Statistic

About: Statistic is a research topic. Over the lifetime, 9019 publications have been published within this topic receiving 308785 citations. The topic is also known as: sample statistic.

Use of Ranks in One-Criterion Variance Analysis

Abstract: Given C samples, with n i observations in the ith sample, a test of the hypothesis that the samples are from the same population may be made by ranking the observations from from 1 to Σn i (giving each observation in a group of ties the mean of the ranks tied for), finding the C sums of ranks, and computing a statistic H. Under the stated hypothesis, H is distributed approximately as χ2(C – 1), unless the samples are too small, in which case special approximations or exact tables are provided. One of the most important applications of the test is in detecting differences among the population means.* * Based in part on research supported by the Office of Naval Research at the Statistical Research Center, University of Chicago.

Practical Meta-Analysis

Abstract: Introduction Problem Specification and Study Retrieval Selecting, Computing and Coding the Effect Size Statistic Developing a Coding Scheme and Coding Study Reports Data Management Analysis Issues and Strategies Computational Techniques for Meta-Analysis Data Interpreting and Using Meta-Analysis Results

Understanding interobserver agreement: the kappa statistic.

Abstract: Items such as physical exam findings, radiographic interpretations, or other diagnostic tests often rely on some degree of subjective interpretation by observers. Studies that measure the agreement between two or more observers should include a statistic that takes into account the fact that observers will sometimes agree or disagree simply by chance. The kappa statistic (or kappa coefficient) is the most commonly used statistic for this purpose. A kappa of 1 indicates perfect agreement, whereas a kappa of 0 indicates agreement equivalent to chance. A limitation of kappa is that it is affected by the prevalence of the finding under observation. Methods to overcome this limitation have been described.

The Lagrange Multiplier Test and its Applications to Model Specification in Econometrics

Abstract: Many econometric models are susceptible to analysis only by asymptotic techniques and there are three principles, based on asymptotic theory, for the construction of tests of parametric hypotheses. These are: (i) the Wald (W) test which relies on the asymptotic normality of parameter estimators, (ii) the maximum likelihood ratio (LR) procedure and (iii) the Lagrange multiplier (LM) method which tests the effect on the first order conditions for a maximum of the likelihood of imposing the hypothesis. In the econometric literature, most attention seems to have been centred on the first two principles. Familiar " t-tests " usually rely on the W principle for their validity while there have been a number of papers advocating and illustrating the use of the LR procedure. However, all three are equivalent in well-behaved problems in the sense that they give statistics with the same asymptotic distribution when the null hypothesis is true and have the same asymptotic power characteristics. Choice of any one principle must therefore be made by reference to other criteria such as small sample properties or computational convenience. In many situations the W test is attractive for this latter reason because it is constructed from the unrestricted estimates of the parameters and their estimated covariance matrix. The LM test is based on estimation with the hypothesis imposed as parametric restrictions so it seems reasonable that a choice between W or LM be based on the relative ease of estimation under the null and alternative hypotheses. Whenever it is easier to estimate the restricted model, the LM test will generally be more useful. It then provides applied researchers with a simple technique for assessing the adequacy of their particular specification. This paper has two aims. The first is to exposit the various forms of the LM statistic and to collect together some of the relevant research reported in the mathematical statistics literature. The second is to illustrate the construction of LM tests by considering a number of particular econometric specifications as examples. It will be found that in many instances the LM statistic can be computed by a regression using the residuals of the fitted model which, because of its simplicity, is itself estimated by OLS. The paper contains five sections. In Section 2, the LM statistic is outlined and some alternative versions of it are discussed. Section 3 gives the derivation of the statistic for