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PROBLEMS WITH BINOMIAL TWO‐SIDED TESTS AND THE ASSOCIATED CONFIDENCE INTERVALS
Author(s) -
Vos Paul W.,
Hudson Suzanne
Publication year - 2008
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/j.1467-842x.2007.00501.x
Subject(s) - mathematics , confidence interval , binomial (polynomial) , binomial proportion confidence interval , statistics , binomial distribution , robust confidence intervals , continuity correction , negative binomial distribution , econometrics , beta binomial distribution , poisson distribution
Summary Confidence intervals for parameters of distributions with discrete sample spaces will be less conservative (i.e. have smaller coverage probabilities that are closer to the nominal level) when defined by inverting a test that does not require equal probability in each tail. However, the P ‐value obtained from such tests can exhibit undesirable properties, which in turn result in undesirable properties in the associated confidence intervals. We illustrate these difficulties using P ‐values for binomial proportions and the difference between binomial proportions.