Showing papers on "Statistical hypothesis testing published in 1987"

A comparison of the Two One-Sided Tests Procedure and the Power Approach for assessing the equivalence of average bioavailability

Abstract: The statistical test of the hypothesis of no difference between the average bioavailabilities of two drug formulations, usually supplemented by an assessment of what the power of the statistical test would have been if the true averages had been inequivalent, continues to be used in the statistical analysis of bioavailability/bioequivalence studies. In the present article, this Power Approach (which in practice usually consists of testing the hypothesis of no difference at level 0.05 and requiring an estimated power of 0.80) is compared to another statistical approach, the Two One-Sided Tests Procedure, which leads to the same conclusion as the approach proposed by Westlake (2) based on the usual (shortest) 1–2α confidence interval for the true average difference. It is found that for the specific choice of α=0.05 as the nominal level of the one-sided tests, the two one-sided tests procedure has uniformly superior properties to the power approach in most cases. The only cases where the power approach has superior properties when the true averages are equivalent correspond to cases where the chance of concluding equivalence with the power approach when the true averages are notequivalent exceeds 0.05. With appropriate choice of the nominal level of significance of the one-sided tests, the two one-sided tests procedure always has uniformly superior properties to the power approach. The two one-sided tests procedure is compared to the procedure proposed by Hauck and Anderson (1).

Confirmation, Disconfirmation, and Information in Hypothesis Testing

Abstract: Strategies for hypothesis testing in scientific investigation and everyday reasoning have interested both psychologists and philosophers. A number of these scholars stress the importance of disconfir. marion in reasoning and suggest that people are instead prone to a general deleterious "confirmation bias" In particula~ it is suggested that people tend to test those cases that have the best chance of verifying current beliefs rather than those that have the best chance of falsifying them. We show, howeve~ that many phenomena labeled "confirmation bias" are better understood in terms of a general positive test strate~. With this strategy, there is a tendency to test cases that are expected (or known) to have the property of interest rather than those expected (or known) to lack that property. This strategy is not equivalent to confirmation bias in the first sense; we show that the positive test strategy can be a very good heuristic for determining the truth or falsity of a hypothesis under realistic conditions~ It can, howeve~ lead to systematic errors or inefficiencies. The appropriateness of human hypotheses-testing strategies and prescriptions about optimal strategies must he understood in terms of the interaction between the strategy and the task at hand.

Hypothesis Testing with Efficient Method of Moments Estimation

Abstract: Efficient method of moments estimation techniques include many commonly used techniques, including ordinary least squares, two- and three-stage least squares, quasi maximum likelihood, and versions of these for nonlinear environments. For models estimated by any efficient method of moments technique, the authors define analogues to the maximum likelihood based Wald, likelihood ratio, Lagrange multiplier, and minimum chi-squared statistics. They prove the mutual asymptotic equivalence of the four in an environment that allows for disturbances that are auto correlated and heteroskedastic. They also describe a very convenient way to test a linear hypothesis in a linear model. Copyright 1987 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Regression analysis of natural selection statistical inference and biological interpretation

Abstract: Recent theoretical work in quantitative genetics has fueled interest in measuring natural selection in the wild. We discuss statistical and biological issues that may arise in applications of Lande and Arnold's (1983) multiple-regression approach to measuring selection. We review assumptions involved in estimation and hypothesis testing in regression problems, and we note difficulties that frequently arise as a result of violation of these assumptions. In particular, multicollinearity (extreme intercorrelation of characters) and extrinsic, unmeasured factors affecting fitness may seriously complicate inference regarding selection. Further, violation of the assumption that residuals are normally distributed vitiates tests of significance. For this situation, we suggest applications of recently developed jackknife tests of significance. While fitness regression permits direct assessment of selection in a form suitable for predicting selection response, we suggest that the aim of inferring causal relationships about the effects of phenotypic characters on fitness is greatly facilitated by manipulative experiments. Finally, we discuss alternative definitions of stabilizing and disruptive selection.

Latent Growth Curves within Developmental Structural Equation Models.

Abstract: This report uses structural equation modeling to combine traditional ideas from repeated-measures ANOVA with some traditional ideas from longitudinal factor analysis. A longitudinal model that includes correlations, variances, and means is described as a latent growth curve model (LGM). When merged with repeated-measures data, this technique permits the estimation of parameters representing both individual and group dynamics. The statistical basis of this model allows hypothesis testing of various developmental ideas, including models of alternative dynamic functions and models of the sources of individual differences in these functions. Aspects of these latent growth models are illustrated with a set of longitudinal WISC data from young children and by using the LISREL V computer program.

Foundations of Statistics

Abstract: Diagrams and Tables. Measures of Location. Measures of Dispersion and Skewness. Basic Ideas of Probability. Random Variables and Their Probability Distribution. Some Standard Discrete and Continuous Probability Distributions. Approximations to the Binomial and Poisson Distributions. Linear Functions of Random Variables and Joining Distributions. Sample Populations and Point Estimation. Interval Estimation. Hypothesis Tests for the Mean and Variance of Normal Distributions. Hypothesis Tests for the Binomial Parameter p,p. Hypothesis Tests for Independence and Goodness-of-Fit. Non-Parametric Hypothesis Tests. Correlation. Regression. Elements of Experimental Design and Analysis. Quality Control Charts and Acceptance Sampling.

Statistical Methods for the Analysis of Biomedical Data

Abstract: Dedication.Preface to the 1987 Edition. Preface to the 2002 Edition. Acknowledgments. 1. Introduction. 2. Descriptive Statistics. 3. Basic Probability Concepts. 4. Further Aspects of Probability. 5. Confidence Intervals and Hypothesis Testing: General Considerations and Applications. 6. Comparison of Two Groups: t Tests and Rank Tests. 7. Comparison of Two Groups: Chi Square and Related Procedures. 8. Tests of Independence and Measures of Association for Two Random Variables. 9. Least Square Regression Methods: Predicting One Variable from Another. 10. Comparing More Than Two Groups of Observations: Analysis of Variance for Comparing Groups. 11. Comparing More Than Two Groups of Observations: Rank Analysis of Variance for Group Comparisons. 12. Comparing More than Two Groups of Observations: Chi Square and Related Procedures. 13. Special Topics in Analysis of Epidemiologic and Clinical Data: Studying Association between a Disease and a Characteristic. 14. Estimation and Comparison of Survival Curves. 15. Multiple Linear Regression Methods: Predicting One Variable from Two or More Other Variables. Appendix.Topic Index.

A Nonparametric Approach for Assessing Latent Trait Unidimensionality.

Abstract: Assuming a nonparametric family of item response theory models, a theory-based procedure for testing the hypothesis of unidimensionality of the latent space is proposed. The asymptotic distribution of the test statistic is derived assuming unidimensionality, thereby establishing an asymptotically valid statistical test of the unidimensionality of the latent trait. Based upon a new notion of dimensionality, the test is shown to have asymptotic power 1. A 6300 trial Monte Carlo study using published item parameter estimates of widely used standardized tests indicates conservative adherence to the nominal level of significance and statistical power averaging 81 out of 100 rejections for examinee sample sizes and psychological test lengths often incurred in practice.

The analysis of multiple endpoints in clinical trials.

Abstract: Treatment comparisons in randomized clinical trials usually involve several endpoints such that conventional significance testing can seriously inflate the overall Type I error rate. One option is to select a single primary endpoint for formal statistical inference, but this is not always feasible. Another approach is to apply Bonferroni correction (i.e., multiply each P-value by the total number of endpoints). Its conservatism for correlated endpoints is examined for multivariate normal data. A third approach is to derive an appropriate global test statistic and this paper explores one such test applicable to any set of asymptotically normal test statistics. Quantitative, binary, and survival endpoints are all considered within this general framework. Two examples are presented and the relative merits of the proposed strategies are discussed.

Econometric Estimation of Producers' Risk Attitudes

Abstract: General methods are proposed for the identification and econometric estimation of the parameters of the distribution of risk attitudes in a producer population. The proposed methods also provide the basis for the development of statistical tests of model specification and of behavioral hypotheses. Econometric risk attitude estimation is shown to be possible under less restrictive conditions than previously believed. A moment-based version of the general model is applied to Indian data, and the econometrically estimated risk attitudes are presented and compared to experimental results for a similar group of producers.

Maximum-likelihood approaches applied to quantitative genetics of natural populations

Abstract: Growing interest in adaptive evolution in natural populations has spurred efforts to infer genetic components of variance and covariance of quantitative characters. Here, I review difficulties inherent in the usual least-squares methods of estimation. A useful alternative approach is that of maximum likelihood (ML). Its particular advantage over least squares is that estimation and testing procedures are well defined, regardless of the design of the data. A modified version of ML, REML, eliminates the bias of ML estimates of variance components. Expressions for the expected bias and variance of estimates obtained from balanced, fully hierarchical designs are presented for ML and REML. Analyses of data simulated from balanced, hierarchical designs reveal differences in the properties of ML, REML, and F-ratio tests of significance. A second simulation study compares properties of REML estimates obtained from a balanced, fully hier- archical design (within-generation analysis) with those from a sampling design including phenotypic data on parents and multiple progeny. It also illustrates the effects of imposing nonnegativity constraints on the estimates. Finally, it reveals that predictions of the behavior of significance tests based on asymptotic theory are not accurate when sample size is small and that constraining the estimates seriously affects properties of the tests. Because of their great flexibility, likelihood meth- ods can serve as a useful tool for estimation of quantitative-genetic parameters in natural popu- lations. Difficulties involved in hypothesis testing remain to be solved.

Sequential Analysis and Optimal Design

Abstract: Preliminaries on probability Generalities about the conventional theory of design of experiments Optimal sample size Preliminaries on regression Design for linear regression: Elfving's method Maximum-likelihood estimation Locally optimal designs for estimation More design in regression experiments Testing hypotheses Optimal sample size in testing Sequential probability-ratio test Optimality of sequential probability-ratio test Motivation for an approach to sequential design of experiments in testing hypotheses Asymptotic optimality of procedure A in sequential design Extensions and open questions in sequential design The problem of adjacent hypotheses Testing for the sign of a normal mean: no indifference zone Bandit problems Sequential estimation of a normal mean sequential estimation of the common mean of two normal populations.

Stopping Rule for the MLE Algorithm Based on Statistical Hypothesis Testing

Abstract: It is known that when the maximum likelihood estimator (MLE) algorithm passes a certain point, it produces images that begin to deteriorate. We propose a quantitative criterion with a simple probabilistic interpretation that allows the user to stop the algorithm just before this effect begins. The MLE algorithm searches for the image that has the maximum probability to generate the projection data. The underlying assumption of the algorithm is a Poisson distribution of the data. Therefore, the best image, according to the MLE algorithm, is the one that results in projection means which are as close to the data as possible. It is shown that this goal conflicts with the assumption that the data are Poisson-distributed. We test a statistical hypothesis whereby the projection data could have been generated by the image produced after each iteration. The acceptance or rejection of the hypothesis is based on a parameter that decreases as the images improve and increases as they deteriorate. We show that the best MLE images, which pass the test, result in somewhat lower noise in regions of high activity than the filtered back-projection results and much improved images in low activity regions. The applicability of the proposed stopping rule to other iterative schemes is discussed.

An Exact Test for Multiple Inequality and Equality Constraints in the Linear Regression Model

Abstract: In this article we consider the linear regression model y = Xβ + e, where e is N(0, σ2I). In this context we derive exact tests of the form H: Rβ ≥ r versus K: β ∈ RK for the case in which θ2 is unknown. We extend these results to consider hypothesis tests of the form H: R1β ≥ r1 and R2β = r2 versus K: (β ∈ RK . For each of these hypotheses tests we derive several equivalent forms of the test statistics using the duality theory of the quadratic programming. For both tests we derive their exact distribution as a weighted sum of Snedecor's F distributions normalized by the numerator degrees of freedom of each F distribution of the sum. A methodology for computing critical values as well as probability values for the tests is discussed. The relationship between this testing framework and the multivariate one-sided hypothesis testing literature is also discussed. In this context we show that for any size of the hypothesis test H: λ = 0 versus K: β ∈ RK the test statistic and critical value obtained a...

Invariants of phylogenies in a simple case with discrete states

Abstract: Under a simple model of transition between two states, we can work out the probabilities of different data outcomes in four species with any given phylogeny For a given tree topology, if all characters are evolving under the same probabilistic model, there are two quadratic forms in the frequencies of outcomes that must be zero It may be possible to test the null hypothesis that the tree is of a particular topology by testing whether these quadratic forms are zero One of the tests is a test for independence in a simple 2×2 contingency table If there are differences of evolutionary rate among characters, these quadratic forms will no longer necessarily be zero

Are all significant P values created equal? The analogy between diagnostic tests and clinical research.

Abstract: Just as diagnostic tests are most helpful in light of the clinical presentation, statistical tests are most useful in the context of scientific knowledge. Knowing the specificity and sensitivity of a diagnostic test is necessary, but insufficient: the clinician must also estimate the prior probability of the disease. In the same way, knowing thePvalue and power, or the confidence interval, for the results of a research study is necessary but insufficient: the reader must estimate the prior probability that the research hypothesis is true. Just as a positive diagnostic test does not mean that a patient has the disease, especially if the clinical picture suggests otherwise, a significantPvalue does not mean that a research hypothesis is correct, especially if it is inconsistent with current knowledge. Powerful studies are like sensitive tests in that they can be especially useful when the results are negative. Very lowPvalues are like very specific tests; both result in few false-positive results due to chance. This Bayesian approach can clarify much of the confusion surrounding the use and interpretation of statistical tests. (JAMA1987;257:2459-2463)

Model selection and validation methods for non-linear systems

Abstract: The theory of hypothesis testing is used to select a model with the correct structure, and the relation of such a method to the AIC and FPE criteria is investigated. Parametric validation and correlation validation methods are developed for non-non-linear difference equation models. Several shortcomings of traditional methods, especially when applied to non-linear systems, are described.

Testing for Climate Change: An Application of the Two-Phase Regression Model

Abstract: A statistical test for detecting a change in the behavior of an annual temperature series is presented The test is based on the two-phase regression model By trading the hypothesized time of change as an unknown parameter, the approach allows an inference to be made about the time of change The approach also avoids a serious problem, called data-dredging, that can arise in testing for change occurring at a specified time The test is applied to a series of Southern Hemisphere temperatures, and the hypothesis of no change cannot be rejected

A Chi-square test for fault-detection in Kalman filters

Abstract: A test for real-time detection of soft failures in navigation systems using Kalman filters has been proposed by Kerr. The test is based on the overlap between the confidence regions associated with two estimates, one obtained from a Kalman filter using on-line measurements, and the other based solely on a priori information. An alternate computational technique is presented which is based on constructing a chi-square test statistic from the difference between the two estimates and comparing it to a precomputed threshold. The chi-square test avoids the iterative computations required by the two-ellipsoid method for dimensions of two and higher.

Towards a Theory of Point Optimal Testing

Abstract: This paper puts the case for the inclusion of point optimal tests in the econometrician's repertoire. They do not suit every testing situation but the current evidence, which is reviewed here, indicates that they can have extremely useful Small-sample power properties. As well as being most powerful at a nominated point in the alternative hypothesis parameter space, they may also have optimum power at a number of other points and indeed be uniformly most powerful when such a test exists. Point optimal tests can also be used to trace out the maxemum attainable power envelope for a given testing problem, thus providing a benchmark against which test procedures can be evaluated. In some cases, point optimal tests can be constructed from tests of simple null hypothesis against a simple alternative. For a wide range of models of interst to econometricians, this paper shows how one can check whether a point optimal test can be constructed in this way. When it cannot, one may wish to consider approximately point...

Statistics for social workers

Abstract: All chapters conclude with "Concluding Thoughts" and "Study Questions" Preface 1 Introduction to Statistical Analysis Uses of Statistical AnalysisGeneral Methodological TermsLevels of MeasurementLevels of Measurement and Analysis of DataOther Measurement ClassificationsCategories of Statistical Analyses 2 Frequency Distributions and Graphs Frequency DistributionsGrouped Frequency DistributionsUsing Frequency Distributions to Analyze DataMisrepresentation of DataGraphical Presentation of DataA Common Mistake in Displaying Data 3 Central Tendency and Variability Central TendencyVariability 4 Normal Distributions Skewed DistributionsNormal DistributionsConverting Raw Scores to Z Scores and PercentilesDeriving Raw Scores From Percentiles 5 Introduction to Hypothesis Testing Alternative ExplanationsProbabilityRefuting Sampling ErrorResearch HypothesesTesting the Null HypothesisStatistical SignificanceErrors in Drawing Conclusions About RelationshipsStatistically Significant Relationships and Meaningful Findings 6 Sampling Distributions and Hypothesis Testing Sample Size and Sampling ErrorSampling Distributions and InferenceSampling Distribution of MeansEstimating Parameters From StatisticsOther Distributions 7 Selecting a Statistical Test The Importance of Selecting the Correct Statistical TestFactors to Consider When Selecting a Statistical TestParametric and Nonparametric TestsMultivariate Statistical TestsGeneral Guidelines for Test SelectionGetting Help With Data Analyses 8 Correlation Uses of CorrelationPerfect CorrelationsNonperfect CorrelationsInterpreting Linear CorrelationsUsing Correlation For InferenceComputation and Presentation of Person's RNonparametric AlternativesUsing Correlation With Three or More VariablesOther Multivariate Tests that Use Correlation 9 Regression Analyses What is Prediction?What is Simple Linear Regression?Computation of the Regression EquationMore About the Regression LineInterpreting ResultsUsing Regression Analyses in Social Work PracticeRegression With Three or More VariablesOther Types of Regression Analyses 10 Cross-Tabulation The Chi-Square Test of AssociationUsing Chi-Square in Social Work PracticeChi-Square With Three or More VariablesSpecial Applications of the Chi-Square Formula 11 t Tests and Analysis of Variance The Use of t TestsThe One-Sample t TestThe Dependent t TestThe Independent t TestSimple Analysis of Variance (One-Way Anova) Appendix A Using Statistics to Evaluate Practice Effectiveness Evaluating ProgramsEvaluating Individual Practitioner Effectiveness Glossary Index

Test Consistency with Varying Sampling Frequency

Abstract: This Paper Considers the Consistency Property of Some Test Statistics Based on a Time Series of Data. While Th Eusual Consistency Criterion Is Based on Keeping the Sampling Interval Fixed, We Let the Sampling Interval Take Any Path As the Sample Size Increases to Infinity. We Consider Tests of the Null Hypotheses of the Random Walk and Randomness Against Positive Autocorrelation We Show That Tests of the Unit Root Hypothesis Based on the First-Order Correlation Coefficient of the Original Data Are Consistent As Long As the Span of the Data Is Increasing. Tests of the Same Hypothesis Based on the First-Order Correlation Coefficient Using the First-Differenced Data Are Consistent Only If the Span Is Increasing At a Rate Greater Than Square Root of 'T'. on the Other Hand Tests of the Randomness Hypotheses Based on the First-Order Correlation Coefficient Applied to the Original Data Are Consistent As Long As the Span Is Not Increasing Too Fast. We Provide Monte Carlo Evidence on the Power, in Finite Samples, of the Tests Studied Allowing Various Combinations of Span and Sampling Frequencies. It Is Found That the Consistency Properties Summarize Well the Behavior of the Power in Finite Samples. the Power of Tests for a Unit Root Is More Influenced by the Span Than the Number O Observations While Tests of Randomness Are More Powerfull When a Small Sampling Frequency Is Available.

New Statistical Procedures for the Social Sciences: Modern Solutions To Basic Problems

Abstract: Contents: Introduction to Statistics. Probability. Random Variables, Distributions, and Estimation. Binomial and Normal Distributions. Hypothesis Testing. Student's T, Chi-Square, and F Distribution. Comparing Two Means. One-Way ANOVA. Multiple Comparisons. Two-Way ANOVA. Repeated Measures and Randomized Blocks Designs. Selection Techniques. Correlation and Regression. Categorical Data. Nonparametric Procedures. Appendices: Tables. Elementary Matrix Algebra.

Regression models for non‐stationary categorical time series

Abstract: . Categorical time series often exhibit non-stationary behaviour, due to the influence of exogenous variables. A parsimonious and flexible class of models is proposed for the statistical analysis of such data. These models are extensions of regression models for stochastically independent observations. Statistical inference can be based on asymptotic properties of the maximum likelihood estimator and of test statistics for linear hypotheses. Weak conditions assuring these properties are stated. Some tests which are of special interest in the time series situation are treated in more detail, for example tests of stationarity or independence of parallel time series.

On Statistical Testing

Abstract: The statistical testing approaches of Hypothesis Testing (Fisher) and Significance Testing (Neyman-Pearson) are briefly reviewed. Highly related notions of alpha-values, P-values, and magnitude-of-effect are discussed. A statistical testing approach that is a hybrid of Hypothesis Testing and Significance Testing is then advanced. This approach takes into consideration the two decision-error probabilities as well as an alternative hypothesis characterization of interest.

The effects of violations of independence assumptions in the one-way ANOVA

Abstract: This article focuses on the relationship between true Types I and II error probabilities and the effects of departures from independence assumptions on hypothesis testing in the oneway analysis of variance. A method for constructing a useful class of nonidentity error correlation matrices suitable for studying this relationship is offered and explored. Special emphasis is placed on the numerical features of this relationship that can be easily exploited in the classroom. The perspective is adaptable to more complicated designs including regression models.