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CHAPTER 1．INTRODUCTION 1

1．1 General Remarks 1

1．2 Quantitative Statistical Observations 2

1．3 Qualitative Statistical Observations 6

CHAPTER 2．FREQUENCY DISTRIBUTIONS 13

2．1 Frequency Distributions for Ungrouped Measurements 13

2．2 Frequency Distributions for Grouped Measurements 19

2．3 Cumulative Polygons Graphed on Probability Paper 27

2．4 Frequency Distributions － General 29

CHAPTER 3．SAMPLE MEAN AND STANDARD DEVIATION 34

3．1 Mean and Standard Deviation for the Case of Ungrouped Measurements 34

3．11 Definition of the mean of a sample (ungrouped) 34

3．12 Definition of the standard deviation of a sample (ungrouped) 36

3．2 Remarks on the Interpretation of the Mean and Standard Deviation of a Sample 40

3．3 The Mean and Standard Deviation for the Case of Grouped Data 42

3．31 An example 42

3．32 The general case 44

3．4 Simplified Computation of Mean and Standard Deviation 48

3．41 Effect of adding a constant 48

3．42 Examples of using a working origin 49

3．43 Fully coded calculation of means，variances and standard deviations 52

CHAPTER 4．ELEMENTARY PROBABILITY 58

4．1 Preliminary Discussion and Definitions 58

4．2 Probabilities in Simple Repeated Trials 64

4．3 Permutations 68

4．4 Combinations 73

4．41 Binomial coefficients 75

4．5 Calculation of Probabilities 77

4．51 Complementation 78

4．52 Addition of probabilities for mutually exclusive events 78

4．53 Multiplication of probabilities for independent events 79

4．54 Multiplication of probabilities when events are not independent;conditional probabilities 81

4．55 Addition of probabilities when events are not mutually exclusive 83

4．56 Euler diagrams 85

4．57 General remarks about calculating probabilities 90

4．6 Mathematical Expectation 93

4．7 Geometric Probability 95

CHAPTER 5．PROBABILITY DISTRIBUTIONS 98

5．1 Discrete Probability Distributions 98

5．11 Probability tables and graphs 98

5．12 Remarks on the statistical interpretation of a discrete probability distribution 101

5．13 Means，variances and standard deviations of discrete chance quantities 102

5．2 Continuous Probability Distributions 106

5．21 A simple continuous probability distribution 106

5．22 More general continuous probability distributions 109

5．3 Mathematical Manipulation of Continuous Probability Distributions 111

5．31 Probability density functions － a simple case 111

5．32 Probability density functions －a more general case 113

5．33 Continuous probability distributions － the general case 116

5．34 The mean and variance of a continuous probability distribution 116

5．35 Remarks on the statistical interpretation of continuous probability distributions 118

CHAPTER 6．THE BINOMIAL DISTRIBUTION 122

6．1 Derivation of the Binomial Distribution 122

6．2 The Mean and Standard Deviation of the Binomial Distribution 125

6．3 ＂Fitting＂a Binomial Distribution to a Sample Frequency Distribution 128

CHAPTER 7．THE POISSON DISTRIBUTION 133

7．1 The Poisson Distribution as a Limiting Case of the Binomial Distribution 133

7．2 Derivation of the Poisson Distribution 133

7．3 The Mean and Variance of a Poisson Distribution 135

7．4 ＂Fitting＂a Poisson Distribution to a Sample Frequency Distribution 137

CHAPTER 8．THE NORMAL DISTRIBUTION 144

8．1 General Properties of the Normal Distribution 144

8．2 Some Applications of the Normal Distribution 149

8．21 ＂Fitting＂a cumulative distribution of measurements in a sample by a cumulative normal distribution 149

8．22 ＂Fitting＂a cumulative binomial distribution by a cumulative normal distribution 152

8．3 The Cumulative Normal Distribution on Probability Graph Paper 159

CHAPTER 9．ELEMENTS OF SAMPLING 165

9．1 Introductory Remarks 165

9．2 Sampling from a Finite Population 165

9．21 Experimental sampling from a finite population 165

9．22 Theoretical sampling from a finite population 167

9．23 The mean and standard deviation of means of all possible samples from a finite population 169

9．24 Approximation of distribution of sample means by normal distribution 175

9．3 Sampling from an Indefinitely Large Population 179

9．31 Mean and standard deviation of theoretical distributions of means and sums of samples from and indefinitely large population 179

9．32 Approximate normality of distribution of sample mean in large samples from an indefinitely large population 184

9．33 Remarks on the binomial distribution as a theoretical sampling distribution 185

9．4 The Theoretical Sampling Distributions of Sums and Differences of Sample Means 188

9．41 Differences of sample means 188

9．42 Sums of sample means 190

9．43 Derivations 191

CHAPTER 10．CONFIDENCE LIMITS OF POPULATION PARAMETERS 195

10．1 Introductory Remarks 195

10．2 Confidence Limits of p in a Binomial Distribution 195

10．21 Confidence interval chart for p 200

10．22 Remarks on sampling from a finite binomial population 202

10．3 Confidence Limits of Population Means Determined from Large Samples 203

10．31 Remarks about confidence limits of means of finite populations 205

10．4 Confidence Limits of Means Determined from Small Samples 206

10．5 Confidence Limits of Difference between Population Means Determined Large Samples 210

10．51 Confidence limits of the difference p-p1 in two binomial populations 211

10．52 Confidence limits of the difference of two population means in case small samples 212

CHAPTER 11．STATISTICAL SIGNIFICANCE TESTS 216

11．1 A Simple Significance Test 216

11．2 Significance Tests by Using Confidence Limits 217

11．3 Significance Tests without the Use of Population Parameters 219

CHAPTER 12．TESTING RANDOMNESS IN SAMPLES 222

12．1 The Idea of Random Sampling 222

12．2 Runs 222

12．3 Quality Control Charts 228

CHAPTER 13．ANALYSIS OF PAIRS OF MEASUREMENTS 236

13．1 Introductory Comments 236

13．2 The Method of Least Squares for Fitting Straight Lines 240

13．21 An example 240

13．22 The general case 245

13．23 The variance of estimates of Y from X 250

13．24 Remarks on the sampling variability of regression lines 253

13．25 Remarks on the correlation coefficient 255

13．3 Simplified Computation of Coefficients for Regression Line 261

13．31 Computation by using a working origin 262

13．32 Computation by using a fully coded scheme 264

13．4 Generality of the Method of Least Squares 272

13．41 Fitting a line through the origin by least squares 273

13．42 Fitting parabolas and higher degree polynomials 273

13．43 Fitting exponential functions 276

INDEX 281