An Improved Bayesian Procedure for Calculating Sample Sizes in Multinomial Sampling

1993 ◽  
Vol 42 (2) ◽  
pp. 91 ◽  
Author(s):  
C. J. Adcock
Keyword(s):  
Bayesian Procedure ◽  
Sample Sizes ◽  
Multinomial Sampling

scholarly journals Noninformative Bayesian $P$-values for testing marginal homogeneity in $2 \times 2$ contingency tables

2009 ◽  
Vol 40 (4) ◽  
pp. 415-427 ◽  
Author(s):  
Lee-Shen Chen ◽  
Ming-Chung Yang
Keyword(s):  
Contingency Tables ◽  
The Other ◽  
P Value ◽  
Posterior Distributions ◽  
Sample Sizes ◽  
P Values ◽  
Large Sample ◽  
Marginal Homogeneity ◽  
Multinomial Sampling ◽  
Preceding Problem

This article considers the problem of testing marginal homogeneity in $2 \times 2$ contingency tables under the multinomial sampling scheme. From the frequentist perspective, McNemar's exact $p$-value ($p_{_{\textsl ME}}$) is the most commonly used $p$-value in practice, but it can be conservative for small to moderate sample sizes. On the other hand, from the Bayesian perspective, one can construct Bayesian $p$-values by using the proper prior and posterior distributions, which are called the prior predictive $p$-value ($p_{prior}$) and the posterior predictive $p$-value ($p_{post}$), respectively. Another Bayesian $p$-value is called the partial posterior predictive $p$-value ($p_{ppost}$), first proposed by [2], which can avoid the double use of the data that occurs in $p_{post}$. For the preceding problem, we derive $p_{prior}$, $p_{post}$, and $p_{ppost}$ based on the noninformative uniform prior. Under the criterion of uniformity in the frequentist sense, comparisons among $p_{prior}$, $p_{_{{\textsl ME}}}$, $p_{post}$ and $p_{ppost}$ are given. Numerical results show that $p_{ppost}$ has the best performance for small to moderately large sample sizes.

Is Red Really Romantic?

2017 ◽  
Vol 48 (3) ◽  
pp. 174-183 ◽  
Author(s):  
Gabrielle K. Lehmann ◽  
Robert J. Calin-Jageman
Keyword(s):  
Opposite Direction ◽  
Positive Control ◽  
Weak Effect ◽  
Sample Sizes ◽  
Quality Controls

Abstract. Red has been reported to enhance attraction for women rating men ( Elliot et al., 2010 ) and men rating women ( Elliot & Niesta, 2008 ). We replicated one of these studies online and in-person. To ensure rigor, we obtained original materials, planned for informative sample sizes, pre-registered our study, used a positive control, and adopted quality controls. For men, we found a very weak effect in the predicted direction (d = 0.09, 95% CI [−0.17, 0.34], N = 242). For women, we found a very weak effect in the opposite direction (d = −0.09, 95% CI [−0.30, 0.12], N = 360). The original studies may have overestimated the red effect, our studies may be an underestimate, or there could be strong moderation of the effect of red on attraction.

Norm-Block Sample Sizes: A Review of 15 Multidimensional Intelligence Tests

2013 ◽  
Author(s):  
Randy G. Floyd ◽  
Ryan L. Farmer ◽  
Sarah Irby ◽  
Phil Norfolk ◽  
Haley Hawkins ◽  
...  
Keyword(s):  
Intelligence Tests ◽  
Sample Sizes ◽  
Block Sample

On the Mathematical Basis of Zelen’s Prerandomized Designs

1985 ◽  
Vol 24 (03) ◽  
pp. 120-130 ◽  
Author(s):  
E. Brunner ◽  
N. Neumann
Keyword(s):  
Clinical Trial ◽  
Normal Distribution ◽  
Random Variables ◽  
Small Samples ◽  
Selection Effects ◽  
Sample Sizes ◽  
Mathematical Basis ◽  
Additional Assumptions

SummaryThe mathematical basis of Zelen’s suggestion [4] of pre randomizing patients in a clinical trial and then asking them for their consent is investigated. The first problem is to estimate the therapy and selection effects. In the simple prerandomized design (PRD) this is possible without any problems. Similar observations have been made by Anbar [1] and McHugh [3]. However, for the double PRD additional assumptions are needed in order to render therapy and selection effects estimable. The second problem is to determine the distribution of the statistics. It has to be taken into consideration that the sample sizes are random variables in the PRDs. This is why the distribution of the statistics can only be determined asymptotically, even under the assumption of normal distribution. The behaviour of the statistics for small samples is investigated by means of simulations, where the statistics considered in the present paper are compared with the statistics suggested by Ihm [2]. It turns out that the statistics suggested in [2] may lead to anticonservative decisions, whereas the “canonical statistics” suggested by Zelen [4] and considered in the present paper keep the level quite well or may lead to slightly conservative decisions, if there are considerable selection effects.

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