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Showing papers on "Statistical hypothesis testing published in 1977"



Journal ArticleDOI
TL;DR: In this paper, alternative testing criteria in the linear multivariate regression model, and the possibility of conflict among them, are surveyed and a strong result is that a systematic numerical inequality relationship exists; specifically, Wald, LRa LM, and likelihood ratio (LR).
Abstract: This paper surveys alternative testing criteria in the linear multivariate regression model, and investigates the possibility of conflict among them. We consider the asymptotic Wald, likelihood ratio (LR), and Lagrange multiplier (LM) tests. These three test statistics have identical limiting chi-square distributions; thus their critical regions coincide. A strong result we obtain is that a systematic numerical inequality relationship exists; specifically, Wald , LRa LM. Since the equality relationship holds only if the null hypothesis is exactly true in the sample, in practice there will always exist a significance level for which the asymptotic Wald, LR, and LM tests will yield conflicting inference. However, when the null hypothesis is true, the dispersion among the teststatistics will tend to decrease as the sample size increases. We illustrate relationships among the alternative testing criteria with an empirical example based on the three reduced form equations of Klein's Model I of the United States economy, 1921-1941.

269 citations


Journal ArticleDOI
TL;DR: This article pointed out that the statistical textbooks of that period were full of misconceptions, and were rather uniformly unaware of the new and dramatic development of the mathematical discipline of statistical inference, including the improved logic of estimation and of hypothesis testing.
Abstract: Some 40 years ago, Harold Hotelling pointed out that the statistical textbooks of that period were written largely by non-mathematicians. Those books were full of misconceptions, and were rather uniformly unaware of the new and dramatic development of the mathematical discipline of statistical inference. They did not take advantage of the sharpened logic for making decisions about populations on the basis of sample statistics, including the improved logic of estimation and of hypothesis testing. The situation was slowly remedied as more mathematical statisticians began to issue textbooks, until today the pendulum may have swung too far. In some quarters, the symbols of inference rather than the substance may have taken over. This appears to be especially true in the social sciences with which I am most acquainted, and to which this paper is largely (but not exclusively) addressed. For example, referees and editors of some journals insist on decorating tables of various kinds of data with stars and double stars, and on presenting lists of "standard errors", despite the fact that the implied probabilities for significance or confidence are quite erroneous from the point of view of statistical inference (see Problems 3 and 1 below).

234 citations


Journal ArticleDOI
R. Kashyap1
TL;DR: The optimum decision rule is asymptotically consistent and gives a quantitative explanation for the "principle of parsimony" often used in the construction of models from empirical data.
Abstract: This paper deals with the Bayesian methods of comparing different types of dynamical structures for representing the given set of observations. Specifically, given that a given process y(\cdot) obeys one of r distinct stochastic or deterministic difference equations each involving a vector of unknown parameters, we compute the posterior probability that a set of observations {y(1),...,y(N)} obeys the i th equation, after making suitable assumptions about the prior probability distribution of the parameters in each equation. The difference equations can be nonlinear in the variable y but should be linear in the parameter vector in it. Once the posterior probability is known, we can find a decision rule to choose between the various structures so as to minimize the average value of a loss function. The optimum decision rule is asymptotically consistent and gives a quantitative explanation for the "principle of parsimony" often used in the construction of models from empirical data. The decision rule answers a wide variety of questions such as the advisability of a nonlinear transformation of data, the limitations of a model which yields a perfect fit to the data (i.e., zero residual variance), etc. The method can be used not only to compare different types of structures but also to determine a reliable estimate of spectral density of process. We compare the method in detail with the hypothesis testing method, and other methods and give a number of illustrative examples.

156 citations


Journal ArticleDOI
TL;DR: In this article, the problems of nonlinear regression models are discussed, and model selection procedures for both nested and nonnested hypotheses are analyzed including an optimal sequential testing procedure for ordered nested hypotheses.
Abstract: In considering the problems of inference in nonlinear regression models the statistical and computational aspects of parameter estimation are discussed, and model selection procedures for both nested and nonnested hypotheses are analyzed including an optimal sequential testing procedure for ordered nested hypotheses. A distinction is made between tests of specification and tests of misspecification, and is discussed in relationship to the Wald, likelihood ratio, and Lagrange multiplier hypothesis testing principles. Degrees of freedom or small sample adjustments to the asymptotically valid test statistics are also discussed. The choice of production function from a class of CES functions, with either additive or multiplicative error specifications, for a cross section of UK industries, provides an application of the theory. 1. INTRODUCrION THIS PAPER IS CONCERNED WITH a number of methodological points of importance in applied econometrics, and though the particular application chosen is that of production function estimation, the points have a much wider relevance. The general area of concern is nonlinear inference, within which three problems are considered. (i) Nonlinear estimation is discussed and the feasibility and importance of estimating production functions directly for chosen structural specifications, rather than adopting one of the many indirect and approximate methods such as those of Arrow, et al. [4] (hereafter referred to as SMAC) and Kmenta [29], are emphasized. Nonlinear least squares estimates for a range of complex three- and two-factor production functions using United Kingdom industrial cross section data have been obtained. (ii) Problems of hypothesis testing, especially in nonlinear models, are considered and emphasis is placed on the importance of conducting this testing, for the many hypotheses which interest economists (e.g., the degrees of returns to scale and factor substitution) within a rigorous and systematic framework rather than the ad hoc way hypotheses are selected and tested in some studies. (iii) The closely ^lated problem of model selection is also analyzed, and the production function example illustrates the value of classical statistical procedures for ordered and nested hypotheses, while highlighting the problems that arise when there is a lack of unique ordering or nesting. There is, however, no claim to provide a complete solution to the model selection problem; rather an analysis of the problem is presented and a particular solution for the

127 citations


Journal ArticleDOI
Russell Lande1
TL;DR: To test the null hypothesis of evolution by random genetic drift against the alternative hypothesis of natural selection, it is necessary to determine how much of the phenotypic changes are an individual developmental response to a changing environment and how much a result of genetic evolution.
Abstract: Evolutionary biologists tend to ascribe phenotypic changes in populations to natural selection. Plausible hypotheses are regularly offered to explain how certain features of an organism are adaptive for its way of life. Failure to find an adaptive explanation is easily attributed to incompleteness of the study or pleiotropic effects of genes. More rarely, consideration is given to nonadaptive or maladaptive processes in evolution. Since mechanisms of phenotypic change other than natural selection are known (Van Valen, 1960), especially random genetic drift, the prevalent style of evolutionary logic begs the hypothesis of natural selection. It is therefore of interest to develop statistical tests on the pattern and rate of evolution of quantitative characters which can be used to distinguish natural selection from random genetic drift in natural and experimental populations. Pattern tests.-There are two basic types of pattern for which a null hypothesis of randomness may be tested. In natural populations, where there are no replications, the analysis sometimes suffers from lack of a control for relevant environmental variation in time. To test the null hypothesis of evolution by random genetic drift against the alternative hypothesis of natural selection, it is necessary to determine how much of the phenotypic changes are an individual developmental response to a changing environment and how much a result of genetic evolution. However, a time series from a natural population can be used to test the null hypothesis that the phenotypic changes form a random pattern. A variety of standard tests of randomness are available, based on the number and ordering of positive and negative changes, e.g. the sign test, the runs test. For application to fossil populations, it is notable

118 citations


Journal ArticleDOI
TL;DR: In this article, the authors proved a general theorem on the large sample normality of quadratic forms and showed that the conditions given in a similar theorem (Cliff and Ord) are inadequate to ensure normality.
Abstract: Test statistics for testing for spatial correlation in continuous variables have been given by both Moran and Geary and have subsequently been generalized. It has been conjectured for a long time that under the hypothesis of no spatial correlations all these statistics are normally distributed when the sample size is large. This paper proves a very general theorem on the large sample normality of quadratic forms. As corollaries to the theorem the asymptotic normality, under the hypothesis, of all the above-mentioned statistics is established. The necessary conditions are quite unrestrictive. It is also shown, by means of a counter example, that the conditions given in a similar theorem (Cliff and Ord) are inadequate to ensure normality.

57 citations


Journal ArticleDOI
TL;DR: In this paper, a statistical test of whether an additive nonlinear term in the response function should be omitted from a nonlinear regression specification is considered, and the regularity conditions used to obtain the asymptotic distributions of the customary test statistics are violated when the null hypothesis of omission is true.
Abstract: A statistical test of whether an additive nonlinear term in the response function should be omitted from a nonlinear regression specification is considered. The regularity conditions used to obtain the asymptotic distributions of the customary test statistics are violated when the null hypothesis of omission is true. Moreover, standard iterative algorithms are likely to perform poorly when the data support the null hypothesis. Methods designed to circumvent these mathematical and computational difficulties are described and illustrated.

47 citations


Journal ArticleDOI
TL;DR: In this article, three related test procedures are developed to test the composite hypothesis of normality for complete samples, which have their origins in an attempt to formalize the appearance of nonlinearity in probability plots.
Abstract: The problem of testing the composite hypothesis of normality is considered for complete samples. Three related test procedures are developed. The testing procedures have their origins in an attempt to formalize the appearance of nonlinearity in probability plots. The fitting of the ordered observations is accomplished by general linear least squares using the expected values of the standard normal order statistics (snos) as plotting positions. The moments of the snos have been approximated where necessary. The test statistics are ratios involving the squares of linear combinations of order statistics and the usual quadratic estimate of the variance. The percentage points ofthe test statistics aregenerally intractable by analytical methods. However percentage points are estimated using simulation techniques. The test procedures are compared to nine other tests of the composite hypothesis of normality in an empirical power study.

46 citations


Journal ArticleDOI
TL;DR: In this article, the theoretical effect of model misspecification on tests of the Efficient Market Hypothesis (EMH) is discussed. But the power of these tests is not known, since they rely on a certain market model without questioning the validity of the model used.
Abstract: TESTS OF THE Efficient Market Hypothesis (EMH) are in general "weak" tests. The null hypothesis has always been that the market is efficient with no specific alternative of inefficiency. Thus, the power of these tests is not known. The tests usually rely on a certain market model without questioning the validity of the model that was used. A misspecified model may provide test statistics that indicate that the market is efficient when it is not efficient and vice versa. The possibility that the EMH has not been rejected because the wrong market model was used, was never adequately considered. This paper is concerned with the theoretical effect of model misspecification on tests of the efficient market hypothesis. Since tests of the EMH usually use a certain market model, the conclusions are based on the assumption that the model is correctly specified. By deriving the possible biases due to model misspecification, we are actually concerned with the power (or validity) of the EMH tests. Tests of the EMH generally proceed in two stages: First, we estimate the relevant parameters using a certain market model; second, we use the estimated parameters for prediction and use the prediction errors, also called "residuals",' to test market efficiency. The statistical properties of the parameters, estimated in the first stage, depend on how well the market model describes the true underlying stochastic process. Serious misspecifications may yield biased and/or inefficient parameter estimates. This in turn may result in biased and/or inefficient estimates of the residuals in the second stage. The extent to which these misspecifications affect our conclusion about market efficiency depends on the way we use these residuals in testing the EMH. Under certain circumstances (to be specified later) the misspecifications, no matter how serious, will not affect our conclusions with regard to market efficiency. In the remainder of this paper we first consider general cases of misspecification, their effect on parameter estimates and on residual estimates. Then we consider the effects of misspecification in some specific cases. Finally we present the effect of ,B changes on residual estimates.

44 citations


Journal ArticleDOI
TL;DR: In this article, a computer simulation approach was used to generate bivariate normal observations X and Y which were analysed using: (1) an analysis of variance ignoring the covariate; (2) analysis of covariance; (3) an analyses of variance on the ratio Y/X.

Journal ArticleDOI
TL;DR: The lifetime assay for carcinogenicity that subjects groups of 50 animals per sex per dose to three doses and a control is examined for its statistical properties and whether hypothesis testing is a proper use of statistics is questioned, and alternatives are proposed.
Abstract: The lifetime assay for carcinogenicity that subjects groups of 50 animals per sex per dose to three doses and a control is examined for its statistical properties. Using the standard formulation of tests of hypothesis, it is shown that there is a 20–50% chance of having a false positive and that it is possible to define a “weak carcinogen”; in terms of the degree of effect that would produce a false negative less than 5% of the time. Whether hypothesis testing is a proper use of statistics in this context is questioned, and alternatives are proposed.

Journal ArticleDOI
P. de Souza1
TL;DR: It is shown that Itakura's prediction-residual ratio is intuitively unsatisfactory and theoretically misleading as a distance measure, and two slower, but more accurate statistical means of comparison are suggested.
Abstract: This paper considers the problem of comparing two sets of (LPC) coefficients or, more generally, that of comparing two short segments of speech via LPC techniques. It is shown that Itakura's prediction-residual ratio is intuitively unsatisfactory and theoretically misleading as a distance measure. Two slower, but more accurate statistical means of comparison are suggested, and these are supported by evidence from a simulation study.

Journal ArticleDOI
TL;DR: In this article, statistical tests permitting the detection of outliers in groups of X-ray intensity measurements are described, which may also be useful for rejecting the outlying counts automatically rather than discard complete sets of measurements.
Abstract: When used to determine the concentrations of chemical elements in samples, X-ray intensity measurements are processed by correction programmes. These measurements are now usually obtained with fully or partially automated instruments. In order to suppress useless computations on sets of results containing rogue values, statistical tests must first be applied to the original experimental data. From an economic standpoint, it may also be worthwhile to reject the outlying counts automatically rather than discard complete sets of measurements. Statistical tests permitting the detection of outliers in groups of results are described.

Journal ArticleDOI
TL;DR: The approximation joint probability distribution function of the link traffic flows on a network is given, which enables the log-likehood function for the estimation (with link data) of the traffic diversion parameter, Ф, that appears in most stochastic assignment models.

Journal ArticleDOI
TL;DR: In this paper, two methods of estimating the likelihood of committing false positive and false negative decisions with a mastery test were described and then investigated using Monte Carlo techniques, and conditions for obtaining accurate estimates were noted.
Abstract: False-positive and false-negative decisions are the two possible errors committed with a mastery test; yet the estimation of the likelihood of committing these errors has not been investigated. Accordingly, two methods of estimating the likelihood of committing these errors are described and then investigated using Monte Carlo techniques. Conditions for obtaining accurate estimates are noted.

Journal ArticleDOI
TL;DR: Using elementary statistical theory, techniques that can be used to initialize a simulation run and to determine its length are discussed and three practical variance reduction techniques are summarized, namely, control variates, antithetics, and common random numbers.
Abstract: Using elementary statistical theory, we discuss sta tistical techniques that can be used to initialize a simulation run and to determine its length, distin guishing between terminating and nonterminating sys tems and between stationary and nonstationary time series. Confidence intervals and hypothesis tests are included (see Section 2). In the case of k sys tem variants (at least 2), multiple comparison proce dures are presented which can be used to obtain simultaneously valid confidence intervals and to select a subset containing the best population, assuming a fixed number of simulation runs. Other wise ranking procedures can be used to determine the number of runs required to select the best system (Section 3). If many parameters and variables exist, selecting a limited number of combinations requires an experimental design, which must be analyzed with a regression metamodel (Section 4). The metamodel of main effects and interactions applies to both quantitative and qualitative factors; its adequacy ca...

Journal ArticleDOI
TL;DR: Means of solving the problems with the necessary consequences for planning of the experiment and its evaluation are discussed and practical recommendations are given applying also to other mutagenicity tests.
Abstract: Everyone involved in planning and carrying out biological experiments has to concern himself with statistical methods. Thus, descriptive statistics (e. g. calculation of the mean) help to present results briefly and comprehensively and, in addition, statistical test procedures permit decisions to be made even in an uncertain situation. The choice of the appropriate statistical procedure is, however, associated with considerable problems. These problems are discussed in detail using the dominant lethal test as an example. Means of solving the problems with the necessary consequences for planning of the experiment and its evaluation are discussed and practical recommendations are given applying also to other mutagenicity tests.

Journal ArticleDOI
TL;DR: In each of these cases, the appropriate decision rule is formulated, procedures are developed for estimating the preset count which is necessary to achieve a desired probability of detection, and a specific sequence of operations is provided for the worker in the field.
Abstract: The statistical model appropriate to measurements of low-level or background-dominant radioactivity is examined and the derived relationships are applied to two practical problems involving hypothesis testing: “Does the sample exhibit a net activity above background?” and “Is the activity of the sample below some preselected limit?” In each of these cases, the appropriate decision rule is formulated, procedures are developed for estimating the preset count which is necessary to achieve a desired probability of detection, and a specific sequence of operations is provided for the worker in the field.

Journal ArticleDOI
TL;DR: In this article, a directed graph representation for the empirically obtained hierarchy is discussed along with several assumptions that are necessary from a substantive point of view to justify the analysis that ordering theory provides, and a permutation test procedure is introduced that allows a formal comparison of a postulated hierarchy among the n items to the hierarchy elicited from the available data set.
Abstract: Given observations on a set of n dichotomously scored test items representing certain skills or tasks, ordering theory attempts to identify a hierarchical organization among the n items. Using this basic framework, a directed graph representation for the empirically obtained hierarchy is discussed along with several assumptions that are necessary from a substantive point of view to justify the analysis that ordering theory provides. Furthermore, a permutation test procedure is introduced that allows a formal comparison of a postulated hierarchy among the n items to the hierarchy elicited from the available data set.

Journal ArticleDOI
TL;DR: This paper discusses the statistical tests for comparison of the distribution of the length of birth order specific intervals for two or more groups when the distributions are obtained using life table techniques.
Abstract: This paper discusses the statistical tests for comparison of the distribution of the length of birth order specific intervals for two or more groups when the distributions are obtained using life table techniques. Such estimates involve incomplete intervals or arbitrarily censored observations so that conventional statistical test are not appropriate. The following tests are useful in such contexts and are illustrated using data from the 1965 National Fertility Survey. All tests have been constructed to test the null hypothesis that there is no difference in the distribution of birth intervals among the tested groups. (excerpt)

Journal ArticleDOI
TL;DR: In this paper, a multivariate procedure, based on the procedure outlined by Campbell and Stanely, is developed for inferring a treatment effect in the single-group, quasi-experimental time-series design.
Abstract: A multivariate procedure, based on the procedure outlined by Campbell and Stanely, is developed for inferring a treatment effect in the single-group, quasi-experimental time-series design. This procedure, which takes into account the dependent nature of the observations in the time-series experiment, is particularly suitable when the data exhibit linear trends. It is shown that the test statistic has a F distribution, and the procedure is illustrated with an example.

Journal ArticleDOI
TL;DR: In this article, the problem of demonstrating the invariance of factor structures across criterion groups is addressed and procedures are outlined which combine the replication of factor structure across four sex-race groups with the use of the coefficient of invariance to demonstrate the level of correlation associated with the factors identified in a self concept measure (the Self Observation Scales, Intermediate Form A).
Abstract: The problem of demonstrating the invariance of factor structures across criterion groups is addressed. Procedures are outlined which combine the replication of factor structures across four sex-race groups with the use of the coefficient of invariance to demonstrate the level of invariance associated with the factors identified in a self concept measure (the Self Observation Scales, Intermediate Form A). Implications for hypothesis testing are discussed.



ReportDOI
01 Jun 1977
TL;DR: In this paper, the problem of state estimation for discrete systems with parameters which may be switching within a finite set of values was considered, and it was shown that the optimal estimator requires a bank of elemental estimators with its number growing exponentially with time.
Abstract: : This paper considers the problem of state estimation for discrete systems with parameters which may be switching within a finite set of values In the general case it is shown that the optimal estimator requires a bank of elemental estimators with its number growing exponentially with time For the Markov parameter case, it is found that the optimal estimator requires only N squared elemental estimators where N is the number of possible parameter values

Book ChapterDOI
01 Jan 1977
TL;DR: This chapter considers another inference problem, namely, the problem of testing statistical hypotheses, where different types of hypotheses all of which are not statistical hypotheses are known.
Abstract: In Chapter 8 we considered the problem of estimating the parameters in a statistical distribution. Here we will consider another inference problem, namely, the problem of testing statistical hypotheses. This is a remarkable aspect of Statistics but at the same time this has led to many misinterpretations and misuses of statistical methods. Some people claim that anything and everything can be proved by the methods of Statistics. But it should be pointed out that we do not prove anything by Statistical Inference, but we will only make some probability statements regarding some unknown statistical quantities. We are familiar with different types of hypotheses all of which are not statistical hypotheses.

01 Jul 1977
TL;DR: In this paper, the authors treat the "goodness of fit" problem of testing whether the distribution F of a random sample X(1),..., X(n) belongs to a specified location and scale family, with the particular values (alpha, beta) of the locations and scales not both specified.
Abstract: : The authors treat the 'goodness of fit' problem of testing whether the distribution F of a random sample X(1),..., X(n) belongs to a specified location and scale family, with the particular values (alpha, beta) of the location and scale parameters not both specified.

01 Apr 1977
TL;DR: Results indicate that model misidentification leads to-severe perturbations of the nominal probabilities.
Abstract: Campbell (1969) argued for the interrupted time-series experiment as a useful methodology for testing intervention effects in the social sciences. The validity of the statistical hypothesis testing of time-series, is, however, dependent upon the proper identification of the underlying stochastic naturg of the data. Severaltypes of model misidentifications are examined for some commonly encountered models in the social sciences: Analytic expressions for actual Type I error and power probabilities are derived when the mathematics is tractable; simulation techniques are adopted for the remainder of the cases. Results indicate that model misidentification leads to-severe perturbations of the nominal probabilities. (Author)