Analyzing ANOVA Designs(英文版)(pdf 68頁)

Analyzing ANOVA Designs(英文版)目錄：
1 Introduction . . . . 1
2 The Design of an Experiment . . . . . . . . . . . . . . 1
2.1 Factor . . . . . . 2
2.2 Quantitative and Qualitative Factors . . . . . . . . . . . . . . 2
2.3 Random and Fixed Factors . . . . . . . . . . . . 2
2.4 Variance . . . 3
2.5 Crossed and Nested Factors . . . . . . . . . . . . 3
2.6 Experimental Unit . . . . 5
2.7 Element . . . . 6
2.8 Replication . . . . . . . . . . . . . . 6
2.9 Randomization . . . . . . . . . 7
2.10 Balanced and Unbalanced Designs. . . . . . . . . . . 7
3 Analysis of Variance . . . . . . . . 9
3.1 Example . . . . . . . . . . . 10
3.2 Hypothesis Testing . . . . 10
3.3 Terminology . . . . . . . . . . . 11
3.3.1 Model . . . . . . . . . . . . . 11
3.3.2 Sum of squares. . . . . . . . . . . . . . .. . 11
3.3.3 Degrees of freedom . . . . . . . . . . . . . . . 12
3.3.4 Mean squares. . . . . . . . . . . 13
3.4 ANOVA Assumptions . . . . . . . . . . . . .. . . 13
3.5 The Idea behind ANOVA . . . . . . . . . .. . . 14
3.6 ANOVA F-test. . . . . . . . . . . 17
3.7 Concluding Remarks about ANOVA . . . . . . . . . . . 18
4 Multiple Comparisons . . . . . 19
4.1 What is a Comparison? . . . . . . . . . . . . . . . 19
4.2 Drawbacks of Comparisons . . . . . . . . . . . . 20
4.3 Planned Contrasts . . . . 21
4.4 Multiple Comparisons . . . . . . . . . . . . . . . . 22
4.5 Recommendations . . . . . . . . . . . 23
5 Calculating ANOVA with SAS: an Example . .. . . . . 24
5.1 Example . . . . . . . . . . . . . . . . . . . . . 24
5.2 Experimental Design . . . . . . . . . . . 24
5.3 ANOVA Table. . . . . . . . . . . 26
5.4 SAS Program . . . . . . . . . . . 28
6 Experimental Designs . . . . . 33
6.1 Completely Randomized Designs . . . . 34
6.1.1 One-way completely randomized design. . . . . . . . . . . 34
6.1.2 Subsampling . . . . . . . . . . . 36
6.1.3 Factorial completely randomized design . . . . . 38
6.2…………………………………………………………………………

Analyzing ANOVA Designs(英文版)內容提要：
Analysis of variance (ANOVA) is a powerful and popular technique for analyzing data. This handbook is an introduction to ANOVA for those who are not familiar with the subject. It is also a suitable reference for scientists who use ANOVA to analyze their experiments.
Most researchers in applied and social sciences have learned ANOVA at college or university and have used ANOVA in their work. Yet, the technique remains a mystery to many. This is likely because of the traditional way ANOVA is taught — loaded with terminology, notation, and equations, but few explanations. Most of us can use the formulae to compute sums of squares and perform simple ANOVAs, but few actually
understand the reasoning behind ANOVA and the meaning of the F-test.
Today, all statistical packages and even some spreadsheet software (e.g., EXCEL) can do ANOVA. It is easy to input a large data set to obtain a great volume of output. But the challenge lies in the correct usage of the programs and interpretation of the results. Understanding the technique is the key to the successful use of ANOVA.
The concept of ANOVA is really quite simple: to compare different sources of variance and make inferences about their relative sizes. The purpose of this handbook is to develop an understanding of ANOVA without becoming too mathematical.

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