Statistics - Bhattacharyya, Gouri K.

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Résumé :

1 INTRODUCTION TO STATISTICS 1

1 The Subject and Scope of Statistics 2

2 Statistics in Aid of Scientific Inquiry 4

3 Two Basic Concepts-Population and Sample 6

4 The Purposeful Collection of Data 11

Case Study: Statistics in Context 12

5 Objectives of Statistics 14

2 ORGANIZATION AND DESCRIPTION OF DATA 17

1 Main Types of Data 18

2 Describing Data by Tables and Graphs 19

3 Measures of Center 31

4 Measures of Variation 37

5 Checking the Stability of the Observations over Time 47

6 More on Graphics 50

Case Study: Statistics in Context 52

3 DESCRIPTIVE STUDY OF BIVARIATE DATA 64

1 Summarization of Bivariate Categorical Data 65

2 A Designed Experiment for Making a Comparison 69

3 Scatter Diagram of Bivariate Measurement Data 70

4 The Correlation Coefficient-A Measure of Linear Relation 73

5 Prediction of One Variable from another (Linear Regression) 82

4 PROBABILITY 91

1 Probability of an Event 92

2 Methods of Assigning Probability 97

3 Event Operations and Two Laws of Probability 102

4 Conditional Probability and Independence 109

5 Bayes' Theorem 117

6 Random Sampling from a Finite Population 121

Case Study: Statistics in Context 126

5 PROBABILITY DISTRIBUTIONS 134

1 Random Variables 135

2 Probability Distribution of a Discrete Random Variable 138

3 Mean (Expected Value) and Standard Deviation of a Probability Distribution 144

4 Successes and Failures-Bernoulli Trials 150

5 The Binomial Distribution 154

6 The Poisson Distribution and Rare Events 165

6 THE NORMAL DISTRIBUTION 178

1 Probability Model for a Continuous Random Variable 179

2 The Normal Distribution-Its General Features 184

3 The Standard Normal Distribution 186

4 Probability Calculations with Normal Distributions 191

5 The Normal Approximation to the Binomial 194

6 Checking the Plausibility of a Normal Model 199

7 Transforming Observations to Attain Near Normality 202

7 VARIATION IN REPEATED SAMPLES-SAMPLING DISTRIBUTIONS 210

1 The Sampling Distribution of a Statistic 212

2 Distribution of the Sample Mean and the Central Limit Theorem 218

Case Study: Statistics in Context 228

8 DRAWING INFERENCES FROM LARGE SAMPLES 235

1 Two Types of Statistical Inference: Estimation and Testing 236

2 Point Estimation of a Population Mean 238

3 Confidence Interval Estimation of a Population Mean 242

4 Testing Hypotheses about a Population Mean 250

5 Inferences about a Population Proportion 261

9 SMALL SAMPLE INFERENCES FOR NORMAL POPULATIONS 278

1 Student's t Distribution 279

2 Inferences about ?-Small Sample Size 282

3 Relationship between Tests and Confidence Intervals 289

4 Inferences about the Standard Deviation ? (The Chi-Square Distribution) 291

5 Robustness of Inference Procedures 296

10 COMPARING TWO TREATMENTS 303

1 Two Designs: Independent Samples and Matched Pairs Sample 305

2 Inferences about the Difference of Means-Independent Large Samples 307

3 Inferences about the Difference of Means-Independent Small Samples from Normal Populations 314

4 Randomization and Its Role in Inference 323

5 Matched Pairs Comparisons 325

6 Choosing Between Independent Samples and a Matched Pairs Sample 332

7 Comparing Two Population Proportions 333

11 REGRESSION ANALYSIS I

Simple Linear Regression 349

1 Regression with a Single Predictor ...