Efficacy of Statistical Outlier Analysis for Monitoring Quality of Care

Researchers have proposed that hospitals with excessive statistically unexplained mortality rates are more likely to have quality-of-care problems. The U.S. Health Care Financing Administration currently uses this statistical “outlier” approach to screen for poor quality in hospitals. Little is known, however, about the validity of this technique, since direct measures of quality are difficult to obtain. We use Monte Carlo methods to evaluate the performance of the outlier technique as parameters of the true mortality process are varied. Results indicate that the screening ability of the technique may be very sensitive to how widespread quality-related mortality is among hospitals but insensitive to other factors generally thought to be important.     

On Response Surface Methodology and its Computer-Assisted Teaching

Since the teaching of response surface methodology involving the steepest ascent (descent) method requires a fair amount of instructor and student time even to complete one analysis, the routine aspects of the method were computerized. Flowcharts that contain the logic of first- and second-order experimentation to reach optimum conditions were also developed.     

Use of the Correlation Coefficient with Normal Probability Plots

The use of the correlation coefficient is suggested as a technique for summarizing and objectively evaluating the information contained in probability plots. Goodness-of-fit tests are constructed using this technique for several commonly used plotting positions for the normal distribution. Empirical sampling methods are used to construct the null distribution for these tests, which are then compared on the basis of power against certain nonnormal alternatives. Commonly used regression tests of fit are also included in the comparisons. The results indicate that use of the plotting position p_i = (i - .375)/(n + .25) yields a competitive regression test of fit for normality.     

Manipulating Statistical Hypotheses and Tests as Boolean Functions

Statistical hypotheses and test statistics are Boolean functions that can be manipulated using the tools of Boolean algebra. These tools are particularly useful for exploring multiple comparisons or simultaneous inference theory, in which multiparameter hypotheses or multiparameter test statistics may be decomposed into combinations of uniparameter hypotheses or uniparameter tests. These concepts are illustrated with both finite and infinite decompositions of familiar multiparameter hypotheses and tests. The corresponding decompositions of acceptance regions and rejection regions are also shown. Finally, the close relationship between hypothesis and test decompositions and Roy's union—intersection principle is demonstrated by a derivation of the union—intersection test of the univariate general linear hypothesis.     

Multiple Comparison Procedures: The Practical Solution

A practicing statistician looks at the multiple comparison controversy and related issues through the eyes of the users. The concept of consistency is introduced and discussed in relation to five of the more common multiple comparison procedures. All of the procedures are found to be inconsistent except the simplest procedure, the unrestricted least significant difference (LSD) procedure (or multiple t test). For this and other reasons the unrestricted LSD procedure is recommended for general use, with the proviso that it should be viewed as a hypothesis generator rather than as a method for simultaneous hypothesis generation and testing. The implications for Scheffé's test for general contrasts are also discussed, and a new recommendation is made.     

Editor's Report

There are two common methods for statistical inference on 2 × 2 contingency tables. One is the widely taught Pearson chi-square test, which uses the well-known χ²statistic. The chi-square test is appropriate for large sample inference, and it is equivalent to the Z-test that uses the difference between the two sample proportions for the 2 × 2 case. Another method is Fisher’s exact test, which evaluates the likelihood of each table with the same marginal totals. This article mathematically justifies that these two methods for determining extreme do not completely agree with each other. Our analysis obtains one-sided and two-sided conditions under which a disagreement in determining extreme between the two tests could occur. We also address the question whether or not their discrepancy in determining extreme would make them draw different conclusions when testing homogeneity or independence. Our examination of the two tests casts light on which test should be trusted when the two tests draw different conclusions.     

k-POD: A Method for k-Means Clustering of Missing Data

The k-means algorithm is often used in clustering applications but its usage requires a complete data matrix. Missing data, however, are common in many applications. Mainstream approaches to clustering missing data reduce the missing data problem to a complete data formulation through either deletion or imputation but these solutions may incur significant costs. Our k-POD method presents a simple extension of k-means clustering for missing data that works even when the missingness mechanism is unknown, when external information is unavailable, and when there is significant missingness in the data.

[Received November 2014. Revised August 2015.]     

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.     

Exponentiality test based on Renyi distance between equilibrium distributions

ABSTRACT

On the basis of Csiszar's φ-divergence discrimination information, we propose a measure of discrepancy between equilibriums associated with two distributions. Proving that a distribution can be characterized by associated equilibrium distribution, a Renyi distance of the equilibrium distributions is constructed that made us to propose an EDF-based goodness-of-fit test for exponential distribution. For comparing the performance of the proposed test, some well-known EDF-based tests and some entropy-based tests are considered. Based on the simulation results, the proposed test has better powers than those of competing entropy-based tests for the alternatives with decreasing hazard rate function. The use of the proposed test is evaluated in an illustrative example.     

The modified permutation entropy-based independence test of time series

Abstract

In time series, it is essential to check the independence of data by means of a proper method or an appropriate statistical test before any further analysis. Therefore, among different independence tests, a powerful and productive test has been introduced by Matilla-García and Marín via m-dimensional vectorial process, in which the value of the process at time t includes m-histories of the primary process. However, this method causes a dependency for the vectors even when the independence assumption of random variables is considered. Considering this dependency, a modified test is obtained in this article through presenting a new asymptotic distribution based on weighted chi-square random variables. Also, some other alterations to the test have been made via bootstrap method and by controlling the overlap. Compared with the primary test, it is obtained that not only the modified test is more accurate but also, it possesses higher power.