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Adult Education Participation in 2004-05

NCES 2006-077
May 2006

Appendix A: Statistical Tests

The tests of significance used in this report are based on two-tailed tests using Student's t statistics for the comparison of individual estimates and for bivariate relationships. To test the differences between estimates, unbiased estimates of standard errors were used, derived by jackknife replication methods. To test for a difference in proportions between two subgroups in the population having a particular characteristic, say P1 versus P2, the test statistic is computed as:

mathematical equation 1

where 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 the 47 percent of females who reported having participated in any formal adult education in the 12 months prior to the interview, with a standard error of 1.0, and p2 is the 41 percent of males who reported having participated in any formal adult education in the 12 months prior to the interview, with a standard error of 1.2, then the t value is equal to 3.84.

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 mathematical equation 2, where mathematical equation 3 is the value such that the probability that a random variable having a Student's t distribution with df degrees of freedom exceeds that value is a/2.

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