1.2 Unpaired T-Tests Page 3
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Confidence interval for the true mean difference
It would also be useful to calculate a confidence interval for the difference in means to tell
us within what limits the true difference is likely to lie. A 95% confidence interval for the
true difference between the means is given by:
1
1
(¯
¯
)
+
or, equivalently (¯
¯
)
(¯
¯
)
1
2
1
2
1
2
1
2
where
is the 2.5% point of the t-distribution on
+
2 degrees of freedom.
1
2
Using our example:
We have a mean difference of 34.38 calories. The 2.5% point of the t-distribution with 35
degrees of freedom is 2.03. The 95% confidence interval for the true mean difference is
therefore:
34 38
(2 03
7 91) = 34 38
16 06 = (18 3 50 4)
We can be 95% sure that the mean calorie content of beef hotdogs is somewhere between
18 and 50 calories higher than the mean calorie content of poultry hotdogs.
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Carrying out an unpaired t-test in SPSS
– Analyze
– Compare Means
– Independent-Samples T-Test
– Choose your outcome variable (in our case calories) as the Test Variable
– Choose the variable that defines the groups as the Grouping Variable then click on
Define Groups. You will need to enter the two codes which identify your two groups
then click on Continue (in our case, the code 1 was used for Beef and the code 2 for
Poultry, so we would enter 1 in Group 1 and 2 in Group 2). Now click OK.
The output will look something like this:
Group Statistics
GROUP
N
Mean
Std. Deviation Std. Error Mean
CALORIES
Beef
20 156.85
22.642
5.063
Poultry
17 122.47
25.483
6.181
Independent Samples Test
Levene’s test for
Equal Variances
t-test for Equality of Means
Sig.
Mean
SE
95% C.I.
F
Sig.
t
df
(2-tailed)
Diff.
Diff.
Lower
Upper
Eq. variances 1.046
0.314
4.346
35
.000
34.38
7.911 18.318 50.441
assumed
Eq. variances
4.303 32.394
.000
34.38
7.990 18.113 50.646
not assumed
The relevant results in the second table are given in the row where equal variances are
assumed. You are interested in t, the p-value (Sig.(2-tailed)), the mean difference and the
95% confidence interval.
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