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This book provides many kinds of statistical tests available in Statistics, which are widely used in various disciplines, especially very much useful for the researchers who need statistical tools and techniques for their data analysis. This book will help them to interpret their data themselves in a better manner. In this book, frequently used statistical tests are presented in a simple and understandable way with real life examples and exercises

Ghanem reviews '100 Statistical Tests' by Gopal K. Kanji.

In economics and other social sciences, complex processes are often represented by numerical models of reality which more or less well reflect behavioral relationships and interactions. Such attempts are the subject of a lecture course 'Mathematical Theory of Democracy' by the author at the Faculty of Economics of the Karlsruhe Institute of Technology. One new result in this field is presented here in the form of a statistical test to decide whether a political party or coalition of parties represents a majority of the population. For this purpose, party or coalition positions on a sample of policy issues, like introduction of a legal nationwide minimum wage, privatization of railways, and others, are compared with the results of public opinion polls on the same issues. The test is based on estimating the statistical significance of the coincidence observed (i.e. how likely is the coincidence by chance) to the end of accepting or rejecting the representativeness hypothesis. The test is developed for single parties and coalitions of two or three parties. It is illustrated with an estimation of representativeness of five major German parties and their potential coalitions basing on the official party manifestos published before the German parliamentary elections 2009 and on relevant polls of public opinion. ; In der Ökonomie und den anderen Sozialwissenschaften wird immer wieder versucht, komplexe Prozesse der Wirklichkeit durch numerische Modelle abzubilden - was mit Abstraktionen für z. B. Verhaltens- und Wirkungsrelationen mehr oder weniger gut gelingt. Solche Versuche sind Gegenstand einer Vorlesungsreihe 'Mathematische Theorie der Demokratie' des Autors an der Wirtschaftswissenschaftlichen Fakultät des Karlsruhe Institut für Technologie. Ein neues Ergebnis in diesem Bereich wird hier vorgelegt in Form eines statistischen Tests, der entscheiden soll, ob eine politische Partei oder eine Parteienkoalition repräsentativ im Sinn der Bevölkerungsmehrheit agiert. Zu diesem Zweck wird die Übereinstimmung von Parteien- oder Koalitionspositionen mit Ergebnissen von Meinungsumfragen in der Bevölkerung verglichen, etwa zur Einführung eines bundesweiten gesetzlichen Mindestlohns oder der Privatisierung des Schienenverkehrs und anderem mehr. Der Test basiert auf der Einschätzung der statistischen Signifikanz der beobachteten Übereinstimmung (d.h. wie wahrscheinlich ist eine nur zufällige Übereinstimmung), um die Hypothese von der Repräsentativität der Politik zu akzeptieren oder abzulehnen. Die Studie spielt die Repräsentativität von einzelnen Parteien sowie von Zweier- und Dreier-Koalitionen durch. Darunter ist auch die Konstellation der fünf großen deutschen Parteien und ihrer potentiell möglichen Koalitionen auf der Basis der Bundestagswahl von 2009.

In the paper, a selection of statistical tests for median are presented. In particular, parametric and nonparametric significance tests are considered. In the case of parametric tests the critical regions are constructed on the basis of the known population distribution and the form of the alternative hypothesis. For chosen distributions the critical values are presented. In the case of nonparametric tests we consider tests for which the sample median dispersion is estimated based on order statistics of appropriate ranks. The use of the bootstrap method for the median dispersion estimation in the test statistic construction is the author's own proposal. The simulation analysis of the nonparametric tests' properties allows to compare these tests with each other, showing better results for the bootstrap variant, especially for small samples.

AbstractHyperparameter tuning is one of the most time-consuming parts in machine learning. Despite the existence of modern optimization algorithms that minimize the number of evaluations needed, evaluations of a single setting may still be expensive. Usually a resampling technique is used, where the machine learning method has to be fitted a fixed number of k times on different training datasets. The respective mean performance of the k fits is then used as performance estimator. Many hyperparameter settings could be discarded after less than k resampling iterations if they are clearly inferior to high-performing settings. However, resampling is often performed until the very end, wasting a lot of computational effort. To this end, we propose the sequential random search (SQRS) which extends the regular random search algorithm by a sequential testing procedure aimed at detecting and eliminating inferior parameter configurations early. We compared our SQRS with regular random search using multiple publicly available regression and classification datasets. Our simulation study showed that the SQRS is able to find similarly well-performing parameter settings while requiring noticeably fewer evaluations. Our results underscore the potential for integrating sequential tests into hyperparameter tuning.

In recent years, there has been a growing interest in the use of local measures such as Anselin's LISAs and Ord and Getis G statistics to identify local patterns of spatial association. The statistical significance test based on local statistics is one of the most important aspects in performing this kind of analysis, and a randomized permutation approach and normal approximation are commonly used to derive the p-values of the statistics. To circumvent some of the shortcomings of these existing methods and to offer a more formal approach in line with classical statistical framework, we develop in this paper an exact method for computing the p-values of the local Moran's Ii, local Geary's ci, and the modified Ord and Getis G statistics based on the distributional theory of quadratic forms in normal variables. Furthermore, an approximate method, called three-moment χ2 approximation, with explicit calculation formulae is also proposed to achieve a computational cost lower than the exact method. Numerical evaluation on the accuracy of the approximate null distributions of the local statistics demonstrates that the proposed three-moment χ2 method is useful in some situations although it is inappropriate for approximating the null distribution of Ii. The study not only provides an exact test for local patterns of spatial association, but also put the tests of several local statistics within a unified statistical framework.