PubMed Health⌕ Search

PubMed · 1961329

[Statistics (4). Tossing for decision making: one sample, dichotomy].

Abstract

A coin, suspected to be biased, may be distinguished from a fair one by tossing it a number of times and applying the binomial test. Taking into account the probabilities of all possible outcomes (the theoretical sampling distribution), a too large occurrence of heads (or tails) will lead to rejection of the null hypothesis implying that the coin is not fair.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

A H Schuurs, M A van 't Hof, H J Duivenvoorden. 1991. [Statistics (4). Tossing for decision making: one sample, dichotomy].. https://pubmed.ncbi.nlm.nih.gov/1961329/

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related citations

Early stopping clinical trials of binomial response with an exact group sequential method.

In Phase II clinical trials much slower patient enrollment and intervening results of comparable trials can make it desirable to stop trials early when the data indicate no relevant effect. For a binomial response, we adopt an exact group sequential method as a decision tool to assess whether the trial could be stopped early or not. We have applied the exact group sequential method to a Phase II Tuberculosis clinical trial, and the results have been compared with that from error spending and conditional power approaches. We conclude that the exact group sequential method is more efficient for interim analysis in clinical trials than the error spending and conditional power approaches. Published in 2007 by John Wiley & Sons, Ltd.

Binomial Distribution↗

Computational simulations of vocal fold vibration: Bernoulli versus Navier-Stokes.

The use of the mechanical energy (ME) equation for fluid flow, an extension of the Bernoulli equation, to predict the aerodynamic loading on a two-dimensional finite element vocal fold model is examined. Three steady, one-dimensional ME flow models, incorporating different methods of flow separation point prediction, were compared. For two models, determination of the flow separation point was based on fixed ratios of the glottal area at separation to the minimum glottal area; for the third model, the separation point determination was based on fluid mechanics boundary layer theory. Results of flow rate, separation point, and intraglottal pressure distribution were compared with those of an unsteady, two-dimensional, finite element Navier-Stokes model. Cases were considered with a rigid glottal profile as well as with a vibrating vocal fold. For small glottal widths, the three ME flow models yielded good predictions of flow rate and intraglottal pressure distribution, but poor predictions of separation location. For larger orifice widths, the ME models were poor predictors of flow rate and intraglottal pressure, but they satisfactorily predicted separation location. For the vibrating vocal fold case, all models resulted in similar predictions of mean intraglottal pressure, maximum orifice area, and vibration frequency, but vastly different predictions of separation location and maximum flow rate.

Binomial Distribution↗

The number distribution for involved lymph nodes in cancer.

The number of involved lymph nodes exhibits considerable heterogeneity within populations. Here, the implications of population heterogeneity are explored with respect to the kinematics of nodal metastases. Data from the National Cancer Institute's Surveillance, Epidemiology, and End Results program for 224656 breast, 12404 gastric, 18015 rectal, 4117 cervical and 2443 laryngeal cancers as well as 9118 melanomas were used to construct frequency distributions for the number of involved nodes which were then fitted to the negative binomial distribution. The negative binomial distribution described the heterogeneity in nodal involvement well. The patterns of nodal involvement can be explained by either of two models: one where involved nodes could seed further nodal metastases, the other where the number of nodal metastases in any individual was randomly distributed, with the deviations between patients accounted for by population heterogeneity. Since the number of sampled nodes similarly approximated a negative binomial distribution, random involvement with superimposed population heterogeneity would more credibly explain both sets of observations.

Binomial Distribution↗