
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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
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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Situation #2
Situation #1
W W
M W
M W
M W
M W
1 2 3 4 5 6 7 8
Mean: M = 4, W = 5
M M MW
1 2 3 4
Mean: M = 4,
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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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2. Formal t-test
◦ use the numbers in the sample
◦ scale by the “spread” [variance]
◦ (use the “standard error”)
◦ how many standard errors apart?
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2. t-test
◦ Formula:
 X1 - X2
 S.D./sqrt of n [number of subjects]
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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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dianaid
Frequency
60
40
20
Mean =3.02
Std. Dev. =0.859
N =755
0
1.00
2.00
3.00
4.00
5.00
dianaid
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Group Statistics
dianaid
sex
male
female
N
277
461
Mean
2.6136
3.2656
Std. Deviation
.82723
.78627
Std. Error
Mean
.04970
.03662
Independent Samples Test
Levene's Test for
Equality of Variances
F
dianaid
Equal variances
as sumed
Equal variances
not ass umed
1.634
Sig.
.202
t-test for Equality of Means
t
df
Sig. (2-tailed)
Mean
Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower
Upper
-10.697
736
.000
-.65207
.06096
-.77175
-.53239
-10.562
558.271
.000
-.65207
.06174
-.77334
-.53080
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
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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Independent Samples Test
Levene's Test for
Equality of Variances
F
dianaid
Equal variances
as sumed
Equal variances
not ass umed
1.634
Sig.
.202
t-test for Equality of Means
t
df
Sig. (2-tailed)
Mean
Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower
Upper
-10.697
736
.000
-.65207
.06096
-.77175
-.53239
-10.562
558.271
.000
-.65207
.06174
-.77334
-.53080
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