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Explores mathematical statistics in its entirety—from the fundamentals to modern methods This book introduces readers to point estimation, confidence intervals, and statistical tests. Based on the general theory of linear models, it provides an in-depth overview of the following: analysis of variance (ANOVA) for models with fixed, random, and mixed effects; regression analysis is also first presented for linear models with fixed, random, and mixed effects before being expanded to nonlinear models; statistical multi-decision problems like statistical selection procedures (Bechhofer and Gupta) and sequential tests; and design of experiments from a mathematical-statistical point of view. Most analysis methods have been supplemented by formulae for minimal sample sizes. The chapters also contain exercises with hints for solutions. Translated from the successful German text, Mathematical Statistics requires knowledge of probability theory (combinatorics, probability distributions, functions and sequences of random variables), which is typically taught in the earlier semesters of scientific and mathematical study courses. It teaches readers all about statistical analysis and covers the design of experiments. The book also describes optimal allocation in the chapters on regression analysis. Additionally, it features a chapter devoted solely to experimental designs. Classroom-tested with exercises included Practice-oriented (taken from day-to-day statistical work of the authors) Includes further studies including design of experiments and sample sizing Presents and uses IBM SPSS Statistics 24 for practical calculations of data Mathematical Statistics is a recommended text for advanced students and practitioners of math, probability, and statistics.

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"Mathematische Statistik" hat wegen des gro?en Anwendungsbedarfes stetig an Attraktivitat gewonnen – und auch theoretisch sind neue Ansatze entwickelt worden. Ein besonderer Schwerpunkt liegt auf der Versuchsplanung, die haufig gegenuber der Auswertung vernachlassigt wird. Unter konsequenter Berucksichtigung der Entwicklungen der letzten Jahrzehnte ist ein neues Buch entstanden. Kenntnisse in der Ma?theorie und der Wahrscheinlichkeitsrechnung sind hilfreich, aber nicht notwendig, da die Autoren die Materie leicht verstandlich beschrieben haben. Ein Schwerpunkt liegt auf der Versuchsplanung, die zu oft vernachlassigt wird und oft neben der Auswertung benachteiligt ist. Konsequenterweise nimmt in diesem Buch die Planung des Stichprobenumfangs und die Beschreibung von Versuchsanlagen einen gro?en Raum ein – immer eingebettet in die passenden Auswertungsverfahren wie die Varianz- und Regressionsanalyse. Ein Muss fur alle Natur- und Ingenieurwissenschaftler, die empirisch arbeiten und daneben auch an der Begrundung der Methoden interessiert sind.

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Statistics in Psychology covers all statistical methods needed in education and research in psychology. This book looks at research questions when planning data sampling, that is to design the intended study and to calculate the sample sizes in advance. In other words, no analysis applies if the minimum size is not determined in order to fulfil certain precision requirements. The book looks at the process of empirical research into the following seven stages: Formulation of the problem Stipulation of the precision requirements Selecting the statistical model for the planning and analysis The (optimal) design of the experiment or survey Performing the experiment or the survey Statistical analysis of the observed results Interpretation of the results.

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