Showing papers on "Nonparametric statistics published in 1979"

Applied statistics for the behavioral sciences

Abstract: This introductory text provides students with a conceptual understanding of basic statistical procedures, as well as the computational skills needed to complete them. The clear presentation, accessible language, and step-by-step instruction make it easy for students from a variety of social science disciplines to grasp the material. The scenarios presented in chapter exercises span the curriculum, from political science to marketing, so that students make a connection between their own area of interest and the study of statistics. Unique coverage focuses on concepts critical to understanding current statistical research such as power and sample size, multiple comparison tests, multiple regression, and analysis of covariance. Additional SPSS coverage throughout the text includes computer printouts and expanded discussion of their contents in interpreting the results of sample exercises. 1. Introduction. 2. Organizing and Graphing Data. 3. Describing Distributions: Individual Scores, Central Tendency, and Variation. 4. The Normal Distribution. 5. Correlation: A Measure of Relationship. 6. Linear Regression: Prediction. 7. Sampling, Probability, and Sampling Distributions. 8. Hypothesis Testing: One-Sample Case for the Mean. 9. Estimation: One-Sample Case for the Mean. 10. Hypothesis Testing: One-Sample Case for Other Statistics. 11. Hypothesis Testing: Two-Sample Case for the Mean. 12. Hypothesis Testing: Two-Sample Case for Other Statistics. 13. Determining Power and Sample Size. 14. Hypothesis Testing, K-Sample Case: Analysis of Variance, One-Way Classification. 15. Multiple-Comparison Procedures. 16. Analysis of Variance, Two-Way Classification. 17. Linear Regression: Estimation and Hypothesis Testing. 18. Multiple Linear Regression. 19. Analysis of Covariance. 20. Other Correlation Coefficients. 21. Chi-Square (X2) Tests for Frequencies. 22. Other Nonparametric Tests.

A Non-Parametric Approach to the Change-Point Problem

Abstract: Non‐parametric techniques are introduced for the change‐point problem. Exact and approximate results are obtained for testing the null hypothesis of no change. The methods are illustrated by the analysis of three sets of data illustrating the techniques for zero–one observations, Binomial observations and continuous observations. Some comparisons are made with methods based on cusums.

Robust Estimation of Population Size When Capture Probabilities Vary Among Animals

Abstract: A model is given for multiple recapture studies on closed populations which allows capture probabilities to vary among individuals. The capture probability of each individual is assumed to be constant over time. Based on this model we give a nonparametric estimation procedure for population size. The estimator involves selecting one of a sequence of estimators which are each linear combinations of the capture frequencies. The individual estimators are derived from the generalized jackknife method. We also give a goodness of fit test for the model's assumption that individual capture probabilities do not change during the study. The robustness of this estimation procedure is investigated with a simulation study. By virtue of this study, and the theoretical nature of the estimator, it is judged to be robust to moderate variations in individual capture probabilities which may occur in commonly used short—term livetrapping studies. See full-text article at JSTOR

Computers and the Theory of Statistics: Thinking the Unthinkable

Abstract: This is a survey article concerning recent advances in certain areas of statistical theory, written for a mathematical audience with no background in statistics. The topics are chosen to illustrate a special point: how the advent of the high-speed computer has affected the development of statistical theory. The topics discussed include nonparametric methods, the jackknife, the bootstrap, cross-validation, error-rate estimation in discriminant analysis, robust estimation, the influence function, censored data, the EM algorithm, and Cox’s likelihood function. The exposition is mainly by example, with only a little offered in the way of theoretical development.

A Non-parametric Approach to the Change-point Problem

Abstract: SUMMARY Non-parametric techniques are introduced for the change-point problem. Exact and approximate results are obtained for testing the null hypothesis of no change. The methods are illustrated by the analysis of three sets of data illustrating the techniques for zero-one observations, Binomial observations and continuous observations. Some comparisons are made with methods based on CUSUMS.

Introduction to the theory of nonparametric statistics

Abstract: Distribution-Free Statistics. Power Functions and Their Properties. Asymptotic Relative Efficiency of Tests. Confidence Intervals and Bounds. Point Estimation. Linear Rank Statistics Under the Null Hypothesis. Two-Sample Location and Scale Problems. The One-Sample Location Problem. Additional Methods for Constructing Distribution-Free Procedures. Other Important Problems. Appendix. Index.

Nonparametric Statistical Data Modeling

Abstract: This article attempts to describe an approach to statistical data analysis which is simultaneously parametric and nonparametric. Given a random sample X 1, …, X n of a random variable X, one would like (1) to test the parametric goodness-of-fit hypothesis H 0 that the true distribution function F is of the form F(x) = F0[(x − μ)/σ)], where F 0 is specified, and (2) when H 0 is not accepted, to estimate nonparametrically the true density-quantile function fQ(u) and score function J(u) = − (fQ)'(u). The article also introduces density-quantile functions, autoregressive density estimation, estimation of location and scale parameters by regression analysis of the sample quantile function, and quantile-box plots.

Applied Nonparametric Statistics

Abstract: Cengage Learning, 2000. Book Condition: New. Brand New, Unread Copy in Perfect Condition. A+ Customer Service! Summary:

Using Weighted Rankings in the Analysis of Complete Blocks with Additive Block Effects

Abstract: The standard nonparametric procedures for testing the hypothesis of no treatment effects in a complete blocks experiment depend entirely on the within-block rankings. If block effects are assumed additive, however, then between-block information may be recovered by weighting these rankings according to their credibility with respect to treatment ordering. (For the special case of only two treatments, the sign test exemplifies use of unweighted rankings and the signed-rank test weighted.) A general family of weighted-rankings test statistics for comparing two or more treatments is presented. They are simple to compute, are strictly distribution free, and have asymptotic chi-squared distributions.

Procedures for Determining the Parameters of the First-Order Canonical Models of Class A and Class B Electromagnetic Interference [10]

Abstract: Simple approximate methods as well as various more precise, analytical procedures for determining the first-order parameters of both the approximate and exact Class A and B noise models are derived and illustrated for both the ideal case of infinite sample data and the practical cases of finite data samples. It is shown that all first-order parameters of these models can, in principle, be obtained, exactly or approximately, from the ideal or practical measurements. (All first-order parameters of Class A but only the (first-order) even moments of the Class B models are exactly obtainable in the ideal cases.) Procedures for establishing meaningful measures of the accuracy of the parameter estimates in the practical cases are also identified: these include suitably adjusted, nonparametric, small-sample tests of " goodness-of-fit" (such as Kolmogorov-Smirnov tests), which provide the principal techniques for establishing accuracy, at an appropriately selected significance level (?0). Questions of robustness and stability of the models, parameters, and their estimators are also discussed.

Goodness-of-fit test statistics that dominate the Kolmogorov statistics

Abstract: Two statistics are proposed for the simple goodness-of-fit problem. These are derived from a general principle for combining dependent test statistics that has been discussed elsewhere by the authors. It is shown that these statistics are relatively optimal in the sense of Bahadur efficiency and consequently, are more efficient than any weighted Kolmogorov statistic at every alternative. A curious pathology occurs: Under certain alternatives, the sequence of statistics has a Bahadur efficacy or exact slope only in the weak sense of convergence in law.

A Nonparametric Procedure for Process Control Based on Within-Group Ranking

Abstract: A nonparametric procedure is developed for the problem of quickly detecting any shift in the mean of a sequence of observations from a specified control value. The proposed procedure is based on Wilcoxon signed-rank statistics where ranking is within groups. A cumulative sum control chart type stopping rule is used with the Wilcoxon statistics. Using a Markov chain approach, the average run length of the procedure can be computed exactly for any distribution for which the distribution of the Wilcoxon signed-rank statistic is known. The procedure has the same average run length for any continuous distribution which is symmetric about the control value.

The Use of Chi-squared Statistics for Categorical Data Problems

Abstract: SUMMARY The use of x2 statistics for categorical data problems was initiated by Karl Pearson, but it took several years before the asymptotic distribution of these statistics was well understood. The general structure of asymptotic results for x2 statistics is reviewed and the applicability of the general structure to a variety of problems of practical interest is discussed. These problems include the use of x2 statistics in small-sample situations and in large sparse tables, in cluster sampling, and in cases where they do not have asymptotic x2 distributions.

An introduction to business statistics

Abstract: This chapter presents a brief introduction of business statistics. The word statistics was originally applied to the collection of numerical facts by the State. More recently, the meaning of statistics has broadened to include not only a set of numerical data, but also the processes used in the collection, presentation, analysis, and interpretation of these data. It is convenient to divide statistics into two parts: (1) descriptive statistics and (3) analytical statistics. Sources can be biased. This means that instead of the statistics being completely objective, some subjective consideration causes them to lean in a particular direction. The things that statisticians seek to measure—height, weight, wages, unemployment, prices, etc.—are known as variables. As the term implies, variables are studied because some variation in their value is anticipated. Variables are divided into two types: discrete variables and continuous variables. Primary statistics are collected by the investigator when he searches out new information. Secondary statistics are those which an investigator obtains from other sources.

Nonparametric flow cytometry analysis.

Abstract: A nonparametric statistical test for the analysis of flow cytometry derived histograms is presented. The method involves smoothing and translocation of data, area normalization, channel by channel determination of the mean and S.D., and use of Bayes' theorem for unknown histogram classification. With this statistical method, different sets of histograms from numerous biological systems can be compared.

A Measure of Association for Nonparametric Statistics

Abstract: A number of x2 based nonparametric tests are used to determine the level of statistical significance. Once the significance level is determined with x2, Cramer's V can be used to measure the strength of association. Values for the maximum possible x2 are given for six nonparametric tests in order to facilitate the computation of an extension of V denoted as V'. An example is given where V' is applied to a one-way analysis of variance test for ranked data. Chi square based measures of association have been applied almost exclusively to nominal level contingency tables. The most often used x2 based measure of association is Cramer's

Multiple-comparisons procedures. Informal report

Abstract: 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 summary description is given for other nonparametric methods, which may be used with the completely randomized or randomized blocks designs. 3 tables.

Sequential point estimation of estimable parameters based on u-statistics

Abstract: Asymptotically risk-efficient sequential point estimation of regular functionals of distribution functions based on U-statistics is considered under appropriate regularity conditions. Some auxiliary results on U-statistics are also considered in this context.

A nonparametric measure of intraclass correlation

Abstract: A nonparametric measure of intraclass correlation based on the probability of certain types of concordances among the observations and which can be estimated from ranked data is proposed. One estimator whose variance can be estimated in an unbiased way is shown to be asymptotically normally distributed. Properties of the measure and its estimator are studied for a normal model; in particular the method is shown to provide a relatively powerful test of the null hypothesis of zero intraclass correlation in a normal population. The intraclass correlation coefficient is often used as a measure of the degree to which individuals from the same family resemble one another in some variable such as height or weight. From a random sample of families and a random selection of individuals from each family, both the between and within family components of variance can be estimated and an estimate of the intraclass correlation obtained. When the observations are ranks this approach is not feasible since direct estimates of the components of variance are not available. An example occurs in a study of aggressiveness in male red grouse (Moss, Watson & Parr, 1974). One measure of aggressiveness of an individual bird is a dominance rank, the position of that bird in the dominance hierarchy of a given group of birds. Comparison of the degree of familial resemblance in different populations is complicated by the fact that the data are ranks and that dominance hierarchies can be variable in size with different family sizes. The development of standard test statistics, such as the Kruskal-Wallis statistic (Kruskal, 1952), as measures of intraclass correlation is unsatisfactory because of the complicated dependence on the structure of the sample; see ? 6. In this paper a measure of intraclass correlation is proposed which overcomes this problem. It is independent of the structure of the sample and it can be estimated in an unbiased way from ranked data. The interclass rank correlation coefficients, Kendall's Xr and Spearman's p (Kendall, 1955), can be interpreted in terms of probabilities of concordances among the observations from a bivariate distribution. In response to Hill (1974), Kerridge (1975) has used this probabilistic interpretation of r in an analysis of Football League results. The measure presented in the present paper is based on concordances among observations from a population in which individuals occur in families. Its properties for a general class of populations are discussed and some particular results for a one-way classification model with normally distributed effects are presented. The power of the associated test is assessed for a normal model for a range of sample structures.

A Nonparametric Approach to Accelerated Life Testing

Abstract: A nonparametric model of acceleration is introduced. Based on this model, a procedure is suggested for estimating the nonaccelerated life distribution from accelerated observations. Unlike previous nonparametric estimation procedures, our method does not require nonaccelerated observations. A relationship between the accelerated and the nonaccelerated distributions is assumed but there is variety in that choice. A comparison of our method with the power rule method under the assumption of exponential lifetimes reveals that in some instances our method is asymptotically equivalent to the maximum likelihood method for estimating the nonaccelerated mean lifetime. Simulation for small sample sizes completes the comparison.

Test Theory without True Scores

Abstract: This paper traces the course of the consequences of viewing test responses as simply providing dichotomous data concerning ordinal relations. It begins by proposing that the score matrix is best considered to be items-plus-persons by items-plus-persons, and recording the wrongs as well as the rights. This shows how an underlying order is defined, and was used to provide the basis for a tailored testing procedure. It also was used to define a number of measures of test consistency. Test items provide person dominance relations, and the relations provided by one item can be in one of three relations with a second one: redundant, contradictory, or unique. Summary statistics concerning the number of relations of each kind are easy to get and provide useful information about the test, information which is related to but different from the usual statistics. These concepts can be extended to form the basis of a test theory which is based on ordinal statistics and frequency counts and which invokes the concept of true scores only in a limited sense.

Nonparametric Prediction Intervals for a Future Sample Median

Abstract: In this article distribution-free prediction intervals for a future sample median are discussed. Large-sample normal approximations to the coverage probabilities are presented. Asymptotic relative efficiency comparisons are made between the distribution-free procedures and analogous parametric prediction intervals, the resulting values demonstrating the good properties of the nonparametric prediction intervals.

Ordinal data: An alternative distribution

Abstract: To date, virtually all techniques appropriate for ordinal data are based on the uniform probability distribution over the permutations. In this paper we introduce and examine an alternative probability model for the distribution of ordinal data. Preliminary to deriving the expectations of Spearman's rho and Kendall's tau under this model, we show how to compute certain conditional expectations of rho and tau under the uniform distribution. The alternative probability model is then applied to ordinal test theory, and the calculation of true scores and test reliability are discussed.