Quantitative Methods Custom Book

Contents

1Introduction1


1.1 Introduction to Statistical Methodology . ......... .... .... 1

1.2 Descriptive Statistics and Inferential Statistics ...... .... .... 4

1.3 The Role of Computers in Statistics ........ .... .... .... 6

1.4 Chapter Summary. ........ .... ..... .... .... .... 7


2SamplingandMeasurement11


2.1 Variables and Their Measurement ......... .... .... .... 11

2.2 Randomization . . ........ .... ..... .... .... .... 15

2.3 Sampling Variability and Potential Bias . ......... .... .... 18

2.4 Other Probability Sampling Methods∗ . ......... .... .... 21

2.5 Chapter Summary. ........ .... ..... .... .... .... 24


3DescriptiveStatistics31


3.1 Describing Data with Tables and Graphs ......... .... .... 31

3.2 Describing the Center of the Data ......... .... .... .... 38

3.3 Describing Variability of the Data ......... .... .... .... 46

3.4 Measures of Position ....... .... ..... .... .... .... 51

3.5 Bivariate Descriptive Statistics ...... ..... .... .... .... 55

3.6 Sample Statistics and Population Parameters . . . ........ .... 58

3.7 Chapter Summary. ........ .... ..... .... .... .... 59


4ProbabilityDistributions73


4.1 Introduction to Probability ........ ..... .... .... .... 73

4.2 Probability Distributions for Discrete and Continuous Variables . . . 75

4.3 The Normal Probability Distribution . . ......... .... .... 78

4.4 Sampling Distributions Describe How Statistics Vary ...... .... 85

4.5 Sampling Distributions of Sample Means ......... .... .... 89

4.6 Review: Population, Sample Data, and Sampling Distributions .... 95

4.7 Chapter Summary. ........ .... ..... .... .... .... 99


5StatisticalInference:Estimation107


5.1 Point and Interval Estimation ...... ..... .... .... .... 107

5.2 Con?dence Interval for a Proportion . . ......... .... .... 110

5.3 Con?dence Interval for a Mean . ......... .... .... .... 116

5.4 Choice of Sample Size ....... .... ..... .... .... .... 124

5.5 Con?dence Intervals for Median and Other Parameters∗ ........ 129

5.6 Chapter Summary. ........ .... ..... .... .... .... 132


6StatisticalInference:Signi?canceTests143


6.1 The Five Parts of a Signi?cance Test ....... .... .... .... 144

6.2 Signi?cance Test for a Mean ....... ..... .... .... .... 147

6.3 Signi?cance Test for a Proportion ......... .... .... .... 156


Sections or subsections marked with an asterisk have less importance for a ?rst introduction to statistics and are optional.


6.4 Decisions and Types of Errors in Tests . ......... .... .... 159

6.5 Limitations of Signi?cance Tests . ......... .... .... .... 163

6.6 Calculating P(Type II Error)∗ ...... ..... .... .... .... 166

6.7 Small-Sample Test for a Proportion—the Binomial Distribution∗ ... 169

6.8 Chapter Summary. ........ .... ..... .... .... .... 173


7ComparisonofTwoGroups183


7.1 Preliminaries for Comparing Groups . . ......... .... .... 183

7.2 Categorical Data: Comparing Two Proportions . ........ .... 187

7.3 Quantitative Data: Comparing Two Means ........ .... .... 191

7.4 Comparing Means with Dependent Samples ....... .... .... 193

7.5 Other Methods for Comparing Means∗ . ......... .... .... 197

7.6 Other Methods for Comparing Proportions∗ ....... .... .... 201

7.7 Nonparametric Statistics for Comparing Groups∗ ........ .... 205

7.8 Chapter Summary. ........ .... ..... .... .... .... 208


9LinearRegressionandCorrelation255


9.1 Linear Relationships ....... .... ..... .... .... .... 256

9.2 Least Squares Prediction Equation . . . ......... .... .... 259

9.3 The Linear Regression Model ...... ..... .... .... .... 265

9.4 Measuring Linear Association: The Correlation . ........ .... 269

9.5 Inferences for the Slope and Correlation ......... .... .... 276

9.6 Model Assumptions and Violations ........ .... .... .... 283

9.7 Chapter Summary. ........ .... ..... .... .... .... 288


10IntroductiontoMultivariateRelationships301


10.1 Association and Causality ........ ..... .... .... .... 301

10.2 Controlling for Other Variables . ......... .... .... .... 304

10.3 Types of Multivariate Relationships ........ .... .... .... 307

10.4 Inferential Issues in Statistical Control . ......... .... .... 313

10.5 Chapter Summary. ........ .... ..... .... .... .... 314


11MultipleRegressionandCorrelation321


11.1 The Multiple Regression Model. ......... .... .... .... 321

11.2 Example with Multiple Regression Computer Output ...... .... 326

11.3 Multiple Correlation and R2 ....... ..... .... .... .... 331

11.4 Inference for Multiple Regression Coef?cients ...... .... .... 335

11.5 Interaction between Predictors in Their Effects . ........ .... 340

11.6 Comparing Regression Models ...... ..... .... .... .... 345

11.7 Partial Correlation∗ ........ .... ..... .... .... .... 347

11.8 Standardized Regression Coef?cients∗ . ......... .... .... 351

11.9 Chapter Summary. ........ .... ..... .... .... .... 354