W. J. Conover

Practical Nonparametric Statistics

A self-contained introduction to the theory and methods of non-parametric statistics. Presents a review of probability theory and statistical inference and covers tests based on binomial and multinomial distributions and methods based on ranks and empirical distributions. Includes a thorough collection of statistics tables, hundreds of problems and references, detailed numerical examples for each procedure, and an instant consultant chart to guide the student to the appropriate procedure.

A comparison of three methods for selecting values of input variables in the analysis of output from a computer code

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.

Rank Transformations as a Bridge between Parametric and Nonparametric Statistics

Abstract 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 for developing nonparametric procedures to solve new problems.

A distribution-free approach to inducing rank correlation among input variables

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 correlation of input variables is a meaningful concept. A Monte Carlo study provides an estimate of the bias and variability associated with the method. Input variables used in a model for study of geologic disposal of radioactive waste provide an example of the usefulness of this procedure. A textbook example shows how the output may be affected by the method presented in this paper.

A Comparative Study of Tests for Homogeneity of Variances, with Applications to the Outer Continental Shelf Bidding Data

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 sizes, reveal a few tests that are robust and have good power. These tests are further compared using data from outer continental shelf bidding on oil and gas leases.

Small sample sensitivity analysis techniques for computer models.with an application to risk assessment

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 desired to perform sensitivity studies of the input-output relationships. A variety of situations require that decisions and judgments be made in the face of uncertainty, such as lack of knowledge about probability distributions associated with input variables, different hypothesized future conditions, or different strategies associated with a decision making process. In this paper a generalization of Latin hypercube sampling is given that allows these areas to be investigated without making additional computer runs.

The Use of the Rank Transform in Regression

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 Wood [8] are considered for purposes of illustrating the rank transform in simple and multiple regression. Also given are the results of a Monte Carlo study which compares regression on ranks with some published Monte Carlo results on isotonic regression. This Monte Carlo study is also modified to compare regression on ranks with robust regression. Another illustration gives the results of analyses on large computer codes by regression on ranks. The rank transform is a simple, repeatable process that compares favorably with other methods such as given by Andrews [1]. Our studies indicate the method works quite well on monotonic data.

On some alternative procedures using ranks for the analysis of experimental designs

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 which first standardises the data by subtracting an appropriate estimate of location, then replaces the data with ranks t and finally uses an appropriate test statistic which has asymptotically a chi-square distribution The second procedure is the rank transform which first replaces all of the data with the ranks, and then employs the usual parametric methods, but computed on the ranks instead of the data Some Monte Carlo simulations for a test of interaction in a two way layout with replication enable the robustness and pover of these tvo methods to be compared with the usual analysis of variancs.

A Kolmogorov Goodness-of-Fit Test for Discontinuous Distributions

Abstract 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 distribution functions, whether continuous or not continuous. Several examples of the application of this extension of the Kolmogorov test are also included.

A measure of top-down correlation

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 Spearmans rho or Kendalls coefftcient of concordance in this setting is that they are equally influenced by disagreement on the assignment of rankings at all levels. In this article, a concordance measure is provided that is more sensitive to agreement on the top rankings. The statistics used in this setting are functions of the ordinary correlation coeRicient computed on Savage (1956) scores. The asymptotic distributions of these statistics are presented, and a summary of the quantiles of the exact distribution for the two sample case are provided for n = 3(1)14. The statistic for the two-sample case is shown to provide a locally most powerful rank test for a model given by Hajek and Sidak (1967).