance]
– e.g., how many standard deviations apart?
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Comparison of means: Graphically
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Comparison of means: Graphically
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Comparison of means
2. t-test
– Formula:
• X1 - X2
• S.D./sqrt of n [number of subjects]
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Comparison of means
2. t-test (continued)
– compare observed “t”
– to t “critical” from table [A-4]
• d.f. = n [number of subjects] - 1
• e.g., t [29] @ .05 = 1.699 [two tailed]
• t [29] @ .025 = 2.045 [one tailed]
– if t > t critical, difference in population
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Comparison of means: Output
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Unequal variances: The problem
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Unequal variance: The solution
• A useful rule of thumb is:
– the difference in standard deviations is seldom
a problem until one is more than twice the
other.
• In that instance, do a t-test using
“separate” variance estimates.
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The End
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