Correlation Coefficient Revisited

Elementary approaches to prove basic properties of the correlation coefficient are of pedagogical interest. Besides posing another proof, this article gives variations of the proofs already existing in the statistical literature     

LogXact 4.1 for Windows

Box's paper helicopter has been used to teach experimental design for more than a decade. It is simple, inexpensive, and provides real data for an involved, multifactor experiment. Unfortunately it can also further an all-too-common practice that Professor Box himself has repeatedly cautioned against, namely ignoring the fundamental science while rushing to solve problems that may not be sufficiently understood. Often this slighting of the science so as to get on with the statistics is justified by referring to Box's oft-quoted maxim that “All models are wrong, however some are useful.” Nevertheless, what is equally true, to paraphrase both Professor Box and George Orwell, is that “All models are wrong, but some are more wrong than others.” To experiment effectively it is necessary to understand the relevant science so as to distinguish between what is usefully wrong, and what is dangerously wrong.

This article presents an improved analysis of Box's helicopter problem relying on statistical and engineering knowledge and shows that this leads to an enhanced paper helicopter, requiring fewer experimental trails and achieving superior performance. In fact, of the 20 experimental trials run for validation—10 each of the proposed aerodynamic design and the conventional full factorial optimum—the longest 10 flight times all belong to the aerodynamic optimum, while the shortest 10 all belong to the conventional full factorial optimum. I further discuss how ancillary engineering knowledge can be incorporated into thinking about—and teaching—experimental design.     

2008 North American Serials Interest Group Conference: Taking the Sting out of Serials!

Abstract

The twelfth annual MOBIUS Conference was held June 7–9, 2011, at the Holiday Inn Executive Center in Columbia, Missouri. The MOBIUS consortium of Missouri is currently composed of fifty-nine academic libraries, two public libraries, and the Missouri State Library. The conference offered various opportunities, including a keynote address by Meredith Farkas and a networking dessert session on the first night. The second day featured six concurrent sessions, each having six different presentations, along with delicious food, generous door prizes, and the chance to meet with vendors. The third day consisted of four different four-hour post-conference training sessions. Presentations are available for download from the conference Web site.¹     

Quantile plots for mean effects in the presence of variance effects for 2k-p designs

In robust parameter design, variance effects and mean effects in a factorial experiment are modelled simultaneously. If variance effects are present in a model, correlations are induced among the naive estimators of the mean effects. A simple normal quantile plot of the mean effects may be misleading because the mean effects are no longer iid under the null hypothesis that they are zero. Adjusted quantiles are computed for the case when one variance effect is significant and examples of 8-run and 16-run fractional factorial designs are examined in detail. We find that the usual normal quantiles are similar to adjusted quantiles for all but the largest and smallest ordered effects for which they are conservative. Graphically, the qualitative difference between the two sets of quantiles is negligible (even in the presence of large variance effects) and we conclude that normal probability plots are robust in the presence of variance effects.     

Simulation-Based Tests that Can Use Any Number of Simulations

Conventional procedures for Monte Carlo and bootstrap tests require that B, the number of simulations, satisfy a specific relationship with the level of the test. Otherwise, a test that would instead be exact will either overreject or underreject for finite B. We present expressions for the rejection frequencies associated with existing procedures and propose a new procedure that yields exact Monte Carlo tests for any positive value of B. This procedure, which can also be used for bootstrap tests, is likely to be most useful when simulation is expensive.     

A Metropolis algorithm to obtain co-sufficient samples with applications in conditional tests

ABSTRACT

Conditional tests are constructed by conditioning a fit measure to a minimal sufficient statistic. To calculate the p-value of these tests, Monte Carlo methods with co-sufficient samples can be used. In this paper we show how to simulate co-sufficient samples when the data distribution belongs to the exponential family with doubly transitive sufficient statistics. The proposed method is illustrated using the beta distribution.     

A correlation type procedure for assessing multivariate normality

A correlation-type statistic for assessing multivariate normality is described. Its estimated finite sample distribution is tabulated, and its performance against certain alternatives is compared with that of a competing Cramer-von Mises type statistic in a Monte Carlo power study. A set of quadrivariate data is examined as illustration of the procedure.     

On sequential closed testing dose groups with a control

Methods for a sequential test of a dose-response effect in pre-clinical studies are investigated. The objective of the test procedure is to compare several dose groups with a zero-dose control. The sequential testing is conducted within a closed family of one-sided tests. The procedures investigated are based on a monotonicity assumption. These closed procedures strongly control the familywise error rate while providing information about the shape of the dose-responce relationship. Performance of sequential testing procedures are compared via a Monte Carlo simulation study. We illustrae the procedures by application to a real data set.     

Diagnostic tests for the distribution of random effects in multivariate mixed effects models

Abstract

Fourier methods are proposed for testing the distribution of random effects in classical and robust multivariate mixed effects models. The test statistics involve estimation of the characteristic function of random effects. Theoretical and computational issues are addressed while Monte Carlo results show that the new procedures compare favorably with other methods.