Showing papers on "Statistical hypothesis testing published in 1974"

A new look at the statistical model identification

Abstract: The history of the development of statistical hypothesis testing in time series analysis is reviewed briefly and it is pointed out that the hypothesis testing procedure is not adequately defined as the procedure for statistical model identification. The classical maximum likelihood estimation procedure is reviewed and a new estimate minimum information theoretical criterion (AIC) estimate (MAICE) which is designed for the purpose of statistical identification is introduced. When there are several competing models the MAICE is defined by the model and the maximum likelihood estimates of the parameters which give the minimum of AIC defined by AIC = (-2)log-(maximum likelihood) + 2(number of independently adjusted parameters within the model). MAICE provides a versatile procedure for statistical model identification which is free from the ambiguities inherent in the application of conventional hypothesis testing procedure. The practical utility of MAICE in time series analysis is demonstrated with some numerical examples.

Biostatistics: A Foundation for Analysis in the Health Sciences

Abstract: Introduction to Biostatistics Descriptive Statistics Some Basic Probability Concepts Probability Distributions Some Important Sampling Distributions Estimation Hypothesis Testing Analysis of Variance Simple Linear Regression and Correlation Multiple Regression and Correlation Regression Analysis - Some Additional Techniques The Chi-Square Distribution and the Analysis of Frequencies Nonparametric and Distribution-Free Statistics Vital Statistics.

Hypothesis testing and information theory

Abstract: The testing of binary hypotheses is developed from an information-theoretic point of view, and the asymptotic performance of optimum hypothesis testers is developed in exact analogy to the asymptotic performance of optimum channel codes. The discrimination, introduced by Kullback, is developed in a role analogous to that of mutual information in channel coding theory. Based on the discrimination, an error-exponent function e(r) is defined. This function is found to describe the behavior of optimum hypothesis testers asymptotically with block length. Next, mutual information is introduced as a minimum of a set of discriminations. This approach has later coding significance. The channel reliability-rate function E(R) is defined in terms of discrimination, and a number of its mathematical properties developed. Sphere-packing-like bounds are developed in a relatively straightforward and intuitive manner by relating e(r) and E (R) . This ties together the aforementioned developments and gives a lower bound in terms of a hypothesis testing model. The result is valid for discrete or continuous probability distributions. The discrimination function is also used to define a source code reliability-rate function. This function allows a simpler proof of the source coding theorem and also bounds the code performance as a function of block length, thereby providing the source coding analog of E (R) .

On Use of Multiple Tests of Significance in Psychological Research

Abstract: The evaluation of a series of statistical tests in psychological research is a common problem faced by many investigators. As the number of statistical tests increases, the probability of making a ...

Test Statistics for Mixture Models

Abstract: Regression models of the forms proposed by Scheffe and by Becker have been widely and usefully applied to describe the response surfaces of mixture systems. These models do not contain a constant term. It has been common practice to test the statistical significance of these mixture models by the same statistical procedures used for other regression models whose constant term is absent (e.g., because the regression must pass through the origin). In this paper we show that the common practice produces misleading reslllts for mixtures. The mixture models require a different set of F, R 2, and R A 2 statistics. The correct mixture statistics correspond to a physically consistent null hypothesis and are also consistent with the expression of the mixture model in the older “slack-variable” form. An illustrative example is included.

Measuring agreement when two observers classify people into categories not defined in advance

Abstract: Basic to many psychological investigations is the question of agreement between observers who independently categorize people. Several recent studies have proposed measures of agreement when a set of nominal scale categories has been predefined and imposed on two observers. This study, in contrast, develops a measure of agreement for settings where observers independently define their own categories. Thus it is possible for observers to delineate different numbers of categories, with different names. Computational formulae for the mean and variance of the proposed measure of agreement are given; further, a statistic with a large-sample normal distribution is suggested for testing the null hypothesis of random agreement. A computer-based comparison of the large-sample approximation with the exact distribution of the test statistic shows a generally good fit, even for moderate sample sizes. Finally, a worked example involving two psychologists' classifications of children illustrates the computations.

Hypothesis Testing in Linear Models (Eisenhart Model I)

Abstract: The results from an analysis of balanced data are frequently summarized in an analysis of variance (AOV) table. Each sum of squares (SS) in the AOV table is uniquely associated with testing a particular hypothesis in the linear model. These hypotheses are well known and cause no confusion among statisticians as to what is being tested. Results from an analysis of unbalanced data, however, cannot be uniquely summarized in an AOV table, and, consequently, statisticians are often confused about the hypotheses being tested. Some statisticians prefer an orthogonal partitioning of the SS (paralleling the balanced case) as the appropriate analysis; others prefer various forms of nonorthogonal analyses. The purpose of this paper is to show (and, hopefully, clarify) the hypotheses that are being tested in various unbalanced AOV tables.

Testing structural specification using the unrestricted reduced form

Abstract: In the first section of this paper the overidentifying restrictions on a system of linear simultaneous equations are expressed in terms of restrictions on the reduced form parameters. These restrictions provide the basis of a test of the structure using only the unrestricted reduced form parameter estimates. Under Ho the test proposed is asymptotically equivalent to a likelihood ratio test. The test may be applied as a single equation or complete system procedure and it may be presented as either a x2 or an F statistic. The case is also made here for system overidentification tests rather than single equation procedures, the arguments being drawn from the statistical literature on hypothesis testing by induction. The computational advantages of the present proposals are substantial when compared to FIML based likelihood -ratio tests and Monte Carlo experiments confirm that a system version of the test performs well in large samples. The system version of the test behaves like the FIML likelihood ratio test in large sample situations both under Ho and H1. However, the Monte Carlo studies indicate that both the single equation and system versions of the test perform poorly in small samples. THE AIM OF THIS paper is to investigate the possibility of deciding on the specification of a simultaneous equation model prior to the estimation of the structure. A well established test procedure is suggested which uses OLS estimates of the reduced form parameters; it enables the null hypothesis, that the model specified is not significantly different from the model which generated the sample, to be tested. Because of the one-to-one correspondence between the overidentified structure and the restricted reduced form, it is possible to make inferences about the structure from the observed compatibility of the reduced form restrictions with the sample information. In addition, the reduced form restrictions resulting from a particular equation may be isolated and tested separately, if desired. The principle underlying the test would appear to be due to Wald [17J; namely, that if the null hypothesis is correct and the structure postulated as the maintained hypothesis was responsible for the generation of the observed sample, then the unrestricted reduced form parameter estimates will tend, if the sample size is large enough, to satisfy the reduced form restrictions advanced under the maintained hypothesis. A number of problems relating to identification of linear simultaneous equations make life a little difficult and are discussed subsequently. Now, take the linear structure

Hypothesis testing procedures for separate families of hypotheses

Abstract: Hypothesis test procedures for tests of separate families of hypotheses are defined. These procedures are then compared using Monte Carlo samples as data for five pairs of invariant distributions. The comparisons are made by calculating an approximate relative efficiency for each procedure with respect to the likelihood ratio procedure, which for three pairs of distributions considered is uniformly most powerful among the class of invariant procedures.

On Symmetric Compound Decision Rules for Dichotomies

Abstract: When an admissible symmetric compound decision rule is applied to a sequence of simple hypothesis testing problems, the decisions are shown to exactly reflect the ordering of the component likelihood ratios. This leads to a characterization of admissible procedures which is closely related to the method ordinarily used in constructing compound decision rules. The extension to estimation problems is indicated.

Nonorthogonal Analysis of Variance Using Iterative Improvement and Balanced Residuals

Abstract: A method is developed for computing an exact nonorthogonal analysis of variance using cell means. This is accomplished without forming or using computer storage for X 0, or X′0 X 0, or an orthogonal transformation of X 0, where X 0 is the N × p nonorthogonal design matrix. The method is a convergent iterative method which utilizes balanced analysis-of-variance estimates and residuals iteratively in solving the relevant normal equations and conducting tests of hypotheses. A monotonicity property of the method is derived to minimize iteration for nonsignificant factors or interactions in hypothesis testing.

To Pool or Not to Pool in Hypothesis Testing

Abstract: Necessary and sufficient conditions for admissibility are given for test procedures based on a preliminary test of significance. Three types of problems are studied—testing the normal mean, fixed effects models of the analysis of variance and random effects models. Admissibility in this instance is equivalent to the intuitive and practical condition that acceptance regions of the procedures have convex sections in certain variables, while other variables are fixed. It is easy to check when the conditions hold. A discussion of optimality properties of these and other types of pooling procedures is given.

A Survey of "Felt" Versus "Real" Needs of Physical Therapists

Abstract: Constantly emerging knowledge has made continual learning a necessity for health-related professionals. This research deter mined some educational needs of one professional group, physical therapists, to help plan necessary continuing education. A ques tionnaire was administered to 77 physical therapists to determine and compare felt needs (personal perceptions symptomatic of problems) and real needs (actual knowledge or skill weaknesses). A literature review prompted the hypothesis (null form) of no correlation between perceived felt needs and demonstrated real needs. Statistical testing (Pearson correlation) suggested a failure to reject the null hypothesis (.05 level). The differences existing between felt and real needs indicates the complexity of the needs assessment process and the limitations of a mailed questionnaire that only solicits perceptions of need in planning continuing edu cation programs.

Statistical Tests and Surveys of Power: A Critique.

Abstract: Cohen (1962) and Brewer (1972) surveyed statistical tests reported in the Journal of Abnormal and Social Psychology and the American Educational Research Journal, respectively, to determine the amount of power of those tests for the various sample sizes used and various magnitudes of effect sizes. Both authors concluded that the levels of power were low, and each author made negative comments about the situation or state of the art. Brewer went much further, even suggesting that two-thirds of the researchers surveyed would do better by flipping coins and not spending the time in data collection. In addition, he interpreted power as indicating the probability of a valid rejection of the null hypothesis after the statistical test was performed. Cohen (1973) applauded Brewer's survey, but was critical of most of Brewer's interpretations and recommendations, mostly relating to power after the fact and Brewer's alternate reporting schemes. Dayton et al. (1973) also pointed out the conditional nature of power. In their discussion they refer to the Bayesian inference model and while not necessarily intending to imply that Brewer is correct if interpreted Bayesianly, some readers might infer this from their comments.

Decision analysis of a gamma hydrologic variate

Abstract: Hydrologists have studied the statistical nature of summer-type storms and the decision problems associated with containing their runoff. In this tradition, winter storms are examined here. In contrast to summer storms the gamma family rather than the exponential fits the Tucson rainfall record. Use of the gamma law entails greatly increased computational complexity, and a major effort is made to achieve efficiency of calculation. This study begins by reporting statistical tests indicating that the gamma family describes the precipitation process. A natural conjugate family for the gamma law is derived and discussed. Numerical methods for Bayesian analysis of the (somewhat recalcitrant) gamma variate are explained and tested on simulated data. The concluding sections give examples (return time and levee height) of decision making when the gamma family is the underlying law. The method of decision analysis is applicable to other hydrologic problems in which the gamma distribution (also called the Pearson type 3) is a plausible model. Moreover, it is believed that the bulk of the numerical methods derived herein will prove useful in significantly many other Bayesian decision theory contexts.

On neyman's paradox and the theory of statistical tests

Abstract: H is not rejected on the grounds that the hypothesis that D has the distribution H implies that it has is 'falsified'. D is used as a criterion to directly test H. Thus this theory is free of the difficulties faced by Gillies's rule. It is unscathed by the arguments of Neyman discussed by Gillies in section 4 of his paper, because all sorts of judgments of evidential support are incorporated in the definition of a D-function for a particular problem. It does not generate any of the counterintuitive falsification classes mentioned by Gillies, although there may be several candidates for D-functions which do not strictly agree. The modified Fisherian theory of significance testing is not free of difficulties, however. It is mistaken in its view that P(D > D(O)) given H is an index of the evidential weight of data O, as I have shown in an unpublished paper on the logic of significance testing. My own view on the general problem of providing a falsifying rule for probability statements is that no solution exists if subjective appraisals of the credibility of hypotheses in relation to all one knows and judgments of inductive probability are ruled inadmissible ingredients of a solution. If (which I doubt) Popper's claim, cited by Gillies on p. 232, that 'the physicist knows well enough when to regard a probability assumption as falsified' does hold water, the rule that accurately describes the behaviour of physicists would incorporate the subjective ingredients mentioned above. More precisely, it would conform to a Bayesian analysis.

Computer analysis for case-control studies with individual matching.

Abstract: A time-sharing computer program written in BASIC language has been developed to analyse data from case-control epidemiologic studies with individual matching. The program will handle the data from matched studies with any number of controls matched to each case, including a varying number of controls for each case. The program computes point and interval estimates for the risk ratio parameter, performs statistical hypothesis testing, and permits a posteriori evaluation of the efficacy of the matching.

Statistical analysis of continuous data records

Abstract: Simple stochastic techniques permit efficient utilization of information contained in continuous data records. Statistical parameters are analogous to corresponding random variable quantities, and straightforward procedures yield the number of equivalent independent data values for a given sample record. Evaluation of typical autocovariance functions provides approximate results for a large number of physical phenomena. Simply hypothesis testing techniques follow directly from the procedures presented. Actual subway noise data illustrate application of the techniques.

A test for multivariate normality

Abstract: We propose a practical method to test the hypothesis of multivariate normality. The multivariate normal distribution is characterized by the fact that all its joint cumulants of order higher than two are zero, so that a simple and natural way to test the hypothesis of multivariate normality will be to use sample cumulants as test statistics. In view of this, we suggest to compute exact conditional moments of sample cumlants given sample variances and covariances. And by applying asymptotic normality, we calculate exact second order conditional moments of the third cumulants, which will be used to test the normality.

Some Statistical Aspects of Similarity and Identification

Abstract: We consider the problem of assessing the significance of trace material which may connect suspect and crime. We demonstrate the application of statistical method when measured data is subject to random (uncontrollable) components of variability. Through simplified model situations we describe the kind of criteria employed in the design of appropriate statistical tests. We examine the consequences of applying a test frequently used in the analysis of forensic data. We also illustrate the need to apply statistical procedures to the problem of assessing the evidential importance of implied similarities between trace and source.

Testing structural specification using the unrestricted reduced form

Abstract: In the first section of this paper the overidentifying restrictions on a system of linear simultaneous equations are expressed in terms of restrictions on the reduced form parameters. These restrictions provide the basis of a test of the structure using only the unrestricted reduced form parameter estimates. Under Ho the test proposed is asymptotically equivalent to a likelihood ratio test. The test may be applied as a single equation or complete system procedure and it may be presented as either a x2 or an F statistic. The case is also made here for system overidentification tests rather than single equation procedures, the arguments being drawn from the statistical literature on hypothesis testing by induction. The computational advantages of the present proposals are substantial when compared to FIML based likelihood -ratio tests and Monte Carlo experiments confirm that a system version of the test performs well in large samples. The system version of the test behaves like the FIML likelihood ratio test in large sample situations both under Ho and H1. However, the Monte Carlo studies indicate that both the single equation and system versions of the test perform poorly in small samples. THE AIM OF THIS paper is to investigate the possibility of deciding on the specification of a simultaneous equation model prior to the estimation of the structure. A well established test procedure is suggested which uses OLS estimates of the reduced form parameters; it enables the null hypothesis, that the model specified is not significantly different from the model which generated the sample, to be tested. Because of the one-to-one correspondence between the overidentified structure and the restricted reduced form, it is possible to make inferences about the structure from the observed compatibility of the reduced form restrictions with the sample information. In addition, the reduced form restrictions resulting from a particular equation may be isolated and tested separately, if desired. The principle underlying the test would appear to be due to Wald [17J; namely, that if the null hypothesis is correct and the structure postulated as the maintained hypothesis was responsible for the generation of the observed sample, then the unrestricted reduced form parameter estimates will tend, if the sample size is large enough, to satisfy the reduced form restrictions advanced under the maintained hypothesis. A number of problems relating to identification of linear simultaneous equations make life a little difficult and are discussed subsequently. Now, take the linear structure

Distribution-free statistical hypotheses testing for stochastic processes

Abstract: This paper extends some well known distribution-free structural results in the univariate and multivariate hypothese testing to stochastic processes. The study of distribution-free tests is essentially the study of similar sets and test functions. It is found that (i) all distribution-free statistics are based on permuations through of the basic PITMAN functions; (ii) the optimal tests are based on the likelihoood function of the alternatives; (iii) that a generation of DARMOIS-PITMAN-KOOPMAN families. Furthermore, it is observed that for martingales and MARKOV processes asymptotically optimal tests can be constructed by employing various limit theorems.

The use of spectral analysis to validate peanning models

Abstract: Statistical fit of model predictions to empirical evidence is found to be an insufficient condition for establishing the validity of a planning model where the dynamic behavior is of particular importance The paper describes a spectral analysis statistical test that can be used to validate the structure of a planning model by comparing the time series generated by the model with the actual time series of events for the real system under study Validation of an ambulance simulation model is reported in which the model apparently was valid based on classical goodness of fit tests of aggregate data However, following a spectral analysis of the simulation results, an entirely new method of generating incidents was found to be necessary The resulting model then was able to duplicate realistically the essential cyclical nature of hourly demand for emergency care observed in the real system which periodically created excessive busy and idle periods not realized in the structure of the original model