《Elementary Statistical Analysis》

CHAPTER 1．INTRODUCTION1

1．1General Remarks1

1．2 Quantitative Statistical Observations2

1．3 Qualitative Statistical Observations6

CHAPTER 2．FREQUENCY DISTRIBUTIONS13

2．1Frequency Distributions for Ungrouped Measurements13

2．2 Frequency Distributions for Grouped Measurements19

2．3 Cumulative Polygons Graphed on Probability Paper27

2．4 Frequency Distributions － General29

CHAPTER 3．SAMPLE MEAN AND STANDARD DEVIATION34

3．1Mean and Standard Deviation for the Case of Ungrouped Measurements34

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 Sample40

3．3The Mean and Standard Deviation for the Case of Grouped Data42

3．31 An example42

3．32 The general case44

3．4Simplified Computation of Mean and Standard Deviation48

3．41 Effect of adding a constant48

3．42 Examples of using a working origin49

3．43 Fully coded calculation of means，variances and standard deviations52

CHAPTER 4．ELEMENTARY PROBABILITY58

4．1Preliminary Discussion and Definitions58

4．2 Probabilities in Simple Repeated Trials64

4．3 Permutations68

4．4Combinations73

4．41 Binomial coefficients75

4．5Calculation of Probabilities77

4．51 Complementation78

4．52 Addition of probabilities for mutually exclusive events78

4．53 Multiplication of probabilities for independent events79

4．54 Multiplication of probabilities when events are not independent;conditional probabilities81

4．55 Addition of probabilities when events are not mutually exclusive83

4．56 Euler diagrams85

4．57 General remarks about calculating probabilities90

4．6 Mathematical Expectation93

4．7 Geometric Probability95

CHAPTER 5．PROBABILITY DISTRIBUTIONS98

5．1Discrete Probability Distributions98

5．11 Probability tables and graphs98

5．12 Remarks on the statistical interpretation of a discrete probability distribution101

5．13 Means，variances and standard deviations of discrete chance quantities102

5．2Continuous Probability Distributions106

5．21 A simple continuous probability distribution106

5．22 More general continuous probability distributions109

5．3Mathematical Manipulation of Continuous Probability Distributions111

5．31 Probability density functions － a simple case111

5．32 Probability density functions －a more general case113

5．33 Continuous probability distributions － the general case116

5．34 The mean and variance of a continuous probability distribution116

5．35 Remarks on the statistical interpretation of continuous probability distributions118

CHAPTER 6．THE BINOMIAL DISTRIBUTION122

6．1Derivation of the Binomial Distribution122

6．2 The Mean and Standard Deviation of the Binomial Distribution125

6．3 ＂Fitting＂a Binomial Distribution to a Sample Frequency Distribution128

CHAPTER 7．THE POISSON DISTRIBUTION133

7．1The Poisson Distribution as a Limiting Case of the Binomial Distribution133

7．2 Derivation of the Poisson Distribution133

7．3 The Mean and Variance of a Poisson Distribution135

7．4 ＂Fitting＂a Poisson Distribution to a Sample Frequency Distribution137

CHAPTER 8．THE NORMAL DISTRIBUTION144

8．1General Properties of the Normal Distribution144

8．2Some Applications of the Normal Distribution149

8．21 ＂Fitting＂a cumulative distribution of measurements in a sample by a cumulative normal distribution149

8．22 ＂Fitting＂a cumulative binomial distribution by a cumulative normal distribution152

8．3 The Cumulative Normal Distribution on Probability Graph Paper159

CHAPTER 9．ELEMENTS OF SAMPLING165

9．1Introductory Remarks165

9．2Sampling from a Finite Population165

9．21 Experimental sampling from a finite population165

9．22 Theoretical sampling from a finite population167

9．23 The mean and standard deviation of means of all possible samples from a finite population169

9．24 Approximation of distribution of sample means by normal distribution175

9．3Sampling from an Indefinitely Large Population179

9．31 Mean and standard deviation of theoretical distributions of means and sums of samples from and indefinitely large population179

9．32 Approximate normality of distribution of sample mean in large samples from an indefinitely large population184

9．33 Remarks on the binomial distribution as a theoretical sampling distribution185

9．4The Theoretical Sampling Distributions of Sums and Differences of Sample Means188

9．41 Differences of sample means188

9．42 Sums of sample means190

9．43 Derivations191

CHAPTER 10．CONFIDENCE LIMITS OF POPULATION PARAMETERS195

10．1Introductory Remarks195

10．2Confidence Limits of p in a Binomial Distribution195

10．21 Confidence interval chart for p200

10．22 Remarks on sampling from a finite binomial population202

10．3Confidence Limits of Population Means Determined from Large Samples203

10．31 Remarks about confidence limits of means of finite populations205

10．4 Confidence Limits of Means Determined from Small Samples206

10．5Confidence Limits of Difference between Population Means Determined Large Samples210

10．51 Confidence limits of the difference p-p1 in two binomial populations211

10．52 Confidence limits of the difference of two population means in case small samples212

CHAPTER 11．STATISTICAL SIGNIFICANCE TESTS216

11．1A Simple Significance Test216

11．2 Significance Tests by Using Confidence Limits217

11．3 Significance Tests without the Use of Population Parameters219

CHAPTER 12．TESTING RANDOMNESS IN SAMPLES222

12．1The Idea of Random Sampling222

12．2 Runs222

12．3 Quality Control Charts228

CHAPTER 13．ANALYSIS OF PAIRS OF MEASUREMENTS236

13．1Introductory Comments236

13．2The Method of Least Squares for Fitting Straight Lines240

13．21 An example240

13．22 The general case245

13．23 The variance of estimates of Y from X250

13．24 Remarks on the sampling variability of regression lines253

13．25 Remarks on the correlation coefficient255

13．3Simplified Computation of Coefficients for Regression Line261

13．31 Computation by using a working origin262

13．32 Computation by using a fully coded scheme264

13．4Generality of the Method of Least Squares272

13．41 Fitting a line through the origin by least squares273

13．42 Fitting parabolas and higher degree polynomials273

13．43 Fitting exponential functions276

INDEX281