Theory Of Statistical Testing Research Articles

“What exactly are you inferring?” A closer look at hypothesis testing

This critical review describes the confused application of significance tests in environmental toxicology and chemistry that often produces incorrect inferences and indefensible regulatory decisions. Following a brief review of statistical testing theory, nine recommendations are put forward. The first is that confidence intervals be used instead of hypothesis tests whenever possible. The remaining recommendations are relevant if hypothesis tests are used. They are as follows: Define and justify Type I and II error rates a priori; set and justify an effect size a priori; do not confuse p(E|H0) and p(H0|E); design tests permitting Positive Predictive Value estimation; publish negative results; estimate a priori, not post hoc, power; as warranted by study goals, favor null hypotheses that are not conventional nil hypotheses; and avoid definitive inferences from isolated tests.

Performance analysis of an ad hoc network for emergency and collaborative environments

Ad hoc networks can be used for quickly set up small spontaneous networks, such as in emergency situations or during sessions of cooperative works as in conferences, teaching rooms or meetings. Real-life tests of such networks are invaluable in order to assess models used in simulation. However, the number of factors affecting the performance of an ad hoc network is high, theoretically infinite. There are, for example, system factors, such as routing protocols, MAC and physical layer protocols and their cross-layer interaction, as well as environment factors, such as the presence of walls, foliage and surrounding moving objects. In order to optimize protocols, it is important both to design repeatable experiments of the network and to identify the parameters which really affect the system behavior. We accomplish the former demand by building a simple network by means of off-the-shelf hardware and software. For the latter point, we propose to use methods of statistical testing theory to identify these parameters in a compact manner. In particular, we use OLSR as a routing protocol. Results from real experiments in outdoor and indoor scenarios confirm the horizon effect of ad hoc multi-hop networks and show that there is a treatment effect caused by the window size of OLSR.

Identification of essentially derived varieties with molecular markers: an approach based on statistical test theory and computer simulations

Genetic similarities (GS) based on molecular markers have been proposed as a tool for identification of essentially derived varieties (EDVs). Nevertheless, scientifically reliable criteria for discrimination of EDVs and independently derived varieties with GS estimates are scanty, and implementation into practical breeding has not yet taken place. Our objectives were to (1) assess the influence of chromosome number and length, marker density, and distribution, as well as the degree of polymorphism between the parental inbreds on the distribution of GS between parental inbreds and their progenies [GS(P1,O)] derived from F2 and different backcross populations and (2) evaluate these factors with regard to the power for distinguishing F2- versus BC1- and BC1- versus BC2-derived lines with molecular markers. We developed an approach based on statistical test theory for the identification of EDVs with molecular markers. Standard deviations and overlaps of distributions of GS(P1,O) of F2-, BC1-, and BC2-derived lines were smaller with (1) increasing chromosome number and length, (2) increasing marker density, and (3) uniformly instead of randomly distributed markers, approaching a lower boundary determined by the genetic parameters. The degree of polymorphism between the parental inbreds influenced the power only if the remaining number of polymorphic markers was low. Furthermore, suggestions are made for (1) determining the number of markers required to ascertain a given power and (2) EDV identification procedures.

Testing for a Unit Root in ARIMA Processes

A unit root has important long-run implications for many time series in economics and finance. This paper develops a unit-root test of an ARIMA(p−1, 1, q) with drift null process against a trend-stationary ARMA(p, q) alternative process, where the order of the time series is assumed known through previous statistical testing or relevant theory. This test uses a point-optimal test statistic, but it estimates the null and alternative variance-covariance matrices that are used in the test statistic. Consequently, this test approximates a point-optimal test. Simulations show that its small-sample size is close to the nominal test level for a variety of unit-root processes, that it has a robust power curve against a variety of stationary alternatives, that its combined small-sample size and power properties are highly competitive with previous unit-root tests, and that it is robust to conditional heteroskedasticity. An application to post-Second World War real per capita gross domestic product is provided.

A New Similarity Measure Based on Intraclass Statistics for Biometric Systems

A biometric system determines the identity of a person by measuring physical features that can distinguish that person from others. Since biometric features have many variations and can be easily corrupted by noises and deformations, it is necessary to apply machine learning techniques to treat the data. When applying the conventional machine learning methods in designing a specific biometric system, however, one first runs into the difficulty of collecting sufficient data for each person to be registered to the system. In addition, there can be an almost infinite number of variations of non-registered data. Therefore, it is difficult to analyze and predict the distributional properties of real data that are essential for the system to deal with in practical applications. These difficulties require a new framework of identification and verification that is appropriate and efficient for the specific situations of biometric systems. As a preliminary solution, this paper proposes a simple but theoretically well-defined method based on a statistical test theory. Our computational experiments on real-world data show that the proposed method has potential for coping with the actual difficulties in biometrics.

The Incompleteness of Probability Models and the Resultant Implications for Theories of Statistical Inference

It is argued that statistical testing has been overvalued because it is perceived as an optimal, objective, algorithmic method of testing hypotheses. Researchers need to be made aware of the subjective nature of statistical inference in order not to make too much of it. Examples are given of aspects of data that are ignored in the computation of p values but are relevant to their interpretation. These include the fit of the chance distribution, the presence of influential points, the possibilities for post hoc selectivity, the presence of expected and unexpected trends in the data, and the amount of sampling variability that is present. Researchers should be taught that although probabilistic reasoning is a deductive process, making inferences from data is not. There is always potentially relevant information available over and above that which has been taken account of by any p value. Indeed, it is noted that a probability can never characterize all the uncertainty regarding an event because of problems to do with self-reference. Theories of statistical inference need to be weakened to take these ideas into account. Statistical tests assess the implausibility of supposing that the sign of a difference can be explained away as due to sampling error and they work only to the extent that this implausibility can be inferred from the size of the test statistic. The process of inferring plausibility is a subjective one and is inconsistent with the Neyman-Pearson Theory of statistical testing and Fisher's notion of fiducial statistical tests. Probabilities need to be assessed in the context of what they have and have not taken into account and this weakens Bayesian statistical inferences as well as classical ones.

Lan Based Asymptotic Theory for Time Series

The local asymptotic normality (LAN) , introduced by LeCam, is the most fundamental concept in the statistical asymptotic theory. If LAN property for a class of statistical models is established, then the asymptotic optimality of estimator and test can be described in terms of the central sequence. This concept gives a unified view for the statistical estimation and testing theory. Recently the LAN concept has been introduced to the asymptotic theory for time series. This paper provides a personal overview of the LAN results for linear processes, nonlinear processes, diffusion processes, long-memory processes, and locally stationary processes, etc.. The results are applied to the asymptotic estimation, testing theory, and discriminant analysis in time series. Then, construction of asymptotically optimal estimator, test and discriminator is discussed.

Majorization, polyhedra, and statistical testing problems

There are important connections between majorization and convex polyhedra. Both weak majorization and majorization are preorders related to certain simple convex cones. We investigate the facial structure of a polyhedral cone C associated with a layered directed graph. A generalization of weak majorization based on C is introduced. It defines a preorder of matrices. An application in statistical testing theory is discussed in some detail.

Análise rotineira de dados de vigilância em saúde pública: que procedimentos estatísticos utilizar?

In recent years an increasing interest in epidemiological surveillance (that we prefer to label public health surveillance) has emerged. The viewpoint that the ease of access to computers and statistical software may permit the use of more sophisticated statistical methodologies in the analysis of surveillance data has been profounded in many studies. It is a cause of concern that this attitude, when used indiscriminated by, may lead to analysis lacking in theoretical support. Thus, first, a viewpoint about surveillance in public health is presented and the basic propositions of the theory of statistical hypothesis tests and interval estimation are described briefly and without technicalities. The nature of surveillance data, their nonsampling character and non-random selection are also commented on. Some descriptive procedures that may be used without loss of quality in analysis are described than some procedures that are proposed in the relevant international literature but that need fuller investigation before being introduced in routine data analysis are given.

Die Falsifikation Statistischer Hypothesen

It is widely held that falsification of statistical hypotheses is impossible. This view is supported by an analysis of the most important theories of statistical testing: these theories are not compatible with falsificationism. On the other hand, falsificationism yields a basically viable solution to the problems of explanation, prediction and theory testing in a deterministic context. The present paper shows how to introduce the falsificationist solution into the realm of statistics. This is done mainly by applying the concept of empirical content to statistical hypotheses. It is shown that empirical content is a substitute for ‘power’ as defined by Neyman and Pearson. Since the empirical content of a hypothesis is independent of alternative hypotheses, the proposed theory of statistical testing allows for tests of isolated hypotheses.

Models for testing : A secondary note.

This is a comment on a note by Solow (1990). It is shown that Solow's simulation results indicate that Bulmer's test for density dependence is non-robust to a particular kind of second-order Markovity that might well be overlooked by an ecologist. It is suggested that Solow's claim that Bulmer's test is insensitive is not wholly justified. Some scepticism concerning the applicability of statistical testing theory to animal population data is expressed.

空間相関関数とその統計的検定の実用的計算手法と視覚化 : 実用的メッシュデータ解析システム構築のための空間相関分析法の体系化 その1

The space correlation analysis (SCA) was proposed with its possibility of application on urban analysis in our previous papers. The calculating program of SCA, however, is not easy to develop for urban planners because the program has a relatively large size and complicated. The calculating theory is reconstructed to make SCA fit for practical use. The following possibilities of calculating method of SCA are shown ; 1) the space influence function (SIF) can be calculated by using ordinary library program, 2) the space correlation function (SCF) can be calculated very rapidly by using FFT (fast Fourier transform). Also presented in this paper are visual representation methods of SCA model with reliable range of estimated parameters. It is very important in actual planning to know the structure of spatial influence relation of urban activities accurately and intuitionally. Using the statistical range estimation and testing theory, 1) the method for getting the confidence interval of SCF is shown, and 2) the method for grouping the value of SCF is shown. The visual presentation of the results of the above methods are very effective to assist urban planners to understand the characteristics of spatial relation of urban activities.

Comments on Oakes on the Foundations of Statistical Inference in the Social and Behavioral Sciences: The Market for Statistical Significance

A recent book by psychologist M. Oakes (1986) surveys the practice and logical foundations of statistical tests in the social and behavioral sciences. The book is aimed at producers and consumers of statistical research reports in these disciplines and has as its objective a shift in common practice from “significance” tests (however interpreted) to their more complete and informative analogs, confidence intervals. Much is made of the writings of the great English scientist and statistician Sir Ronald Fisher, to whom, most of all, the received theory of statistical tests is due. Oakes misrepresents Fisher's position on points of logic. There is also some overstatement of the case for confidence intervals. More interesting is the author's positive explanation for the widespread acceptance of significance tests among applied researchers, for there is no less settled logic or scheme of inference within theoretical statistics, as instantiated by the current papers of Casella and Berger (1987) and Berger and Sellke (1987) in the Journal of the American Statistical Association. That research workers in applied fields continue to use significance tests routinely may be explained by forces of supply and demand in the market for statistical evidence, where the commodity traded is not so much evidence, but “statistical significance.”

Photogrammetry as a tool for detecting recent crustal movements

Progress in model building and in advanced exposure and evaluation methods is leading photogrammetry up into the field of precise point determination, up to now solved by classical geodetic triangulation and/or trilateration. In combination with the statistical test theory, photogrammetry can be used as a tool to detect recent crustal movements or deformations of man-made constructions, such as in coal mining or oil and gas exploitation. For these reasons, this paper deals with model building for modern aerial triangulation with respect to hypothesis tests to detect point displacements greater than the measurement noise. An example from brown-coal mining demonstrates accuracies and the application of some statistical tests shows the efficiency of advanced aerial photogrammetry.

On objectivity and subjectivity in statistical inference: A response to Mayo

In this paper we respond to the article ‘An Objective Theory of Statistical Testing’ by D. G. Mayo (1983). We argue that the theory of testing developed by Mayo, NPT*, is neither novel nor objective. We also respond to the claims made by Mayo against Bayesian theory.

An objective theory of statistical testing

Theories of statistical testing may be seen as attempts to provide systematic means for evaluating scientific conjectures on the basis of incomplete or inaccurate observational data. The Neyman-Pearson Theory of Testing (NPT) has purported to provide an objective means for testing statistical hypotheses corresponding to scientific claims. Despite their widespread use in science, methods of NPT have themselves been accused of failing to be objective; and the purported objectivity of scientific claims based upon NPT has been called into question. The purpose of this paper is first to clarify this question by examining the conceptions of (I) the function served by NPT in science, and (II) the requirements of an objective theory of statistics upon which attacks on NPT's objectivity are based. Our grounds for rejecting these conceptions suggest altered conceptions of (I) and (II) that might avoid such attacks. Second, we propose a reformulation of NPT, denoted by NPT*, based on these altered conceptions, and argue that it provides an objective theory of statistics. The crux of our argument is that by being able to objectively control error frequencies NPT* is able to objectively evaluate what has or has not been learned from the result of a statistical test.

Book Reviews

Book reviewed in this article:Probability Theory: Independence, Interchangeability, Martingales. By Y. S. Chow and H. Teicher.Gaussian Random Processes. By I. A. Ibragimov & Y. A. Rozanov.Stochastic Approximation Methods for Constrained and Unconstrained Systems. By Harold J. Kushner & Dean S. Clark.Random Walks with Stationary Increments. By H. C. P. Berbee.Asymptotic Optimality Theory for Testing Problems with Restricted Alternatives. By T. A. B. Snijders.Large Deviation and Asymptotic Efficiencies. By P. Groeneboom.Asymptotic Theory of Statistical Tests and Estimation. Edited by I. M. Chakravarti.Developments in Statistics, Vol. 1. Edited by P. R. Krishnaiah.Developments in Statistics, Vol. 2. Edited by P. R. Krishnaiah.The Analysis of Cross‐Classified Categorical Data. By S. E. Feinberg.Analysis of Qualitative Data, Volume 2. By Shelby J. Haberman.Introduction to Statistics. By M. R. Heyworth & J. R. Sealy.Identification of Outliers. By D. M. Hawkins.Randomization Tests. By Eugene S. Edgington.Tables for Normal Tolerance Limits, Sampling Plans, and Screening. By Robert E. Odeh & D. B. Owen.The Algebra of Econometrics. By D. S. G. Pollock.Decision Theory and Social Ethics. Edited by Hans W. Gottinger and Werner Leinfellner.

Asymptotic Theory of Statistical Tests and Estimation: In Honor of Wassily Hoeffding.

Asymptotic Theory of Statistical Tests and Estimation: In Honor of Wassily Hoeffding.

Dielectric Permittivity, Conductivity, and Breakdown Characteristics of Polymer-MICA Composites

Novel and economically promising polyethylene (PE) mica composites containing up to 50% mica by weight have been produced by the following procedure: Highaspect-ratio mica flakes (-40 +70 mesh) were treated in a "cold" microwave plasma in ethylene vapor, then blended with PE powder and compression molded. Improvements in mechanical and rheological properties of plasma-treated composites have prompted us to carry out "diagnostic" measurements of the interfacial polarization [Maxwell-Wagner (M-W) effect]. As the major axes of the mica "ellipsoids" are well aligned by the molding process, Sillars' modification of M-W theory should describe the dielectric permittivity of the composites adequately: satisfactory agreement between experimental and theoretical data support this interpretation. The high-voltage insulating properties of the present composite materials have been evaluated by means of dc conductivity and breakdown measurements. A novel high-voltage endurance test based on a cylinder-plane geometry has been devised, where the cylinder is a thin wire electrode embedded beneath one surface of a sample plaque. This procedure has the advantage of providing an infinite number of possible initiation sites for breakdown, as required by the theory of statistical life testing. Experimental Weibull plots indicate, firstly, that breakdown characteristics are extremely sensitive to sample quality (e.g. residual porosity) and, secondly, that plasma treatment of the mica substantially enhances high-voltage endurance relative to that encountered with untreated mica. The ultimate value of mica as a filler in PE-based high-voltage insulation is, as yet, uncertain.

The Logic of Tests of Significance

In spite of the fact that the Neyman–Pearson theory of testing is the official theory of statistical testing, most research publications in the social sciences use a pattern of inductive reasoning that is characteristic of Fisherian tests of significance. The exact structure and rationale of this pattern of reasoning is widely misunderstood. The goal of the paper is to describe precisely the pattern and its rationale, and to show that while it is far more cogent than Fisher's critics have realized, it does not logically sustain the inferences it sanctions.