Statistical Analysis for Education and Psychology Researchers

independent

samples—

8.18

In this example t 1 −α/2 with 18 df is 2.101 and the 95 per cent CI is 13.2−19.5 +/−2.101
(4.643) (0.4472), the lower bound estimate is −10.663 and the upper bound estimate is
−1.937.

Interpretation

The difference between the sample mean correct score in 6- and 7-year-old pupils was
−6.3 with a 95 per cent CI from −10.663 to −1.937, the equal variance t-ratio, two-tailed
test, was −3.034, with 18 degrees of freedom and an associated p-value of 0.05. The
interval does not include zero which corresponds to a rejection of the null hypothesis
(zero difference between means is equivalent to the null hypothesis). The interval width
is rather large probably because of the small sample size. We are 95 per cent certain that
the mean difference could, with rounding, be as small as −2 or as large as −11 but the
most likely value is −6.
Output from a SAS programme for computing a Confidence Interval for the difference
between two means for independent samples (see the SAS programme in Figure 17,
Appendix A3) is shown in Figure 8.10.
mean
(gp 1)

mean (gp 2) variance (gp

1)

variance

(gp 2)

sample

size (gp

1)

sample

size (gp

1) 10 10 13.2 19.5 25.733 17.389

Alpha Critical t-

value

Lower

Confidence

Limit

Upper

Confidence

Limit

0.05 2.101 −10.663 −1.937

Figure 8.10:95 per cent Cl for

difference between two means

The values in this output correspond with the 95 per cent CI interval width in the worked
example.

Computer Analysis

The SAS procedure PROC TTEST performs an independent t-test, the following SAS
code produced the output shown in Figure 8.11,

proc ttest;

class age;

var score;

run;

Statistical analysis for education and psychology researchers 302