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2nd hidition
TARO YAMANE NEW Y O R K
UNIVERSITY
STATISTICS; An Introductory Analysis
A HARPER INTERNATIONAL EDITION jointly published by
HARPER & ROW, NEW YORK, EVANSTON & LONDON AND JOHN WEATHERHILL, INC., TOKYO
CONTENTS Preface: Note on Uses and Organization Preface to the Second Edition
.
Acknowledgments
1
1.1. Statistical Techniques 1.2. Statistical Tables 1.3. Graphic Presentation
2 3 5
2. Frequency Distribution
6
The Concept of a Variable Frequency Distribution Graphic Presentation Cumulative Frequency Distribution Relative Frequencies
3. Measures of Location
3.1. 3.2. 3.3. 3.4. 3.5.
xvii xix
1. Introduction
2.1. 2.2. 2.3. 2.4. 2.5.
xv
6 10 14 20 29 35
The Arithmetic Mean The Median The Mode Comparison of the Mean, Median, and Mode The Geometric Mean vii
37 47 51 53 54
viii
CONTENTS
4. Measures of Dispersion
4.1. 4.2. 4.3. 4.4.
The Range Mean Deviations The Standard Deviation Relative Dispersion (Coefficient of Variation)
5. Probability Theory
5.1. 5.2. 5.3. 5.4. 5.5. 5.6. 5.7. 5.8. 5.9.
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
6. The Normal Curve and Normal Area Table
6.1. Introduction 6.^. Heuristic Explanation of the Normal Curve and Normal Area Table 6.3. Discussion of the Normal Distribution 6.4. Continuity Correction 6.5. Ordinate of the Normal Distribution 7. Sampling Distribution
7.1. 7.2. 7.3. 7.4. 7.5. 7.6.
All Possible Samples Simple Random Sampling Some Practical Problems Sampling Distribution Comments on the Standard Error Formula The Sampling Distribution of the Sample Proportion
8. Testing Hypotheses
8.1. 8.2. 8.3. 8.4.
Introduction of New Terminology Type I and Type II Errors Testing Hypotheses Simple Decision Problems
59
59 60 61 75 78
79 86 94 96 99 105 107 110 112 113
113 115 122 124 126 129
129 133 138 139 161 162 168
168 172 174 188
CONTENTS
8.5. 8.6. 8.7. 8.8.
ix
Examples Using the Sample Mean . Decision Rules Concerning Proportions Changing the Sample Size Calculations of the Decision Rule when /8 is Given
9. Decision Theory
9.1. Introduction-Payoff Table 9.2. Expected Values of an Act
204 215 222 224 227
228 232
10. Estimation
237
10.1. 10.2. 10.3. 10.4. 10.5. 10.6. 10.7.
237 240 241 242 244 245
Introduction—Estimation and Estimators Unbiasedness Consistent Estimator Efficiency Sufficiency Method of Maximum Likelihood (ML) The Relationship among the Error, Risk, and Sample Size 10.8. Interval Estimation
11. Index Numbers
11.1. 11.2. 11.3. 11.4. 11.5. 11.6. 11.7. 11.8.
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
12. Time Series—Trend Line
12.1. 12.2. 12.3. 12.4. 12.5. 12.6. 12.7.
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
251 259 265
265 273 275 281 286 294 297 304 330
330 332 334 336 337 339 345
x
CONTENTS
13. Seasonal and Cyclical Movement
13.1. 13.2. 13.3. 13.4. 13.5. 13.6. 13.7.
350
Definitions of Terms Seasonal Variation The Method of Simple Averages Ratio-to-Moving Average Method Seasonally Adjusted Data Cyclical Fluctuations Comments on Time Series
14. Linear Regression Analysis
350 353 354 . 357 360 362 363 ,
14.1. 14.2. 14.3. 14.4. 14.5. 14.6.
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 crY\ and the Coefficient of Determination r2 14.7. Estimating
