STATISTICS; An Introductory Analysis. 2nd hidition TARO YAMANE NEW YORK UNIVERSITY A HARPER INTERNATIONAL EDITION
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1 2nd hidition TARO YAMANE NEW YORK UNIVERSITY STATISTICS; An Introductory Analysis A HARPER INTERNATIONAL EDITION jointly published by HARPER & ROW, NEW YORK, EVANSTON & LONDON AND JOHN WEATHERHILL, INC., TOKYO
2 CONTENTS Preface: Note on Uses and Organization xv Preface to the Second Edition. xvii Acknowledgments xix 1. Introduction Statistical Techniques Statistical Tables Graphic Presentation 5 2. Frequency Distribution The Concept of a Variable Frequency Distribution Graphic Presentation Cumulative Frequency Distribution Relative Frequencies Measures of Location The Arithmetic Mean The Median The Mode Comparison of the Mean, Median, and Mode The Geometric Mean 54 vii
3 viii CONTENTS 4. Measures of Dispersion The Range Mean Deviations The Standard Deviation Relative Dispersion (Coefficient of Variation) Probability Theory Preliminary Ideas The Objective Approach to Probability The Subjective Approach Postulates of Probability Theory Conditional Probabilities A Rule for Multiplication of Probabilities Statistical Independence Mathematical Expectation and Random Variable Summary The Normal Curve and Normal Area Table Introduction ^. Heuristic Explanation of the Normal Curve and Normal Area Table Discussion of the Normal Distribution Continuity Correction Ordinate of the Normal Distribution Sampling Distribution All Possible Samples Simple Random Sampling Some Practical Problems Sampling Distribution Comments on the Standard Error Formula The Sampling Distribution of the Sample Proportion Testing Hypotheses Introduction of New Terminology Type I and Type II Errors Testing Hypotheses Simple Decision Problems 188
4 CONTENTS 8.5. Examples Using the Sample Mean Decision Rules Concerning Proportions Changing the Sample Size Calculations of the Decision Rule when /8 is Given 224 ix 9. Decision Theory Introduction-Payoff Table Expected Values of an Act Estimation Introduction Estimation and Estimators Unbiasedness Consistent Estimator Efficiency Sufficiency Method of Maximum Likelihood (ML) The Relationship among the Error, Risk, and Sample Size Interval Estimation Index Numbers Weighted Relative Price Index Weighted Aggregative Price Index Variations of the Weighted Price Indices Chain Index Numbers Splicing and Shifting the Base of Index Numbers Deflating Prices and Income Comments on Price Indices Quantity Index Numbers Time Series Trend Line Review Introduction The Freehand Method Method of Semiaverages The Method of Moving Averages The Method of Least Squares Changing the Unit Value and Shifting the Origin 345
5 x CONTENTS 13. Seasonal and Cyclical Movement Definitions of Terms Seasonal Variation The Method of Simple Averages Ratio-to-Moving Average Method Seasonally Adjusted Data Cyclical Fluctuations Comments on Time Series Linear Regression Analysis, Introduction The Regression Problem Estimation of A and B Type I Population Case Finding a Regression Function Sample Standard Deviation (Standard Error of Estimate) Interpretation of cr Y \ and the Coefficient of Determination r Estimating <j\ and <T\ Summary Estimating^ and B Type II Population Tests Concerning a and b Confidence Interval for cr YX Confidence Interval for Y Comments on Regression Analysis Correlation Analysis The Bivariate Distribution Correlation Coefficient: Case I The Bivariate Distribution and Regression Analysis The Correlation Coefficient: Case II Comments and Summary Tests of Hypothesis Concerning Correlation Coefficients Rank Correlation Random Variables and Probability Distributions Sets Sample Space Axioms 478
6 CONTENTS xi Random Variable Conditional Probability The t Distribution Expected Value of Sample Variance Pooled Variance Degrees of Freedom The t Distribution Examples Tests Concerning the Difference of Two Means Confidence Intervals for a Mean Confidence Interval for the Difference Between Means from Two Populations when the Standard Deviations Are Known Confidence Interval for the Difference Between Means from Two Normal Populations when the Standard Deviations Are Unknown The Binomial Distribution Bernoulli Trials A Geometrical Interpretation Finding the Binomial Distribution Tables of the Binomial Probability Distribution The Sampling Distribution of the Sample Proportion p Tests of Hypotheses, Using the Binomial Distribution Calculation of the OC Curve Estimators of 77 and o- p The Normal Distribution as an Approximation of the Binomial Distribution Confidence Interval Determining the Sample Size n by Use of a Confidence Interval Comparison of Two Percentages The Poisson Distribution The Poisson Distribution as the Limit of the Binomial Distribution The Poisson Process 594
7 xii CONTENTS Finding the Poisson Distribution Estimation of X and Applications The Multinomial Distribution The Hypergeometric Distribution The Chi-Square Distribution x 2 Distribution and Its Properties K. Pearson's Approximation The Goodness-of-Fit Test Tests of Independence: Contingency Tables Test of Homogeneity Confidence Interval for cr The F Distribution The F Distribution TheF Table Testing the Equality of Variances Other Tests Using the F Distribution Analysis of Variance Fixed Effects, Completely Randomized, 1-Way Classification Model Fixed Effects, Randomized Block, 1-Way Classification Model Fixed Effects, Completely Randomized, 2-Way Classification, 1 Observation Per Cell Model Fixed Effects, Completely Randomized, 2-Way Classification, n Observations Per Cell Model Fixed Effects, Randomized Blocks, 2-Way Classification, n Observations Per Cell Random Effects, Completely Randomized, 1-Way Classification Model Random Effects, Randomized Blocks, 1-Way Classification Model Random Effects, Completely Randomized, 2-Way Classification, 1 Observation Per Cell Model Random Effects, Completely Randomized, 2-Way Classification, n Observations Model Random Effects, Randomized Blocks, 2-Way Classification, n Observations Model 746
8 CONTENTS xiii 22. Multiple Linear Regression Introduction Estimation of Parameters Estimating o Interpretation of the Regression Equation The Coefficient of Multiple Determination Partial Correlation Gauss Multipliers Example Tests of Hypotheses of the Regression Coefficients Summary Regression Analysis and Analysis of Variance Addition of Variables The Durbin-Watson Test Generalization of the Partial Correlation Coefficient Graphic Correlation Multiplicative Forms of Regression Functions Appendix: Matrix Algebra Time Series (II) The Trend Line The Moving Average Tests of Independence Stationary Time Series 869 Tables 876 Index 915
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Chapter 10. Chapter 10. Multinomial Experiments and. Multinomial Experiments and Contingency Tables. Contingency Tables.
Chapter 10 Multinomial Experiments and Contingency Tables 1 Chapter 10 Multinomial Experiments and Contingency Tables 10-1 1 Overview 10-2 2 Multinomial Experiments: of-fitfit 10-3 3 Contingency Tables: