The Analysis of Variance

Fixed, Random and Mixed Models
1. Auflage 2000
ISBN: 978-0-8176-4012-5
Verlag: Birkhäuser

Buch, Englisch, 742 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 2790 g

The analysis of variance (ANOYA) models have become one of the most widely used tools of modern statistics for analyzing multifactor data. The ANOYA models provide versatile statistical tools for studying the relationship between a dependent variable and one or more independent variables. The ANOYA mod­ els are employed to determine whether different variables interact and which factors or factor combinations are most important. They are appealing because they provide a conceptually simple technique for investigating statistical rela­ tionships among different independent variables known as factors. Currently there are several texts and monographs available on the sub­ ject. However, some of them such as those of Scheffe (1959) and Fisher and McDonald (1978), are written for mathematically advanced readers, requiring a good background in calculus, matrix algebra, and statistical theory; whereas others such as Guenther (1964), Huitson (1971), and Dunn and Clark (1987), although they assume only a background in elementary algebra and statistics, treat the subject somewhat scantily and provide only a superficial discussion of the random and mixed effects analysis of variance.

Zielgruppe

Research

Autoren/Hrsg.

Sahai, Hardeo

Ageel, Mohammed I.

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Mathematische Analysis Elementare Analysis und Allgemeine Begriffe
• Mathematik | Informatik Mathematik Mathematische Analysis Variationsrechnung
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Datenanalyse, Datenverarbeitung

Inhaltsverzeichnis

1. Introduction.- 2. One-Way Classification.- 3. Two-Way Crossed Classification Without Interaction.- 4. Two-Way Crossed Classification With Interaction.- 5. Three-Way and Higher-Order Crossed Classifications.- 6. Two-Way Nested (Hierarchical) Classification.- 7. Three-Way and Higher-Order Nested Classifications.- 8. Partially Nested Classifications.- 9. Finite Population and Other Models.- 10. Some Simple Experimental Designs.- 11. Analysis of Variance Using Statistical Computing Packages.- Appendices.- B Chi-Square Distribution.- E Noncentral Chi-Square Distribution.- I Studentized Range Distribution.- J Studentized Maximum Modulus Distribution.- K Satterthwaite Procedure and Its Application to.- Analysis of Variance.- L Components of Variance.- M Intraclass Correlation.- N Analysis of Covariance.- Q Expected Value and Variance.- R Covariance and Correlation.- S Rules for Determining the Analysis of Variance Model.- T Rules for Calculating Sums of Squares and Degrees of Freedom.- U Rules for Finding Expected Mean Squares.- V Samples and Sampling Distribution.- W Methods of Statistical Inference.- X Some Selected Latin Squares.- Y Some Selected Graeco-Latin Squares.- Z PROC MIXED Outputs for Some Selected.- Worked Examples.- Statistical Tables and Charts.- Tables.- I Cumulative Standard Normal Distribution.- II Percentage Points of the Standard Normal Distribution.- IV Critical Values of the Chi-Square Distribution.- X Critical Values of the Studentized Range Distribution.- XI Critical Values of the Dunnett’s Test.- XII Critical Values of the Duncan’s Multiple Range Test.- XIV Critical Values of the Dunn-Sidák’s Multiple Comparison Test.- XV Critical Values of the Studentized Maximum Modulus Distribution.- XVI Critical Values of the Studentized AugmentedRange
Distribution.- XVIII Coefficients of Order Statistics for the Shapiro-Wilk’s W Test for Normality.- XIX Critical Values of the Shapiro-Wilk’s W Test for Normality.- XXI Critical Values of the Bartlett’s Test for Homogeneity of Variances.- XXIII Critical Values of the Cochran’s C Test for Homogeneity of Variances.- XXIV Random Numbers.- Charts.- IV Curves of Constant Power for Determination of Sample Size in a One-Way Analysis of Variance (Fixed.- Effects Model): Feldt-Mahmoud Charts.- References.- Author Index.