Confidence Interval for Difference Between Means, Separate Variances
When sample sizes are unequal, one should always use a separate variances
standard error and adjusted degrees of freedom (Some properties of preliminary tests of
equality of variances in the two-sample location problem, Journal of General
Psychology, 1996, 123, 217-231). This is very easily done with SPSS:
T-TEST
GROUPS = iup(0 1)
/MISSING = ANALYSIS
/VARIABLES = Pups
/CRITERIA = CI(.95) .
Independent Samples Test
t-test for Equality of Means
t
Pups
Equal variances
as sumed
Equal variances
not ass umed
df
Sig. (2-tailed)
Mean
Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower
Upper
-2.253
19
.036
-7.1923
3.1921
-13.8734
-.5112
-2.784
15.096
.014
-7.1923
2.5831
-12.6951
-1.6896
With SAS (release 9.1 or lower) it is a bit more difficult to get the separate
variances confidence interval. Proc TTest provides pooled and separate variances t,
but only the pooled confidence interval. If you have SAS release 9.2 or higher, you get
both confidence intervals. The output here is from release 9.1.
proc ttest; class iup; var pups; run;
-----------------------------------------------------------------------------------------------The TTEST Procedure
Statistics
Variable
iup
pups
N
Lower CL
Mean
Mean
Upper CL
Mean
Lower CL
Std Dev
Std Dev
Upper CL
Std Dev
Std Err
8
38.357
40.5
42.643
1.6949
2.5635
5.2174
0.9063
13
42.422
47.692
52.963
6.254
8.7215
14.397
2.4189
-13.87
-7.192
-0.511
5.4022
7.1036
10.375
3.1921
0
pups
pups
1
Diff (1-2)
T-Tests
Variable
Method
Variances
pups
pups
Pooled
Satterthwaite
Equal
Unequal
DF
t Value
Pr > |t|
19
15.1
-2.25
-2.78
0.0363
0.0138
Equality of Variances
Variable
Method
pups
Folded F
Num DF
Den DF
F Value
Pr > F
12
7
11.57
0.0034
*****************************************************************************
One can use PROC MIXED to get the separate variances confidence interval.
“iup” is the grouping variable and “pups” the criterion variable.
PROC MIXED; CLASS iup; MODEL pups = iup / DDFM = SATTERTH;
REPEATED / GROUP = iup; LSMEANS iup / PDIFF CL; RUN;
-----------------------------------------------------------------------------------------------The Mixed Procedure
Type 3 Tests of Fixed Effects
Effect
Num
DF
iup
1
Den
DF
15.1
F Value
7.75
Pr > F
0.0138
Differences of Least Squares Means
Effect
group
_group
iup
0
1
Estimate
Standard
Error
DF
t Value
Pr > |t|
Alpha
Lower
Upper
-7.1923
2.5831
15.1
-2.78
0.0138
0.05
-12.6951
-1.6896
Verification that SPSS and SAS correctly computed the separate variances error term:
2.5635 2 8.7215 2

 2.5831
8
13
Karl L. Wuensch
Psychology, East Carolina University
26. November 2008