The descriptive comparisons were tested in this report using Student’s t statistic. Differences between estimates are tested against the probability of a Type I error⁶, or significance level. The significance levels were determined by calculating the Student’s t values for the differences between each pair of means or proportions and comparing these to published tables of significance levels for two-tailed hypothesis testing.

Student’s t values may be computed to test the difference between estimates with the following formula:

where E1 and E2 are the estimates to be compared and se1 and se2 are their corresponding standard errors. This formula is valid only for independent estimates. When estimates are not independent, a covariation term must be added to the formula:

where r is the correlation between the two variables.⁷ The denominator in this formula will be at its maximum when the two estimates are perfectly negatively correlated, that is, when r = –1. This means that a conservative dependent test may be conducted by using –1 for the correlation in this formula as follows:

The estimates and standard errors are obtained from the DAS.

There are hazards in reporting statistical tests for each comparison. First, comparisons based on large t statistics may appear to merit special attention. This can be misleading since the magnitude of the t statistic is related not only to the observed differences in means or percentages but also to the number of respondents in the specific categories used for comparison. Hence, a small difference compared across a large number of respondents would produce a large t statistic.

Comparisons were made in this report only when p < .05. The alpha level of .05 selected for findings in this report indicates that a difference of a certain magnitude or larger would be produced no more than one time out of twenty when there was no actual difference in the quantities in the underlying population. When we test hypotheses that show t values at the .05 level or smaller, we treat this finding as rejecting the null hypothesis that there is no difference between the two quantities.