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Limiting Comparisons Involving Extreme Percentages

The statistical testing procedures used for NAEP are appropriate for testing differences of both means and nonextreme percentages. The approximation for the test for percentages works best when sample sizes are large, and the percentages being tested have magnitude relatively close to 50 percent. In some cases NAEP cannot provide reliable standard errors. An example of this would be extreme percentages. Extreme percentages are those that are close to 0 or 100 as defined below.

Differences in percentages are treated as involving "extreme" percentages if for either percentage, P:

P is less than P sub lim, which equals 200 divided by the quantity N sub e f f plus two

or

One hundred minus P is less than P sub lim, which equals 200 divided by the quantity N sub e f f plus two

where the effective sample size is

N sub e f f equals P times the quantity one hundred minus P divided by SE sub J K squared

and SEJK is the jackknife standard error of P. In either extreme case, the normal approximation to the distribution is a poor approximation, and the value of P was reported, but no standard errors are estimated and hence no significance tests are conducted.


Last updated 15 July 2008 (DR)

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