## Appendix A: Technical Notes- Statistical Tests

All specific statements of comparisons have been tested for statistical significance at the .05 level using Student's t statistics to ensure that the differences are larger than those that might be expected owing to sampling variation. No adjustments were made for multiple comparisons. Readers are cautioned not to draw causal inferences based on the results presented. Many of the variables examined in this report may be related to one another, but the complex interactions and relationships among them have not been explored. The variables examined here are also just a few of those that can be examined in these data.

The tests of significance used in this report are based on Student's t statistics for the comparisons of percentages. To test for a difference between the percentages of two subgroups in the population having a particular characteristic, say p1 versus p2, the test statistic is computed as

where pi is the estimated percentage 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 72 percent of male students in kindergarten through grade 12 whose parent reported attending a school or class event, with a standard error of 0.6, and p2 is the 76 percent of female students in kindergarten through grade 12 who had a parent who reported attending a school or class event, with a standard error of 0.7, the t value is equal to 4.34.

The decision rule is to reject the null hypothesis if there is a measurable difference between the two groups in the population in terms of the percentage having the characteristic, if , where is the value such that the probability a Student's t random variable with df degrees of freedom exceeds that value is . All tests in this report are based on a significance level of 0.05, that is, . When the degrees of freedom are large, greater than 120, .

In the example above, the t value is large enough for the null hypothesis to be rejected (4.34>1.96), so we conclude that there is a measurable difference between the percent of male and female students whose parents reported attending a school or class event.

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National Center for Education Statistics - http://nces.ed.gov
U.S. Department of Education