Inverse Sampling for McNemar's Test

Inverse sampling for McNemars test is studied. Sampling is conducted until a pre-specified number of discordant pairs is observed instead of sampling until a pre-specified total number of pairs is observed. The joint likelihood is decomposed into a product of a negative binomial distribution for the number of pairs required to observe r discordant pairs, a binomial distribution for the number of successes in the concordant observations, and a binomial distribution for the number of successes in the discordant observations. Since inference in this problem is based on the discordant observations, inverse sampling controls the type II error when small numbers of discordant observations are observed and the exact binomial test is required. The control results from fixing the sample size for the exact binomial test. Standard sampling instead lets the sample size for the exact binomial test vary and then performs the test conditionally on the observed number of discordant pairs.

Variable satellite placement in spoken Dutch

This article presents a corpus study of the variable placement of adverbial satellites in spoken Dutch. It is widely contended that the relative order of satellites is motivated by three general principles: information status, length and the proximity principle. The proximity principle maintains that the placement of satellites is motivated by their semantic relationship with the sentence verb. We investigated the effect of the proximity principle on the relative placement of 8 different satellite classes based on a corpus sample of 202 combinations of two satellites retrieved from the Corpus of Spoken Dutch. The exact binomial test was used to evaluate the statistical significance of the observed orders. Our main results corroborate the hypothesis that the proximity principle influences satellite ordering. We also found, however, that the placement of certain satellite classes appeared very restricted, which suggests that the proximity principle does not play an active role in their placement.