目    录
Part I  Descriptive Statistics
Unit 1  Statistics	3
1.1  What is Statistics?	4
1.1.1  Meanings of Statistics	4
1.1.2  Definition of Statistics	5
1.1.3  Types of Statistics	6
1.1.4  Applications of Statistics	6
1.2  The language of Statistics	9
1.2.1  Population and Sample	9
1.2.2  Kinds of Variables	11
1.3  Measurability and Variability	14
1.4  Data Collection	16
1.4.1  The Data Collection Process	17
1.4.2  Sampling Frame and Elements	18
1.5*  Single-Stage Methods	21
1.5.1  Simple Random Sample	21
1.5.2  Systematic Sample	22
1.6*  Multistage Methods	25
1.7*  Types of Statistical Study	27
1.8  The Process of a Statistical Study	31
Glossary	34
Reading English Materials	35
Passage 1. What is Statistics?	35
Passage 2. From Data to Foresight	35
Problems	36
Unit 2  Descriptive Analysis of Single-Variable Data	40
2.1  Graphs, Pareto Diagrams, and Stem-and-Leaf Displays	41
2.1.1  Qualitative Data	41
2.1.2  Quantitative Data	43
2.2  Frequency Distributions and Histograms	47
2.2.1  Frequency Distribution	47
2.2.2  Histograms	51
2.2.3  Cumulative Frequency Distribution and Ogives	53
2.3  Measures of Central Tendency	55
2.3.1  Finding the Mean	55
2.3.2  Finding the Median	56
2.3.3  Finding the Mode	57
2.3.4  Finding the Midrange	58
2.4  Measures of Dispersion	60
2.4.1  Sample Standard Deviation	62
2.5  Measures of Position	64
2.5.1  Quartiles	64
2.5.2  Percentiles	64
2.5.3  Other Measures of Position	66
2.6  Interpreting and Understanding Standard Deviation	70
2.6.1  The Empirical Rule and Testing for Normality	70
2.6.2  Chebyshev’s Theorem	72
Glossary	74
Problems	75
Unit 3  Descriptive Analysis of Bivariate Data	79
3.1  Bivariate Data	80
3.1.1  Two Qualitative Variables	80
3.1.2  One Qualitative and One Quantitative Variable	82
3.1.3  Two Quantitative Variables	83
3.2  Linear Correlation	85
3.2.1  Calculating the Linear Correlation Coefficient, r	86
    *3.2.2  Causation and Lurking Variables	89
3.3  Linear Regression	91
3.3.1  Line of Best Fit	92
3.3.2  Making Predictions	97
Reading English Materials	99
Passage 1. The First Regression	99
Passage 2. Simpson’s Paradox	99
Problems	100
Unit 4  Introduction to Probability	104
4.1  Sample Spaces, Events and Sets	105
4.1.1  Introduction	105
4.1.2  Sample Spaces	105
4.1.3  Events	106
4.1.4  Set Theory	108
4.2  Probability Axioms and Simple Counting Problems	109
4.2.1  Probability Axioms and Simple Properties	109
4.2.2  Interpretations of Probability	111
4.2.3  Classical Probability	112
4.2.4  The Multiplication Principle	113
4.3  Permutations and Combinations	115
4.3.1  Introduction	115
4.3.2  Permutations	116
4.3.3  Combinations	118
4.3.4  The Difference Between Permutations and Combinations	120
4.4  Conditional Probability and the Multiplication Rule	122
4.4.1  Conditional Probability	122
4.4.2  The Multiplication Rule	123
4.5  Independent Events, Partitions and Bayes Theorem	124
4.5.1  Independence	124
4.5.2  Partitions	125
4.5.3  Law of Total Probability	126
4.5.4  Bayes Theorem	126
4.5.5  Bayes Theorem for Partitions	127
Reading English Materials	130
Passage 1. Probability and Odds	130
Passage 2. The Relationship between Odds and Probability	130
Passage 3. How the Odds Change across the Range of the Probability	131
Problems	132
Unit 5  Discrete Probability Models	134
5.1  Introduction, Mass Functions and Distribution Functions	135
5.1.1  Introduction	135
5.1.2  Probability Mass Functions (PMFs)	136
5.1.3  Cumulative Distribution Functions (CDFs)	137
5.2  Expectation and Variance for Discrete Random Quantities	138
5.2.1  Expectation	138
5.2.2  Variance	139
5.3  Properties of Expectation and Variance	140
5.3.1  Expectation of a Function of a Random Quantity	140
5.3.2  Expectation of a Linear Transformation	140
5.3.3  Expectation of the Sum of Two Random Quantities	141
5.3.4  Expectation of an Independent Product	141
5.3.5  Variance of an Independent Sum	142
5.4  The Binomial Distribution	142
5.4.1  Introduction	142
5.4.2  Bernoulli Random Quantities	143
5.4.3  The Binomial Distribution	143
5.4.4  Expectation and Variance of a Binomial Random Quantity	145
5.5  The Geometric Distribution	146
5.5.1  PMF	146
5.5.2  CDF	147
5.5.3  Useful Series in Probability	148
5.5.4  Expectation and Variance of Geometric Random Quantities	148
5.6  The Poisson Distribution	149
5.6.1  Poisson as the Limit of a Binomial	149
5.6.2  PMF	150
5.6.3  Expectation and Variance of Poisson	151
5.6.4  Sum of Poisson Random Quantities	152
5.6.5  The Poisson Process	152
Reading English Materials	154
Passage 1. The Founder of Modern Statistics—Karl Pearson	154
Passage 2. The Relations of Several Discrete Probability Models	154
Problems	155
Unit 6  Discrete Probability Models	158
6.1  Introduction, PDF and CDF	159
6.1.1  Introduction	159
6.1.2  The Probability Density Function	159
6.1.3  The Distribution Function	160
6.1.4  Median and Quartiles	161
6.2  Properties of Continuous Random Quantities	161
6.2.1  Expectation and variance of continuous random quantities	161
6.2.2  PDF and CDF of a Linear Transformation	162
6.3  The Uniform Distribution	163
6.4  The Exponential Distribution	165
6.4.1  Definition and Properties	165
6.4.2  Relationship with the Poisson Process	166
6.4.3  The Memoryless Property	167
6.5  The Normal Distribution	168
6.5.1  Definition	168
6.5.2  Properties	168
6.6  The Standard Normal Distribution	169
6.6.1  Properties of the Standard Normal Distribution	170
6.6.2  Finding Area to The Right of z = 0	171
6.6.3  Finding Area in The Right Tail of a Normal Curve	171
6.6.4  Finding Area to the Left of a Positive z Value	172
6.6.5  Finding Area from a Negative z to z = 0	172
6.6.6  Finding Area in the Left Tail of a Normal Curve	172
6.6.7  Finding Area from A Negative z to a Positive z	172
6.6.8  Finding Area Between two z Values of the Same Sign	173
6.6.9  Finding z-Scores Associated with a Percentile	173
6.6.10  Finding z-scores that Bound an Area	174
6.7  Applications of Normal Distributions	175
6.7.1  Probabilities and Normal Curves	175
6.7.2  Using the Normal Curve and z	176
6.8  Specific z-score	178
6.8.1  Visual Interpretation of z(a)	179
6.8.2  Determining Corresponding z Values for z (a)	179
6.8.3  Determining z-scores for Bounded Areas	180
6.9  Normal Approximation of Binomial and Poisson	181
6.9.1  Normal Approximation of the Binomial	181
6.9.2  Normal Approximation of the Poisson	182
Problems	182
Unit 7  Sampling Distributions and CLT	187
7.1  Sampling Distributions	188
7.1.1  Forming a Sampling Distribution of Means	188
7.1.2  Creating a Sampling Distribution of Sample Means	189
7.2  The Sampling Distribution of Sample Means	192
7.2.1  Central Limit Theorem	193
7.2.2  Constructing a Sampling Distribution of Sample Means	194
7.3  Application of the Sampling Distribution of Sample Means	199
7.3.1  Converting   Information into z-scores	199
7.3.2  Distribution of   and Increasing Individual Sample Size	200
7.4  Advanced Central Limit Theorem	202
7.4.1  Central Limit Theorem (Sample Mean)	203
7.4.2  Central Limit Theorem (Sample Sum)	203
Problems	207
Part II  Inferential Statistics
Unit 8  Introduction to Statistical Inferences	210
8.1  Point Estimation and Interval Estimation	211
8.1.1  Point Estimate	211
8.1.2  Interval Estimate	212
8.2  Estimation of Mean m (s Known)	214
8.2.1  The Principle of Constructing a Confidence Interval	214
8.2.2  Applications	216
8.2.3  Sample Size and Confidence Interval	217
8.3  Introduction to Hypothesis Testing	220
8.3.1  Null Hypothesis and Alternative Hypothesis	220
8.3.2  Four Possible Outcomes in a Hypothesis Test	222
8.4  Formulating the Statistical Null and Alternative Hypotheses	226
8.4.1  Writing Null and Alternative Hypothesis in One-Tailed Situation	226
8.4.2  Writing Null and Alternative Hypothesis in Two-Tailed Situation	227
8.5  Hypothesis Test of Mean m (s Known): A Probability-Value Approach	228
8.5.1  One-Tailed Hypothesis Test Using the p-Value Approach	229
8.5.2  Two-Tailed Hypothesis Test Using the p-Value Approach	233
8.5.3  Evaluating the p-Value Approach	234
8.6  Hypothesis Test of Mean m (s Known): A Classical Approach	235
8.6.1  One-Tailed Hypothesis Test Using the Classical Approach	236
8.6.2  Two-Tailed Hypothesis Test Using the Classical Approach	239
Problems	241
Unit 9  Inferences Involving One Population	246
9.1  Inferences about the Mean m (s Unknown)	247
9.1.1  Using the t-Distribution Table	249
9.1.2  Confidence Interval Procedure	251
9.1.3  Hypothesis-Testing Procedure	252
9.2  Inferences about the Binomial Probability of Success	258
9.2.1  Confidence Interval Procedure	259
9.2.2  Determining Sample Size	261
9.2.3  Hypothesis-Testing Procedure	263
9.3  Inferences about the Variance and Standard Deviation	268
9.3.1  Critical Values of Chi-Square	269
9.3.2  Hypothesis-Testing Procedure	270
Problems	279
Unit 10  Inferences Involving Two Populations	284
10.1  Dependent and Independent Samples	285
10.2  Inferences Concerning the Mean Difference Using Two Dependent Samples	287
10.2.1  Procedures and Assumptions for Inferences Involving Paired Data	287
10.2.2  Confidence Interval Procedure	288
10.2.3  Hypothesis-Testing Procedure	290
10.3  Inferences Concerning the Difference between Means Using Two Independent
      Samples	294
10.3.1  Confidence Interval Procedure	295
10.3.2  Hypothesis-Testing Procedure	297
10.4  Inferences Concerning the Difference between Proportions	301
10.4.1  Confidence Interval Procedure	303
10.4.2  Hypothesis-Testing Procedure	304
10.5  Inferences Concerning the Ratio of Variances Using Two Independent Samples	308
10.5.1  Writing for the Equality of Variances	308
10.5.2  Using the F-Distribution	309
10.5.3  One-Tailed Hypothesis Test for the Equality of Variances	310
10.5.4  Critical F-Values for One- and Two-Tailed Tests	313
Problems	315
Unit 11  An Introduction to Simple Regression	321
11.1  Regression as a Best Fitting Line	322
11.1.1  Regression as a Best Fitting Line	322
11.1.2  Errors and Residuals	324
11.2  Interpreting OLS Estimates	326
11.3  Fitted Values and R2: Measuring the Fit of a Regression Model	328
11.4  Nonlinearity in Regression	331
Reading English Materials	335
Problems	336
Part III  Statistical Methods and Data Science
Unit 12  Statistics and Data Science	339
12.1  Statistics and Data Science (I)	340
12.1.1  What is Data Science	340
12.1.2  Statistics and Data Science	340
12.2  Statistics and Data Science (II)	343
12.2.1  Statistics as Part of Data Science	343
12.2.2  The Modern Statistical Analysis Process	344
12.2.3  Statistician and Data Scientist	345
12.3  Statistical Thinking	348
12.3.1  What is Statistical Thinking	348
12.3.2  The Two Cultures of Statistical Modeling	348
12.3.3  A New Research Community	350
12.4  Distinguishing Analytics, Business Intelligence, Data Science	352
12.4.1  Analytics	352
12.4.2  Business Intelligence	355
12.4.3  Data Science	356
Reading English Materials	359
Problems	361
Commonly Used Statistical Terms	362
Appendix A  Commonly Used Statistical Tables	367
Appendix B  Summary of Univariate Descriptive Statistics and Graphs for the Four
            Level of Measurement	379
Appendix C  Order of Magnitude of Data	380
References 	381