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Activity Number:
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41
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Type:
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Contributed
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Date/Time:
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Sunday, August 11, 2002 : 4:00 PM to 5:50 PM
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Sponsor:
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Section on Survey Research Methods*
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| Abstract - #301592 |
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Title:
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Improved Approximation of the CDF for aT Statistic Based on a Variance Estimated by a Weighted Sum of Chi-Square Random Variables
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Author(s):
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Robert Bell*+ and Daniel McCaffrey
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Affiliation(s):
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AT&T Labs - Research and RAND Corporation
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Address:
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180 Park Avenue, Florham Park, New Jersey, 07974,
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Keywords:
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Satterthwaite approximation ; bias reduced linearization ; complex samples ; degrees of freedom
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Abstract:
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Various t-statistics take the form t = b/sqrt(V), where V is an unbiased estimator of Var(b) formed as a weighted sum of independent chi-square random variables with one degree of freedom. For example, McCaffrey and Bell (2001 Proc. Survey Research Methods Section) propose bias reduced linearization for inference about linear regression coefficients in multi-stage samples. Using a t distribution with the nominal degrees of freedom as the reference distribution can produce liberal P-values and critical values. Several authors have proposed use of Satterthwaite's approximate degrees of freedom based on matching moments of a chi-square distribution with the first two moments of V. Although Satterthwaite's approximation improves inference substantially, we show that the resulting reference t distribution can fit poorly, especially in the tails. We present a simple alternative method tailored to approximate the CDF of the actual t statistic. Simulations show the proposed method produces more accurate P-values than Satterthwaite's approximation. The method can also be used to compute critical values needed for tests and confidence intervals.
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