# William ConoverTexas Tech University | TTU · Department of Mathematics and Statistics

William Conover

PhD

## About

90

Publications

32,085

Reads

**How we measure 'reads'**

A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more

39,359

Citations

Citations since 2016

## Publications

Publications (90)

We propose a distribution‐free cumulative sum (CUSUM) chart for joint monitoring of location and scale based on a Lepage‐type statistic that combines the Wilcoxon rank sum and the Mood statistics. Monte Carlo simulations were used to obtain control limits and examine the in‐control and out‐of‐control performance of the new chart. A direct compariso...

To maintain the desired quality of a product or service it is necessary to monitor the process that results in the product or service. This monitoring method is called Statistical Process Management, or Statistical Process Control. It is in widespread usage in industry. Extensive statistical methodology has been developed to make it possible to det...

Tests for equality of variances using independent samples are widely used in data analysis. Conover et al. [A comparative study of tests for homogeneity of variance, with applications to the outer continental shelf bidding data. Technometrics. 1981;23:351–361], won the Youden Prize by comparing 56 variations of popular tests for variance on the bas...

A nonparametric control chart for variance is proposed. The chart is constructed following the change-point approach through the recursive use of the squared ranks test for variance. It is capable of detecting changes in the behaviour of individual observations with performance similar to a self-starting CUSUM chart for scale when normality is assu...

Quantile estimation is a problem presented in fields such as quality control, hydrology, and economics. There are different techniques to estimate such quantiles. Nevertheless, these techniques use an overall fit of the sample when the quantiles of interest are usually located in the tails of the distribution. Regression Approach for Quantile Estim...

The sequential analysis of series often requires nonparametric procedures, where the most powerful ones frequently use rank transformations. Reranking the data sequence after each new observation can become too intensive computationally. This led to the idea of sequential ranks, where only the most recent observation is ranked. However, difficultie...

Capability analysis corresponds to a set of methods used to estimate and test the ability of an in-control process to provide a specific output. When there is only one quality characteristic that behaves as a continuous random variable, indices like C
p and C
pk can be used to measure how well requirements are met. Under normality, variation is ind...

To improve a system, from a statistical process control approach, tools from the field of design and analysis of experiments might be used. Within this field, experimental and observational studies address the issue of finding causal relationships between potential factors and response variables. To collect data, experimental design techniques are...

The rank transformation refers to replacing the data by their ranks, or average ranks in case of ties, prior to performing standard statistical procedures on the ranks. There are several forms of transforming the data to ranks. RT-1 refers to ranking all of the data together, and giving the smallest observation the rank 1, the second smallest the r...

Students learn to examine the distributional assumptions implicit in the usual t-tests and associated confidence intervals, but are rarely shown what to do when those assumptions are grossly violated. Three data sets are presented. Each data set involves a different distributional anomaly and each illustrates the use of a different nonparametric te...

Statistical methods that do not rely on the assumption of a known population probability distribution function for their validity are called Distribution-free Statistical Methods (also called nonparametric statistical methods). This includes many methods for presenting statistics in graphs, such as histograms, cumulative distribution functions, cor...

The procedure of statistical discrimination is simple in theory but not so simple in practice. An observation x/sub approx.O/, possible multivariate, is to be classified into one of several populations ..pi..â,...,..pi../sub k/, which have, respectively, the density functions fâ(x),...,f/sub k/(x). The decision procedure is to evaluate each densi...

Four examples are given to illustrate the ease and practicality of the procedure for finding locally most powerful rank tests for correlation. The first two examples deal with bivariate exponential models. The third example uses the bivariate normal distribution, and the fourth example analyzes the Morgenstern's general correlation model.

When using parametric empirical Bayes estimation methods for estimating the binomial or Poisson parameter, the validity of the assumed beta or gamma conjugate prior distribution is an important diagnostic consideration. Chi-square goodness-of-fit tests of the beta or gamma prior hypothesis are developed for use when the binomial sample sizes or Poi...

In Balanced Incomplete Block Designs the presence of outliers in the data not only indicate non-normality, so that classical methods of analysis on the data are inappropriate, but also diminish the power of classical methods of analysis that assume normality of the data. One alternative is to use Durbin's nonparametric test. This research examined...

The treatment and the solution of health economic problems by using management concepts is a permanent challenge; the question of control ling the costs or the efficiency of the supply of medical services is concerned. The articles in this book hope to make a concrete contri bution to this subject by reporting on the latest research the authors hav...

Two two-parameter models are developed for testing the hypothesis of no treatment effect against the alternative that a subset of the treated patients will show an improvement. To keep the range of measurements the same for treated and control patients, Lehmann alternatives are used in both models. Locally most powerful rank tests are developed for...

An algorithm is presented for computing an exact nonparametric interval estimate of the slope parameter in a simple linear regression model. The confidence interval is obtained by inverting the hypothesis test for slope that uses Spearman's rho. This method is compared to an exact procedure based on Kendall's tau. The Spearman rho procedure will ge...

Many situations exist in which n objects are ranked by two or more independent sources, where interest centers primarily on agreement in the top rankings and disagreements on items at the bottom of the rankings are of little or no importance. A problem with Spearman's rho or Kendall's coefftcient of concordance in this setting is that they are equa...

The Friedman test (or sign test when k = 2) depends entirely on within-block rankings. In a recent paper, Quade (1979) attempted to provide a test with more power than the Friedman test by considering a k-sample extension of the Wilcoxon signed ranks test. This is done by taking advantage of the between-block information. A third way to approach th...

The limiting null distribution of the usual F statistic for main effects in the two-way layout is shown to have the same limiting distribution when applied to ranks and scores based on ranks as when applied to normal data. The limit is taken as the cell size N increases without bound. The denominator of the F statistic times (J − 1)/J is shown to p...

The rank transformation refers to the replacement of data by their ranks, with a subsequent analysis using the usual normal theory procedure, but calculated on the ranks rather than on the data. Rank transformation procedures have previously been shown by the authors to have properties of robustness and power in both regression and analysis of vari...

A method for inducing a desired rank correlation matrix on a multivariate input random variable for use in a simulation study is introduced in this paper. This method is simple to use, is distribution free, preserves the exact form of the marginal distributions on the input variables, and may be used with any type of sampling scheme for which corre...

Many of the existing parametric and nonparametric tests for homogeneity of variances, and some variations of these tests, are examined in this paper. Comparisons are made under the null hypothesis (for robustness) and under the alternative (for power). Monte Carlo simulations of various symmetric and asymmetric distributions, for various sample siz...

Many of the more useful and powerful nonparametric procedures may be presented in a unified manner by treating them as rank transformation procedures. Rank transformation procedures are ones in which the usual parametric procedure is applied to the ranks of the data instead of to the data themselves. This technique should be viewed as a useful tool...

A method for inducing a desired rank correlation matrix on a multivariate input random variable is introduced in this paper. This method is simple to use, is distribution free, preserves the exact form of the marginal distributions on the input variables, and may be used with any type of sampling scheme for which correlation of input variables is a...

As modeling efforts expand to a broader spectrum of areas the amount of computer time required to exercise the corresponding computer codes has become quite costly. This costly process can be directly tied to the complexity of the modeling, which makes the relationships among the input variables not mathematically tractable. In this setting it is d...

As modeling efforts expand to a broader spectrum of areas the amount of computer time required to exercise the corresponding computer codes has become quite costly (several hours for a single run is not uncommon). This costly process can be directly tied to the complexity of the modeling and to the large number of input variables (often numbering i...

The rank transform is a simple procedure which involves replacing the data with their corresponding ranks. The rank transform has previously been shown by the authors to be useful in hypothesis testing with respect to experimental designs. This study shows the results of using the rank transform in regression. Two sets of data given by Daniel and W...

A Lilliefors test of normality has been applied to data from precision and accuracy studies. Most data sets tested as non-normal. Simulation studies showed that the test is extremely sensitive to the rounded, narrowly distributed data that are typical of method performance studies in clinical chemistry. The Lilliefors test can be modified to be app...

When a two-dimensional map contains points that appear to be scattered somewhat at random, a question that often arises is whether groups of points that appear to cluster are merely exhibiting ordinary behavior that one can expect with any random distribution of points, or whether the clusters are too pronounced to be attributable to chance alone....

Two types of sampling plans are examined as alternatives to simple random sampling in Monte Carlo studies. These plans are shown to be improvements over simple random sampling with respect to variance for a class of estimators that includes the sample mean and the empirical distribution function. 6 figures.

Two types of sampling plans are examined as alternatives to simple random sampling in Monte Carlo studies. These plans are shown to be improvements over simple random sampling with respect to variance for a class of estimators which includes the sample mean and the empirical distribution function.

Eight nonparametric tests are examined in a small-sample setting. Their power functions are compared with the locally most powerful (LMP) linear rank test, primarily to see over which range the LMP test retains good power. All tests are two-sample tests, the populations are governed by the double exponential distribution, and the sample sizes are m...

Exact tables for Spearman’s rho are available only for n ≤ 16 and no ties in the data. Some accurate methods of approximating the distribution with no ties present have been used to obtain approximate tables for larger values of n. Often ties are present in the data so these tables are no longer exact. Also sometimes the tables are not conveniently...

Since the squared ranks test was first proposed by Taha in 1964 it has been mentioned by several authors as a test that is easy to use, with good power in many situations. It is almost as easy to use as the Wilcoxon rank sum test, and has greater power when two populations differ in their scale parameters rather than in their location parameters. T...

The power of some rank tests, used for testing the hypothesis of shift, is found when the underlying distributions contain outliers. The outliers are assumed to occur as the result of mixing two normal distributions with common variance. A small sample case shows how the scores for the rank tests are found and the exact power is computed for each o...

There are several rank tests for analyzing certain experimental designs. This study compares the robustness and power of several of these, including the rank transform, aligned ranks, and joint rank sum procedures. The experimental designs studied include the two-way layout with n = 2 and n = 5 observations per cell, the two-way layout with unequal...

Two types of sampling plans are presented as alternatives to simple random sampling in Monte Carlo studies. These plans are shown to be improvements over simple random sampling with respect to the variance of a class of estimators which includes the sample mean and the sample cumulative distribution function. The partial rank correlation coefficien...

The asymptotic efficiencies are computed for several popular two sample rank tests when the underlying distributions are Poisson, binomial, discrete uniform, and negative binomial The rank tests examined include the Mann-Whitney test, the van der Waerden test, and the median test. Three methods for handling ties are discussed and compared. The comp...

The analysis of data from eseperisental designs is often hampered by the lack of more than one procedure available for the analysis, especially when that procedure is based on assumptions which do not apply in the situation at hand. In this paper tvo classes of alternative procedures are discussed and compared, One is the aligned ranks procedure wh...

In a contingency table with fixed marginal totals, and with row totals or column totals equal to each other, the Yates correction and the Kendall-Stuart correction for continuity improve estimates of the unknown probabilities. Otherwise only the Kendall-Stuart correction may be relied on to improve estimates over the chi-square approximation to the...

Preface.Preface to the Second Edition.Preface to the First Edition.1. An Introduction to Applied Probability.2. Statistical Inference for a Single Proportion.3. Assessing Significance in a Fourfold Table.4. Determining Sample Sizes Needed to Detect a Difference Between Two Proportions.5. How to Randomize.6. Comparative Studies: Cross-Sectional, Nat...

In a contingency table one classification often corresponds to samples from different populations and the other classification to ordered categories. Methods for analyzing data of this type may be compared using recent extensions in the theory of rank tests by Conover (1973) and Vorlickova (1970) to non-continuous distributions. In this paper the K...

Pseudo random numbers were drawn from a variety of Poisson distributions to see how several popular two-sample tests might be affected by the presence of ties in the data. Nearly all tests were conservative under the null hypothesis, with actual α levels averaging about 1.5% less than the nominal α levels. Under various alternative hypotheses, the...

Formulas are given for asymptotic efficiency of the Wilcoxon signed-rank test under several alternative ways of handling ties. Two methods of handling ties at zero, one suggested by Wilcoxon and the other by Pratt, are compared on the basis of their asymptotic efficiencies. Each method is shown to be better than the other in some situations. Two ex...

The theory of rank tests has been developed primarily for continuous random variables. Recently the asymptotic theory of linear rank tests has been extended to include purely discrete random variables under the null hypothesis of randomness (including the two-sample and $k$-sample problems) and under contiguous alternatives, for the two methods of...

The Kolmogorov goodness-of-fit test is known to be conservative when the hypothesized distribution function is not continuous. A method for finding the exact critical level (approximate in the two-sided case) and the power in such cases is derived. Thus the Kolmogorov test may be used as an exact goodness-of-fit test for all completely specified di...

Investment decisions in water resources planning depend on estimation of
unknown parameters. The Bayesian approach to estimation involves use of
the estimator that minimizes the expected risk, where risk is the
expected loss. Bayes' estimators may be used in a wide variety of
situations for which probabilistic models have been specified. In an
exam...

/ '^ 9 § ,ACKNOWLEDGMENTS Since childhood,my parents,have,supported,and encouraged,m\ efforts in all the activities that I chose. Knowing,that no matter what,I did I would be supported, I have done things that I did not think I could do. This paper is m\ first milestone,toward,a professional career,and,I have my parents,to thank for it. I also have...

Some of the more popular multiple-comparisons procedures are discussed and compared. Some new nonparametric methods are introduced. One procedure is an analog to the Fisher's least-significant-difference method for the completely randomized design. Some simulation studies indicate this procedure is a reasonable nonparametric method to use. A summar...

Two types of sampling plans are presented as alternatives to simple random sampling in Monte Carlo studies. These plans are shown to be improvements over simple random sampling with respect to the variance of a class of estimators which includes the sample mean and the sample cumulative distribution function. The partial rank correlation coefficien...

Three examples involving multivariate data are presented in which a regression analysis on the ranks of the data yields useful information concerning the selection of the best set of independent variables. This method of analysis is compared with ordinary regression of independent variables, and the regression analysis on ranks appears to have two...

Several types of statistical analyses are reported on the bidding data for offshore oil leases in the five sales from 1954 to 1967, in an attempt to obtain a method for identifying leases that become productive. These methods include using standardized variables, nonstandardized variables, stepwise regression on the variables, stepwise regression o...

Two nonparametric tests are presented for analyzing data from a one-way layout. Their principal characteristic is ease in computation. One test is intended for k samples of equal size n, and the other is for k samples of possibly unequal sample sizes. Both tests may be regarded as generalizations of Mosteller's slippage test. Multiple decision aspe...

Tsao (1954) deficumulative distribution function $S_n(x) = k/n$ if $X_k \leqq x < X_{k + 1}$, where $X_0 = -\infty$ and $X_{n + 1} = \infty$. Let $Y_1 < Y_2 < \cdots < Y_m$ represent an ordered random sample from the continuous distribution function $G(x)$, with the empirical cumulative distribution function $S'_m (x)$. As test statistics for testi...

Presented here is a new $k$-sample model in order statistics, in which $k$ random samples of equal size are first ordered within themselves in the usual manner, and are then ordered among themselves by considering the size of the maximum value in each sample. The distribution functions and several probabilities relevant to the model are derived. Co...

A statistical model of turbulence for two-dimensional uniform flow in open channels is developed, and this model is used to derive the vertical velocity profile. This profile is defined by a three-parameter hyperbolic function, with two parameters reflecting the effect of bed roughness and fluid viscosity on the shape of the profile. The third para...

## Projects

Project (1)