The tests of significance used in this E.D. TAB report are based on Student's t statistics for the comparisons of individual estimates and comparisons of means. To test the differences between estimates, unbiased estimates of standard errors were used, derived by jackknife replication methods. To test for a difference between two subgroups in the population proportion having a particular characteristic, say P1 versus P2, the test statistic is computed as:
where P1 pi is the estimated proportion of subgroup i (i = 1, 2) having the particular characteristic and s.e.(pi ) is the standard error of that estimate. Thus, if p1 is for the 60 percent of male children with nonparental care arrangements, with a standard error of 0.9, and p2 is for the 59 percent of female children with nonparental care arrangements, with a standard error of 1.2, then the t-value is equal to 0.67.
The decision rule is to reject the null hypothesis (i.e., that there is no difference between the two groups in the population in terms of the proportion having the characteristic) if , where is the value such that the probability that a Student's t random variable with df degrees of freedom exceeds that value is .