Elements of Statistical Method Third Edition【2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载】

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CHAPTER Ⅰ THE NATURE OF STATISTICS1

1．1 Scientific Method1

1．2 Experimental Method1

1．3 Statistical Method2

1．4 Statistics4

1．5 Preliminary Admonitions4

1．6 Suggestions for Further Reading6

CHAPTER Ⅱ THE MEANING OF NUMBERS7

2．1 Accuracy of Measurement7

2．2 Biassed and Compensating Errors8

2．3 Significant Figures10

2．4 Standard Notation13

2．5 Computations with Approximate Nubmers15

2．6 Multiplication and Division of Approximate Numbers16

2．7 Addition and Subtraction of Approximate Numbers18

2．8 A Horrible Example20

2．9 Rounding Off Numbers22

2．10 Suggestions for Further Reading23

Exercises24

CHAPTER Ⅲ THE FREQUENCY DISTRIBUTION26

3．1 The Frequency Table26

3．2 Class Limits28

3．3 Overlapping Class Limits32

3．4 Open-end Classes32

3．5 Class Intervals33

3．6 Class Marks33

3．7 Cumulative Frequency Tables35

3．8 Graphic Presentation：the Histogram36

3．9 Graphic Presentation：the Frequency Polygon37

3．10 Graphic Presentation：the Frequency Curve38

3．11 Graphic Presentation：the Ogive39

3．12 What to Look for in a Frequency Table40

3．13 Common Shapes of Frequency Curves41

3．14 Common Shapes of Ogives43

3．15 Making a Frequency Table：How Many Classes？44

3．16 Making a Frequency Table：Rules of Thumb47

3．17 Making a Frequency Table：Choosing the Class Interval48

3．18 When to Use Unequal Class Intervals49

3．19 How to Use Unequal Class Intervals51

3．20 Logarithmic Frequency Classes53

3．21 Making a Frequency Table：Locating the Class Marks54

3．22 Summary：Directions for Making a Frequency Table57

3．23 Suggestions for Further Reading58

Exercises58

CHAPTER Ⅳ MEASURES OF CENTRAL TENDENCY61

4．1 Averages61

4．2 The Arithmetic Mean：Ungrouped Data61

4．3 Weighted Arithmetic Mean63

4．4 The Median：Ungrouped Data66

4．5 The Mode：Ungrouped Data68

4．6 The Geometric Mean：Ungrouped Data70

4．7 The Harmonic Mean：Ungrouped Data71

4．8 The Quadratic Mean：Ungrouped Data74

4．9 Quartiles，Deciles，and Percentiles：Ungrouped Data75

4．10 Use of Quartiles，Deciles，Etc78

4．11 Summary of Averages with Ungrouped Data79

Exercises80

CHAPTER Ⅴ MEASURES OF CENTRAL TENDENCY(CONTINUED)82

5．1 Averages from Grouped Data82

5．2 The Arithmetic Mean：Grouped Data84

5．3 Arithmetic Mean：Short Method87

5．4 Checking Accuracy of Computations91

5．5 Grouping Error with the Arithmetic Mean92

5．6 The Median：Grouped Data93

5．7 Finding the Median from an Ogive97

5．8 The Mode：Grouped Data98

5．9 The Geometric Mean：Grouped Data99

5．10 The Harmonic Mean：Grouped Data100

5．11 The Quadratic Mean：Grouped Data101

5．12 Quartiles，Deciles，and Percentiles：Grouped Data103

5．13 Summary of Averages with Grouped Data104

5．14 Characteristics of a Good Average106

5．15 Relationships between the Averages108

5．16 Advantages and Disadvantages of the Arithmetic Mean109

5．17 Advantages and Disadvantages of the Median113

5．18 Advantages and Disadvantages of the Mode115

5．19 Advantages and Disadvantages of the Geometric Mean116

5．20 Advantages and Disadvantages of the Harmonic Mean120

5．21 Advantages and Disadvantages of the Quadratic Mean122

5．22 Summary of the Averages123

5．23 Suggestions for Further Reading123

Exercises123

CHAPTER Ⅵ MEASURES OF DISPERSION126

6．1 Variability126

6．2 The Range127

6．3 The Semi-interquartile Range128

6．4 The Average Deviation130

6．5 The Standard Deviation135

6．6 Standard Deviation：Ungrouped Data136

6．7 Standard Deviation：Grouped Data139

6．8 Checking Accuracy of Computations143

6．9 Meaning of the Standard Deviation144

6．10 Variance147

6．11 Measurement of Relative Dispersion149

6．12 Suggestions for Further Reading153

Exercises153

CHAPTER Ⅶ SIMPLE PROBABILITY AND THE NORMAL CURVE155

7．1 Probability155

7．2 Mean and Standard Deviation of Probability Data157

7．3 Elementary Theorems159

7．4 Expansion of the point Binomial160

7．5 The Normal Curve163

7．6 Areas under the Normal Curve167

7．7 Preliminary Tests for Normality172

7．8 Fitting the Normal Curve：Method of Ordinates177

7．9 Fitting the Normal Curve：Method of Areas181

Exercises185

CHAPTER Ⅷ MOMENTS，FREQUENCY CURVES，AND THE CHI-SQUARE TEST187

8．1 The Higher Moments of a Frequency Distribution187

8．2 Computation of the Higher Moments189

8．3 Checking Accuracy of Computations193

8．4 Grouping Error194

8．5 Moments of Probability Distributions196

8．6 Measures of Skewness200

8．7 Measures of Kurtosis206

8．8 Interpretation of Frequency Statistics208

8．9 ThePearsonian System of Frequency Curves211

8．10 Fitting Pearson＇s Type Ⅲ Curve212

8．11 The Poisson Series215

8．12 Goodness of Fit and the Chi-square Test221

8．13 Suggestions for Further Reading229

Exercises230

CHAPTER Ⅸ MEASURES OF RELIABILITY233

9．1 Sample and Universe233

9．2 Standard Error of the Arithmetic Mean236

9．3 The Probable Error242

9．4 Other Standard Errors243

of the Standard Deviation244

of the Median245

of the Alphas245

of a Relative Frequency(Percentage)247

of the Semi-interquartile Range248

of the Average Deviation248

of Either Quartile248

of β2249

of Measures of Skewness249

of the Coefficient of Variation249

of the Difference between Two Measures250

of the Sum of Two Measures253

9．5 The Significance of Differences253

9．6 Fiducial Probability and the Confidence Interval258

9．7 Suggestions for Further Reading261

Exercises261

CHAPTER Ⅹ THE ANALYSIS OF VARIANCE264

10．1 Combining Frequency Distributions264

10．2 Contributions to Combined Variance268

10．3 Purpose of Analysis of Variance269

10．4 The Concept of Degrees of Freedom271

10．5 Computation of Analysis of Variance275

10．6 Summary of Steps in Analysis of Variance284

10．7 Suggestions for Further Reading286

Exercises286

CHAPTER Ⅺ FITTING STRAIGHT LINES289

11．1 The Use of Two Variables289

11．2 The Nature of Relationship291

11．3 Simple Methods of Finding Relationships294

11．4 The Scatter Diagram297

11．5 Regression Lines and Trend Lines301

11．6 The Freehand Linear Trend303

11．7 The Method of Selected Points304

11．8 The Method of Least Squares307

11．9 Fitting a Straight Line by Least Squares311

11．10 Interpreting Results of Regression Formulas316

11．11 The Residuals or Errors320

11．12 Short Cuts with Historical Data322

11．13 The Direction of Dependence328

11．14 Elimination of Trend333

11．15 Suggestions for Further Reading337

Exercises337

CHAPTER Ⅻ CURVE FITTING340

12．1 Discovering Curvilinearity340

12．2 Common Curve Types342

12．3 The Second-degree Parabola344

12．4 The Third-degree Parabola352

12．5 The Semilogarithmic or Exponential Curve354

12．6 The Concept of Half-life359

12．7 The Logarithmic Curve362

12．8 The Reciprocal Curve366

12．9 Deciding the Type of Curve to Fit369

12．10 Comparison with Type Curves371

12．11 The Process of Differencing372

12．12 Plotting＂Distorted Data．＂375

12．13 Plotting Data on Distorted Axes376

12．14 Summary380

12．15 Suggestions for Further Reading382

Exercises382

CHAPTER ⅩⅢ HISTORICAL DATA386

13．1 Types of Movements in Historical Data386

13．2 The Secular Trend389

13．3 The Progressive Mean392

13．4 Advantages and Disadvantages of the Moving Average393

13．5 The Nature of Cyclical Movements394

13．6 Comon Periods of Cycles397

13．7 Seasonal Variation Measured Around the Moving Average399

13．8 Seasonal Variation by Link Relatives408

13．9 The Elimination of Seasonal Movements411

13．10 Random Movements413

13．11 The Concept of the Statistical Normal416

13．12 Suggestions for Further Reading418

Exercises418

CHAPTER ⅩⅣ INDEX NUMBERS420

14．1 A Simple Aggregative Index Number421

14．2 Averages of Relatives422

14．3 Bias in Index Numbers423

14．4 Weighting of Index Numbers424

14．5 Weight Bias428

14．6 Uses of Index Numbers429

14．7 Correcting Prices with Index Numbers431

14．8 The Choice of a Base Period for Index Numbers434

14．9 Link Relatives and Chain Indices435

14．10 Choosing a Formula for Index Numbers437

14．11 Selection of Basic Data439

14．12 Suggestions for Further Reading439

Exercises440

CHAPTER ⅩⅤ SIMPLE CORRELATION442

15．1 Errors of Estimate442

15．2 Correlation446

15．3 Degrees of Freedom450

15．4 Standard Error of Correlation Coefficient451

15．5 The z-transformation452

15．6 Actual Computations454

15．7 Computation of Regression Equations457

15．8 Computing the Standard Error of Estimate457

15．9 Illustrative Problem458

15．10 Interpretation of Correlation Coefficients464

15．11 Correlation of Grouped Data474

15．12 Simple Curvilinear Correlation481

15．13 Corrections for Degrees of Freedom484

15．14 Linear and Curvilinear Correlation Compared486

15．15 Standard Errors in Curvilinear Correlation487

15．16 Suggestions for Further Reading488

Exercises488

CHAPTER ⅩⅥ MULTIPLE CORRELATION493

16．1 Nature of Multiple Relationships493

16．2 Dependent and Independent Variables494

16．3 Multiple-regression Equations495

16．4 Types of Relationship498

16．5 Methods of Computation502

16．6 Effects of Variables Separately506

16．7 Other Correlation Constants508

16．8 Corrections for Degrees of Freedom509

16．9 Standard Errors of Coefficients of Multiple Correlation509

16．10 Suggestions for Further Reading510

Exercises510

APPENDIXES513

Ⅰ．Areas under the Normal Curve514

Ⅱ．Ordinates of the Normal Curve515

Ⅲ．1 Per Cent and 5 Per Cent Significant Points of F516

Ⅳ．Values of r for Various Values of z from 1 to 3520

Author Index521

Subject Index523