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.

1. Introduction.- 1.0 Preview.- 1.1 Historical Developments.- 1.2 Analysis of Variance Models.- 1.3 Concept of Fixed and Random Effects.- 1.4 Finite and Infinite Populations.- 1.5 General and Generalized Linear Models.- 1.6 Scope of the Book.- 2. One-Way Classification.- 2.0 Preview.- 2.1 Mathematical Model.- 2.2 Assumptions of the Model.- 2.3 Partition of the Total Sum of Squares.- 2.4 The Concept of Degrees of Freedom.- 2.5 Mean Squares and Their Expectations.- 2.6 Sampling Distribution of Mean Squares.- 2.7 Test of Hypothesis: The Analysis of VarianceFTest.- Model I (Fixed Effects).- Model II (Random Effects).- 2.8 Analysis of Variance Table.- 2.9 Point Estimation: Estimation of Treatment Effects and Variance Components.- 2.10 Confidence Intervals for Variance Components.- 2.11 Computational Formulae and Procedure.- 2.12 Analysis of Variance for Unequal Number of Observations.- 2.13 Worked Examples for Model I.- 2.14 Worked Examples for Model II.- 2.15 Use of Statistical Computing Packages.- 2.16 Worked Examples Using Statistical Packages.- 2.17 Power of the Analysis of VarianceFTest.- Model I (Fixed Effects).- Model II (Random Effects).- 2.18 Power and Determination of Sample Size.- Sample Size Determination Using Smallest Detectable Difference.- 2.19 Inference About the Difference Between Treatment Means:.- Multiple Comparisons 64 Linear Combination of Means, Contrast and.- Orthogonal Contrasts.- Test of Hypothesis Involving a Contrast.- The Use of Multiple Comparisons.- Tukey's method.- Scheffé's method.- Interpretation of Tukey's and Scheffé's methods.- Comparison of Tukey's and Scheffé's methods.- Other Multiple Comparison Methods.- Least significant difference test.- Bonferroni's test.- Dunn-?idák's test.- Newman-Keuls's test.- Duncan's multiple range test.- Dunnett's test.- Multiple Comparisons for Unequal Sample Sizes and Variances.- Unequal sample sizes.- Unequal population variances.- 2.20 Effects of Departures from Assumptions Underlying the Analysis of Variance Model.- Departures from Normality.- Departures from Equal Variances.- Departures from Independence of Error Terms.- 2.21 Tests for Departures from Assumptions of the Model.- Tests for Normality.- Chi-square goodness-of-fit test.- Test for skewness.- Test for kurtosis.- Other Tests for Normality.- Shapiro-Wilk's W test.- Shapiro-Francia's test.- D'Agostino'sDtest.- Tests for Homoscedasticity.- Bartlett's test.- Hartley's test.- Cochran's test.- Comments on Bartlett's, Hartley's and Cochran's tests.- Other tests of homoscedasticity.- 2.22 Corrections for Departures from Assumptions of the Model..- Transformations to Correct Lack of Normality.- Logarithmic transformation.- Square-root transformation.- Arcsine transformation.- Transformations to Correct Lack of Homoscedasticity.- Logarithmic transformation.- Square-root transformation.- Reciprocal transformation.- Arcsine transformation.- Square transformation.- Power transformation.- Exercises.- 3. Two-Way Crossed Classification Without Interaction.- 3.0 Preview.- 3.1 Mathematical Model.- 3.2 Assumptions of the Model.- 3.3 Partition of the Total Sum of Squares.- 3.4 Mean Squares and Their Expectations.- Model I (Fixed Effects).- Model II (Random Effects).- Model III (Mixed Effects).- 3.5 Sampling Distribution of Mean Squares.- Model I (Fixed Effects).- Model II (Random Effects).- Model III (Mixed Effects).- 3.6 Tests of Hypotheses: The Analysis of VarianceFTests.- Model I (Fixed Effects).- Model II (Random Effects).- Model III (Mixed Effects).- 3.7 Point Estimation.- Model I (Fixed Effects).- Model II (Random Effects).- Model III (Mixed Effects).- 3.8 Interval Estimation.- Model I (Fixed Effects).- Model II (Random Effects).- Model III (Mixed Effects).- 3.9 Computational Formulae and Procedure.- 3.10 Missing Observations.- 3.11 Power of the Analysis of VarianceFTests.- 3.12 Multiple Comparison Methods.- 3.13 Worked Example for Model I.- 3.14 Worked Example for Model II.- 3.15 Worked Example for Model III.- 3.16 Worked Example for Missing Value Analysis.- 3.17 Use of Statistical Computing Packages.- 3.18 Worked Examples Using Statistical Packages.- 3.19 Effects of Violations of Assumptions of the Model.- Exercises.- 4. Two-Way Crossed Classification With Interaction.- 4.0 Preview.- 4.1 Mathematical Model.- 4.2 Assumptions of the Model.- 4.3 Partition of the Total Sum of Squares.- 4.4 Mean Squares and Their Expectations.- Model I (Fixed Effects).- Model II (Random Effects).- Model III (Mixed Effects).- 4.5 Sampling Distribution of Mean Squares.- Model I (Fixed Effects).- Model II (Random Effects).- Model III (Mixed Effects).- 4.6 Tests of Hypotheses: The Analysis of VarianceFTests.- Model I (Fixed Effects).- Test forABinteractions.- Test for factorBeffects.- Test for factor A effects.- Model II (Random Effects).- Test forABinteractions.- Test for factorBeffects.- Test for factorAeffects.- Model III (Mixed Effects).- Test forABinteractions.- Test for factorBeffects.- Test for factor A effects.- Summary of Models and Tests.- 4.7 Point Estimation.- Model I (Fixed Effects).- Model II (Random Effects).- Model III (Mixed Effects).- 4.8 Interval Estimation.- Model I (Fixed Effects).- Model II (Random Effects).- Model III (Mixed Effects).- 4.9 Computational Formulae and Procedure.- 4.10 Analysis of Variance with Unequal Sample Sizes Per Cell.- Fixed Effects Analysis.- Proportional frequencies.- General case of unequal frequencies.- Random Effects Analysis.- Proportional frequencies.- General case of unequal frequencies.- Mixed Effects Analysis.- 4.11 Power of the Analysis of VarianceFTests.- Model I (Fixed Effects).- Test forABinteractions.- Test for factorBeffects.- Test for factor A effects.- Model II (Random Effects).- Test forABinteractions.- Test for factorBeffects.- Test for factor A effects.- Model III (Mixed Effects).- Test forABinteractions.- Test for factorBeffects.- Test for factor A effects.- 4.12 Multiple Comparison Methods.- 4.13 Worked Example for Model I.- 4.14 Worked Example for Model I: Unequal Sample Sizes Per Cell.- 4.15 Worked Example for Model II.- 4.16 Worked Example for Model III.- 4.17 Use of Statistical Computing Packages.- 4.18 Worked Examples Using Statistical Packages.- 4.19 The Meaning and Interpretation of Interaction.- 4.20 Interaction With One Observation Per Cell.- 4.21 Alternate Mixed Models.- 4.22 Effects of Violations of Assumptions of the Model.- Model I (Fixed Effects).- Model II (Random Effects).- Model III (Mixed Effects).- Exercises.- 5. Three-Way and Higher-Order Crossed Classifications.- 5.0 Preview.- 5.1 Mathematical Model.- 5.2 Assumptions of the Model.- 5.3 Partition of the Total Sum of Squares.- 5.4 Mean Squares and Their Expectations.- 5.5 Tests of Hypotheses: The Analysis of Variance…