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Statistics for Experimentalists
1st Edition - January 1, 1969
Author: B. E. Cooper
eBook ISBN:9781483280523
9 7 8 - 1 - 4 8 3 2 - 8 0 5 2 - 3
Statistics for Experimentalists aims to provide experimental scientists with a working knowledge of statistical methods and search approaches to the analysis of data. The book… Read more
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Statistics for Experimentalists aims to provide experimental scientists with a working knowledge of statistical methods and search approaches to the analysis of data. The book first elaborates on probability and continuous probability distributions. Discussions focus on properties of continuous random variables and normal variables, independence of two random variables, central moments of a continuous distribution, prediction from a normal distribution, binomial probabilities, and multiplication of probabilities and independence. The text then examines estimation and tests of significance. Topics include estimators and estimates, expected values, minimum variance linear unbiased estimators, sufficient estimators, methods of maximum likelihood and least squares, and the test of significance method. The manuscript ponders on distribution-free tests, Poisson process and counting problems, correlation and function fitting, balanced incomplete randomized block designs and the analysis of covariance, and experimental design. The publication is a valuable reference for statisticians and researchers interested in the use of statistical methods.
Preface
Chapter 1. Introduction
1.1. Experimental Results
1.2. Experimental Design
1.3. The Power of an Experiment
1.4. Generality of the Conclusions
Chapter 2. Probability
2.1. The Classical Definition of Probability
2.2. Population and Sample
2.3. Probability Distributions
2.4. Probability Notation
2.5. Addition of Probabilities
2.6. Multiplication of Probabilities and Independence
2.7. Binomial Probabilities
2.8. Discrete and Continuous Distributions
2.9. Mean and Variance of a Discrete Probability Distribution
2.10. Crude and Central Moments of Discrete Probability Distributions
2.11. Modal Value of a Discrete Probability Distribution
Chapter 3. Continuous Probability Distributions
3.1. The Normal Probability Distribution
3.2. Mean and Variance of a Continuous Probability Distribution
3.3. Prediction from a Normal Distribution
3.4. Percentage Points and Significance Levels
3.5. Central Moments of a Continuous Distribution
3.6. Notation
3.7. Independence of Two Random Variables
3.8. Properties of Normal Variables
3.9. Properties of Continuous Random Variables
3.10. The Central Limit Theorem
3.11. Distributions Other than Normal
3.12. The Chi-Squared Distribution
Chapter 4. Estimation
4.1. The Random Sample
4.2. Estimators and Estimates
4.3. Expected Values
4.4. Unbiased Estimators
4.5. Minimum Variance Linear Unbiased Estimators
4.6. Efficiency Ratio
4.7. Consistent Estimators
4.8. Sufficient Estimators
4.9. The Method of Maximum Likelihood
4.10. The Joint Estimation of Two Parameters
4.11. The Method of Least Squares
4.12. The Methods of Maximum Likelihood and Least Squares
Appendix
Chapter 5. Tests of Significance—I
5.1. The Test of Significance Method
5.2. Is the Population Mean Equal to a Particular Value?
5.3. Is the Population Variance Equal to a Particular Value?
5.4. Is the Population Distribution of a Particular Form?
Chapter 6. Tests of Significance—II
6.1. Are the Means of Two Populations Equal?
6.2. Are the Variances of Two Populations Equal?
6.3. Are the Variances of More than Two Populations Equal?
Chapter 7. Tests of Significance—III
7.1. Are the Distributions of Several Populations Identical?
7.2. The 2 X 2 Table
7.3. A Test for Independence
7.4. Testing Particular Group Proportions
7.5. Are the Means of Several Populations Equal?
7.6. Robustness of Tests Assuming Normal Populations
7.7. Transformations and Distribution-Free Tests
Chapter 8. Analysis of Variance—I. Hierarchical Designs
8.1. Are the Means of Two or More Populations Equal?
8.2. Fixed-Effect Model for a Hierarchical Design with Three Levels
8.3. Example of a Four-Level Hierarchical Design (Mixed Model)
8.4. The General Method of Computation
8.5. Further Reading on Analysis of Variance
Chapter 9. Analysis of Variance—II. Factorial Designs
9.1. Two-Way Factorial Experiment Without Replication (Fixed-Effect Model)
9.2. Two-Way Experiment with Replication (Fixed-Effect Model)