We prove the following conjecture of Narayana: there are no nontrivial dominance refinements of the Smirnov two-sample test if and only if the two sample sizes are relatively prime. We also count the number of natural significance levels of the Smirnov two-sample test in terms of the sample sizes and relate this to the Narayana conjecture. In particular, Smirnov tests with relatively prime samp...

This article examines effects of sample size and other design features on correspondence between factors obtained from analysis of sample data and those present in the population from which the samples were drawn. We extend earlier work on this question by examining these phenomena in the situation in which the common factor model does not hold exactly in the population. We present a theoretica...

This procedure computes power and sample size for superiority by a margin tests in two-sample designs in which the outcome is a continuous normal random variable. Measurements are made on individuals that have been randomly assigned to one of two groups. This is sometimes referred to as a parallel-groups design. This design is used in situations such as the comparison of the income level of two...

The trustworthiness of meta-analysis, a set of techniques used to quantitatively combine results from different studies, has recently been questioned. Problems with meta-analysis stem from bias in selecting studies to include in a meta-analysis and from combining study results when it is inappropriate to do so. Simple graphical techniques address these problems but are infrequently applied. Fun...

1 IRCCS Fondazione Don C. Gnocchi, 20148 Milan, Italy; pcastiglioni@dongnocchi.it 2 Department of Medicine and Surgery, University of Parma, 43121 Parma, Italy; paolo.coruzzi@unipr.it (P.C.); matteo.bini@yahoo.it (M.B.) 3 Department of Cardiology, Istituto Auxologico Italiano, 20149 Milan, Italy; gianfranco.parati@unimib.it 4 Department of Medicine and Surgery, University of Milano-Bicocca, 201...

where p above is the density function if X is continuous and the mass function if X is discrete. The MLE is denoted θ̂ or θ̂n if we wish to emphasize the sample size. Above, we suppress the dependency of L on X1, . . . , X (n) to emphasize that we are treating the likelihood as a function of θ. Note that both X and θ may be scalars or vectors (not necessarily of the same dimension) and that L may...

We consider the problem of comparing noisy functions, here trial-averaged neuronal firing-rate curves, across multiple experimental conditions. Of interest are comparisons both within neurons and also among populations of individually recorded neurons. We propose likelihood ratio tests to perform comparisons either pointwise or globally over the entire experimental time. A simulation study of p...

• We have evaluated the performance of these diagnoses in three scenario created in R 3.1.0:  Scenario 1: Insufficient burn-in + large sample size for outcome evaluation (20,000)  Scenario 2: Insufficient burn-in + high auto-correlation in the Markov Chain (0.8)  Scenario 3: Insufficient burn-in + correlated outcomes Laliman V1, Roïz J2 1Ensai student, Bruz, France; 2Creativ-Ceutical, London...