Exact unconditional tests for a 2 × 2 matched-pairs design

Berger, R L; Sidik, K
March 2003
Statistical Methods in Medical Research;Mar2003, Vol. 12 Issue 2, p91
Academic Journal
The problem of comparing two proportions in a 2 × 2 matched-pairs design with binary responses is considered. We consider one-sided null and alternative hypotheses. The problem has two nuisance parameters. Using the monotonicity of the multinomial distribution, four exact unconditional tests based on p-values are proposed by reducing the dimension of the nuisance parameter space from two to one in computation. The size and power of the four exact tests and two other tests, the exact conditional binomial test and the asymptotic McNemar's test, are considered. It is shown that the tests based on the confidence interval p-value are more powerful than the tests based on the standard p-value. In addition, it is found that the exact conditional binomial test is conservative and not powerful for testing the hypothesis. Moreover, the asymptotic McNemar's test is shown to have incorrect size; that is, its size is larger than the nominal level of the test. Overall, the test based on McNemar's statistic and the confidence interval p-value is found to be the most powerful test with the correct size among the tests in this comparison.


Related Articles

  • Pooling overdispersed binomial data to estimate event rate. Yinong Young-Xu; Chan, K. Arnold // BMC Medical Research Methodology;2008, Vol. 8, Special section p1 

    Background: The beta-binomial model is one of the methods that can be used to validly combine event rates from overdispersed binomial data. Our objective is to provide a full description of this method and to update and broaden its applications in clinical and public health research. Methods: We...

  • A parametric model fitting time to first event for overdispersed data: application to time to relapse in multiple sclerosis. Siri, Paola; Henninger, Eric; Sormani, Maria // Lifetime Data Analysis;Apr2012, Vol. 18 Issue 2, p139 

    In this article, we propose a parametric model for the distribution of time to first event when events are overdispersed and can be properly fitted by a Negative Binomial distribution. This is a very common situation in medical statistics, when the occurrence of events is summarized as a count...

  • Poisson Poisson and statistics. SHEYNIN, OSCAR // Mathematical Scientist;Dec2012, Vol. 37 Issue 2, p149 

    The author discusses the contributions of mathematician Simeon Denis Poisson to probability theory and further describes the modification of Poisson's work by several other mathematicians and statisticians. It also briefs about the application of Poisson's work in medical statistics. The article...

  • Approaches for estimating prevalence ratios. Deddens, J. A.; Petersen, M. R. // Occupational & Environmental Medicine;Jul2008, Vol. 65 Issue 7, p501 

    The article reviews existing methods and provides examples and recommendations on how to estimate prevalence risk. It examines methods such as logistic regression for modelling binomial health outcomes, the Cox proportional hazard method, the Poisson regression, the COPY method and the maximum...

  • The Delta Binomial Test for Interjudge Reliability. Hornik, Jacob // Current Issues & Research in Advertising;1988, Vol. 11 Issue 1, p67 

    This paper suggests an improved method of reporting the degree of consistency between judges' coding of marketing and advertising content. The method is based on the binomial sampling distribution theory where scores are test scores indicating statistical significance of measures of agreement....

  • An Evaluation of the Negative Binomial Method for Tests of Controls. Wendell, John P.; Gregson, Terry // Journal of Applied Business Research;Spring97, Vol. 13 Issue 2, p65 

    Presents information on a study which examines the computational details and properties of negative binomial method (NBM) from the perspective of established statistical sampling principles. Methodology of the study; Results and discussion on the study; Conclusions.

  • Estimating ordered binomial proportions with the use of group testing. J.M. Tebbs; W.H. Swallow // Biometrika;Jun2003, Vol. 90 Issue 2, p471 

    This paper considers group testing when the probability of response is increasing across the levels of an observed covariate. We illustrate how previously known results in order-restricted inference can be extended to situations wherein data are collected according to a group-testing protocol,...

  • A note on LeCam's bound for the distance between the Poisson binomial and the Poisson distribution. Weba, Michael // Statistical Papers;Jul2002, Vol. 43 Issue 3, p445 

    Provides information on an improved version of LeCam's bound for the distance between the Poisson binomial distribution and Poisson distribution. Details of the modification of LeCam's bound; Theorem and proof.

  • ON AN APPLICATION OF BERNOULLI'S INEQUALITY. Dence, Thomas P.; Dence, Joseph B. // Mathematics & Computer Education;Spring2003, Vol. 37 Issue 2, p234 

    The article presents a mathematical representation of Bernoulli's inequality.


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics