In order to make inferences about the differences between the two groups in
the population, the sample size, mean, and standard deviation for each group
must be known.
These statistics are automatically computed by statistical software when
estimating a confidence interval or conducting a test of significance.
The table labeled “Group Statistics” on the previous page is part of the output
provided by SPSS.
In this example, the mean for females is 10 points higher than the mean for
males.
However, if another two random samples of females and males were
selected, the numbers would be slightly different.
Therefore, instead of only providing the difference in the means, a confidence
interval should be computed for this difference.
For the example, the difference in test scores in the population between
males and females will be estimated with 90% confidence.
If the confidence interval is estimated using statistical software, the results
will be slightly different than if it is done by hand. Statistical software uses a
more complicated formula to compute the degrees of freedom, and tests for
the assumption that the variance of the variable is equal in the two
populations.
The assumption that the variance is equal is almost never met, so the second
row in the SPSS output table should be used.
The interval in this case is quite large due to the small sample size. The small
samples were used to make computations easier for this example, but in
reality confidence intervals should not be estimated for such small samples.