Showing papers on "Statistical hypothesis testing published in 1970"

Distribution-Free Statistical Tests

Abstract: As a result of an extensive survey of the literature, a large number of distribution-free statistical tests are examined. Tests are grouped together primarily according to general type of mathematical derivation or type of statistical \"information\" used in'conducting the test. Each of the more important tests is treated under the headings: Rationale, Null Hypothesis, Assumptions, Treatment of Ties, Efficiency, Application, Discussion, Tables, and Sources. Derivations are given and mathematical interrelationships among the tests are indicated. Strengths and weaknesses of individual tests, and of distribution-free tests as a class compared to parametric tests, are discussed.

Statistical reasoning in psychology and education

Abstract: Partial table of contents: Preliminary Concepts Frequency Distributions, Percentiles, and Percentile Ranks Central Tendency Variability The Normal Curve Derived Scores Correlation Prediction Interpretive Aspects of Correlation and Regression Probability The Basis of Statistical Inference Further Considerations in Hypothesis Testing Testing Hypotheses About the Difference Between Two Independent Means Testing Hypotheses About the Difference Between Two Dependent Means Power and Measure of Effect Size One-Way Analysis of Variance (and Some Alternatives) Factorial Analysis of Variance: The Two-Factor Design Inference About Pearson Correlation Coefficients Chi-Square and Inference About Frequencies Epilogue: The Realm of Statistics Appendices Tables References Index.

The Weighted Likelihood Ratio, Sharp Hypotheses about Chances, the Order of a Markov Chain

Abstract: The Bayesian theory for testing a sharp hypothesis, defined by fixed values of parameters, is here presented in general terms Arbitrary positive prior probability is attached to the hypothesis The ratio of posterior to prior odds for the hypothesis is given by the weighted likelihood ratio, shown here to equal Leonard J Savage's (1963) ratio of a posterior to a prior density (221) This Bayesian approach to hypothesis testing was suggested by Jeffreys (1948), Savage (1959), (1961), Lindley (1961), and Good (1950), (1965), but obscured some what by approximations and unique choices of prior distributions This Bayesian theory is distinct from that of Lindley (1965) and that of Dickey (1967a) Applications are given to hypotheses about multinomial means, for example, equality of two binomial probabilities A new test is presented for the order of a finite-state Markov chain

Extensions of the significance test for one-parameter signal detection hypotheses

Abstract: The basic models of signal detection theory involve the parametric measure,d′, generally interpreted as a detectability index. Given two observers, one might wish to know whether their detectability indices are equal or unequal. Gourevitch and Galanter (1967) proposed a large sample statistical test that could be used to test the hypothesis of equald′ values. In this paper, their large two sample test is extended to aK-sample detection test. If the null hypothesisd 1′=d 2′=...=d K ′ is rejected, one can employ the post hoc confidence interval procedure described in this paper to locate possible statistically significant sources of variance and differences. In addition, it is shown how one can use the Gourevitch and Galanter statistics to testd′=0 for a single individual.

Approximate Power and Sample Size Determination for Common one-Sample and two-Sample Hypothesis Tests:

Abstract: IN the course of preparing a handbook for power analysis (Cohen, 1969), it became apparent that at the cost of (a) working with approximate rather than &dquo;exact&dquo; solutions, and (b) doing a modest amount of computing, many frequently encountered problems of statistical power analysis encountered by hypothesis-testing behavioral scientists could be brought into a simple common framework. Past publications in this program have discussed (Cohen, 1965, pp. 95-101) and documented (Cohen, 1962) the need and relative neglect of statistical power analysis of the Neyman-Pearson (1928, 1933) type in the design and interpretation of research in the behavioral sciences. This article and the more

On a Dilemma of Comparative Factor Analysis: A Study of Factor Matching Based on Random Data.

Abstract: ONE of the most important, but still inadequately resolved issues pertinent to factor analytically oriented research is that of matching factors from two or more independent studies. Powerful though the methods of factor analysis may be for purposes of organizing masses of data within the context of a single multivariate experiment, their use in comprehensive, programmatic research has been severely limited by a lack of equally powerful rotational methods for establishing identity of concepts, as evidenced by matched factors, across a series of researches.

The Eta Coefficient in Complex Anova Designs

Abstract: Tms paper advances several considerations for the use and interpretation of the eta coefficient (7]), or correlation ratio, as a postmortem measure of association for comparative experiments. There is a growing awareness among substantive researchers, as reflected by the increased use of ex post facto measures of association (Johnson and Gade, 1968; Bruning, 1968; Kennedy, 1969), that a meaningful indication of the strength of an effect is not provided by merely reporting a significant test statistic (i.e., a t or F etc.) with its associated p value. As Bakan (1966), among others, has pointed out, the size of a test statistic and thus the p value is to a considerable extent a function of sample size. Since ultimately the null hypothesis can always be rejected, the test statistic simply implies that the observed effect is significant for a given n. The

An approach to testing the goodness of fit of incompletely specified distributions

Abstract: A general method is developed for testing the goodness of fit of a continuous distribution against unspecified alternatives when the null hypothesis specifies only the functional form of the distribution and leaves some or all of its parameters unspecified. The exponential and normal distributions are treated in detail. For these distributions tables of percentile points of the test statistics are provided. Power comparisons of our tests with those developed by Lilliefors are also given. All the numerical results involved are derived using Monte Carlo methods.

Asymptotic properties of rank tests under discrete distributions

Abstract: This paper is devoted to problems of rank tests when samples are drawn from purely discrete distributions. There are considered two ways of treatment of ties, and the distribution of the respective test statistics is derived under the hypothesis of randomness and under the contiguous alternative. Furthermore, their asymptotic power and efficiency are established.

Sifasp a general computer program for simultaneous factor analysis in several populations

Abstract: MF-$0.65 HC-$3.29 *Computer Programs; Factor Analysis; *Factor Structure; Hypothesis Testing; *Mathematical Models; *Research Methodology; *Sampling; Statistical Analysis A computer program for simultaneously factor analyzing dispersion matrices obtained from independent groups is described. This program is useful when a battery of tests has been administered to samples of examinees from several populations and one wants to study similarities and differences in factor structure between the different populations. (CK)

Correcting for Heterogeneity of Covariance for Repeated Measures Designs of the Analysis of Variance.

Abstract: Box (1954), Geisser and Greenhouse (1958) and others have shown that the effect of nonhomogeneous correlations, between treatments, is to introduce a positive bias in jp’ when the correlations are positive but unequal and a negative bias when the correlations are negative but unequal. Various approaches have been suggested to contend with this bias; some are methodological, others focus on the choice of the statistical test, and some attempt to correct the biased F mathematically. In many instances, nonhomogeneous covariances result from such factors as sequence effects, carry-over effects or transfer of training which may occur during collection of data. Suggestions have been made to administer treatments randomly within sub-

A Monte Carlo Method for Testing the Statistical Significance of a Regression Equation

Abstract: A Monte Carlo technique for testing the statistical significance of an estimate by regression is described It is illustrated on a medium-range prediction of precipitation The purpose of the technique is to permit the use of all data available while developing a regression equation This is especially important when the sample is small The need for setting aside a fraction of the data to test the equation on an independent sample, or to estimate degrees of freedom before applying standard statistical tests, is eliminated In the illustration, a stepwise regression procedure was used to select predictors and derive an equation to predict actually observed precipitation Then the procedure was repeated 20 times, each time on a set of bogus values of precipitation drawn at random from the historical population of precipitation values Each of the 20 equations resulting from bogus values of precipitation was used to estimate the precipitation and to give 20 values of per cent reduction of variance

Finite-memory hypothesis testing--A critique (Corresp.)

Abstract: In this correspondence, we critically examine some recent papers that attempt to obtain optimal finite-memory solutions for some hypothesis-testing problems. We point out that these solutions contain hidden memory-consuming elements, and hence are not optimal. We present and examine various possible definitions of finite memory from a finite-state-machine viewpoint.

A Nonparametric Test of an Ordered Hypothesis for k Independent Samples

Abstract: VERY often a researcher employs a multiple group (G) design in which n observations are in each of k independent groups or samples. A randomized groups analysis of variance (ANOVA) or its nonparametric counterpart, the Kruskal-Wallis H test, is typically employed to test the null hypothesis: Gl = G2 = ... = Gk. Similarly, in the randomized blocks or matched groups design, ANOVA or the Friedman x2 test might be employed. In all four of these cases the alternative hypothesis is the omnibus: Gi 0:/= Gj for some i =A j. However, there are also specific alternatives which might be tested, for example, partially ordered hypotheses (Gi = G2 < ...

Applications of space-time decision and estimation theory to antenna processing system design

Abstract: A mathematical solution to the problem of optimum radar target detection and parameter estimation in receiver noise and heavy clutter has been achieved by means of space-time decision theory. The theory leads to a conceptual design for an antenna processing system that is optimum in the sense that it makes least risk parameter estimates and least probability of error decisions. The system can be instrumented by separately demodulating the individual radiator outputs and feeding them simultaneously and in parallel to a digital computer, Hypothesis testing problems such as target detection are formulated by means of a generalized likelihood ratio test. Optimum mean-square estimation is carried out by instrumenting the mean of the parameter in question conditioned on the observed signal. With the aid of a priori statistics available or assumed, the a posteriori likelihood function is derived. From this function, the required generalized likelihood ratio hypothesis tests and parameter estimators are synthesized. Specific illustrations include systems for detection and angular location estimation for one or two targets in a clutter environment. Optimum tests as well as optimum and suboptimum estimators are realized as flow diagrams for computation by the special-purpose digital processor.

Consideration of power for some two sample tests with censoring based on a given order statistic

Abstract: SUMMARY This paper deals with some properties of three nonparametric tests which can be used for detecting a difference in location of two populations wlhen samples are censored on the occurrence of a given order statistic. The null distributions of the test statistics are presented together with some tables of critical values. Exact expressions are obtained for the powers of the tests under exponential and rectangular alternatives. Finally, the expected durations of the tests are compared. A number of tests which permit early termination of an experiment have been proposed for detecting a difference in the location of two populations. These tests have important applications in life-testing situations where testing time may be costly. The criterion for termination may be a preselected period of time from the start of the experiment or the occurrence of a given order statistic in one of the samples or the two samples combined. In this paper we consider three nonparametric tests which may be used to provide a one-sided test for difference in location of two populations. The common feature of the tests is that the experiment is terminated on or before the occurrence of a preselected order statistic in one of the samples. We first consider the distributions of the test statistics under the null hypothesis that the two samples have been drawn randomly from populations with identical cumulative distribution functions. Some tables of critical values are presented. Expressions are given for the test powers under the alternative of a translation in an exponential distribution and for changes in the location and scale parameters of a rectangular distribution. Finally some results are given for the expected durations of the tests.

Statistics According to Bayes

Abstract: Thomas Bayes may not have foreseen that a paper he wrote and friends of his published in 1763, after his death, would serve to tie his name to a branch of statistics that has come into prominence today. Bayesian statistics gets its name from the use and special interpretation of what is known as Bayes' theorem, a simple identity in conditional and unconditional probabilities, contained in the paper by Bayes (1763). The rise of Bayesian statistics in the last couple of decades has been prompted mainly by dissatisfaction with what sometimes is called classical statistics. This is the statistics of hypothesis testing with errors of two kinds and the statistics of confidence intervals, as developed by Neyman and Pearson in this century. Their formalizations were a major achievement, but in practice difficulties are found with classical statistics. One such difficulty rests with the specification of the value of the parameter that is tested in the null hypothesis. In the case of a correla-

Stimulus Selection by Five-, Seven-, and Nine-Year-Old Children.

Abstract: Functional stimulus selection by five-, seven-, and nine-year-old children was examined in a paired-associate learning and recall test. The compound stimuli were of two classes-geometric figures and colors-and the responses were pictures of common objects. Five-, seven-, and nine-year-olds all seemed to select the geometric figures as functional stimuli. Several alternative hypotheses are offered to account for the results, among them an hypothesis of stimulus-habit hierarchy and an hypothesis of alternating stimulus selection. The tendency to select a portion of a compound stimulus and to use that portion as a functional stimulus has been the object of considerable attention. Underwood and Schulz first suggested that stimulus selection plays an important role in paired-associate acquisition, especially when the stimulus elements elicit few associations.1 In a direct test of this hypothesis, Underwood, Ham, and Ekstrand presented convincing evidence for stimulus selection as a function of the relative meaningfulness of the elements within compound stimuli.2 Recently Goulet, in an analysis of verbal learning in children, suggested that young children may tend to fractionate verbal stimulus terms more than older children or adults.3 His rationale was that stimulus integration is a direct function of exposure, which generally corresponds to age. In addition, he offered an alternative suggestion, that differential acquisition rates, varying with age, may be due to non-stimulus selection among young children because of their naivet6 in stimulus selection. Received for publication October 22, 1969. An earlier part of the investigation was supported by PHS Research Grant MH-15722-01, National Institute of Mental Health. The author expresses his gratitude to B. J. Underwood, who generously commented on an earlier draft of the paper. Barbara S. Solso and Sheryl Stice assisted in the gathering of the data, and their contribution is gratefully acknowledged. 1 B. J. Underwood and R. W. Schulz, Meaningfulness and Verbal Learning, 1960. 2 B. J. Underwood, M. Ham, and B. Ekstrand, Cue selection in pairedassociate learning, J. exp. Psychol., 64, 1962, 405-409. The stimuli used in this study were colors and highand low-meaningfulness trigrams. 3 L. R. Goulet, Verbal learning in children: Implications for developmental research, Psychol. Bull., 69, 1968, 359-376.

Pseudo-Random Sequences.

Abstract: : Three definitions of random binary sequences are presented. The consistency of those definitions with the laws of probability theory, and the inclusion relationship of the three sets of random sequences, are investigated. These sequences, considered as characteristic functions of sets are then placed in the Kleene arithmetical hierarchy. Some restrictions on these definitions, using Blum's complexity theory, lead to the definition of pseudo-random sequences, which can be generated effectively. (Author)