Even you can learn statistics : a guide for everyone who has ever been afraid of statistics

305 Pages·2005·7.35 MB·English

by  David M. Levine

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Even You Can
Learn Statistics
A Guide for Everyone Who Has Ever
Been Afraid of Statistics
David M. Levine, Ph.D.
David F. Stephan
PEARSON PRENTICE HALL
An Imprint of PEARSON EDUCATION
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vii
TABLE OF CONTENTS
Table of Contents
Introduction xvii
Chapter 1 Fundamentals of Statistics 1
1.1 The Five Basic Words of Statistics 2
Population 2
Sample 2
Parameter 2
Statistic 3
Variable 3
1.2 The Branches of Statistics 4
Descriptive Statistics 4
Inferential Statistics 5
1.3 Sources of Data 5
Published Sources 5
Experiments 6
Surveys 6
1.4 Sampling Concepts 7
Sampling 7
Probability Sampling 7
Simple Random Sampling 7
Frame 8
1.5 Sample Selection Methods 8
Sampling With Replacement 8
Sampling Without Replacement 8
One-Minute Summary 10
Test Yourself 11
Answers to Test Yourself Questions 14
References 14
Chapter 2 Presenting Data in Charts and Tables 17
2.1 Presenting Categorical Data 17
The Summary Table 17
The Bar Chart 18
The Pie Chart 19
The Pareto Diagram 20
viii
TABLE OF CONTENTS
Two-Way Cross-Classification Tables 22
2.2 Presenting Numerical Data 24
The Frequency and Percentage Distribution 24
Histogram 25
The Dot Scale Diagram 27
The Time-Series Plot 28
The Scatter Plot 28
2.3 Misusing Graphs 30
One-Minute Summary 32
Test Yourself 32
Answers to Test Yourself Questions 35
References 36
Chapter 3 Descriptive Statistics for Numerical Variables 37
3.1 Measures of Central Tendency 37
The Mean 37
The Median 40
The Mode 41
Quartiles 41
3.2 Measures of Variation 45
The Range 45
The Variance and the Standard Deviation 46
Standard (Z) Scores 49
3.3 Shape of Distributions 50
Symmetrical Shape 50
Left-Skewed Shape 50
Right-Skewed Shape 51
The Box-and-Whisker Plot 52
Important Equations 56
One-Minute Summary 56
Test Yourself 57
Answers to Test Yourself Questions 59
References 60
Chapter 4 Probability 61
4.1 Getting Started with Probability 61
Event 61
Elementary Event 62
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TABLE OF CONTENTS
Random Variable 62
Probability 62
Collectively Exhaustive Events 64
4.2 Some Rules of Probability 64
4.3 Assigning Probabilities 67
Classical Approach 67
Empirical Approach 67
Subjective Approach 68
One-Minute Summary 68
Test Yourself 68
Answers to Test Yourself Questions 70
References 70
Chapter 5 Probability Distributions 73
5.1 Probability Distributions for Discrete Variables 73
Discrete Probability Distribution 73
The Expected Value of a Random Variable 75
Standard Deviation of a Random Variable ((cid:1)) 76
5.2 The Binomial and Poisson Probability Distributions 79
The Binomial Distribution 79
The Poisson Distribution 83
5.3 Continuous Probability Distributions and the Normal Distribution 87
Normal Distribution 87
Using Standard Deviation Units 89
Finding the ZValue from the Area Under the Normal Curve 91
5.4 The Normal Probability Plot 94
Important Equations 96
One-Minute Summary 96
Test Yourself 97
Answers to Test Yourself Questions 101
References 102
Chapter 6 Sampling Distributions and
Confidence Intervals 103
6.1 Sampling Distributions 104
Sampling Distribution 104
Sampling Distribution of the Mean and the Central
Limit Theorem 104
x
TABLE OF CONTENTS
Sampling Distribution of the Proportion 107
What You Need to Know About Sampling Distributions 107
6.2 Sampling Error and Confidence Intervals 107
Sampling Error 109
Confidence Interval Estimate 109
6.3 Confidence Interval Estimate for the Mean Using the
tDistribution ((cid:1)Unknown) 111
tDistribution 112
6.4 Confidence Interval Estimation for the Proportion 116
Important Equations 119
One-Minute Summary 119
Test Yourself 119
Answers to Test Yourself Questions 122
References 122
Chapter 7 Fundamentals of Hypothesis Testing 125
7.1 The Null and Alternative Hypotheses 125
Null Hypothesis 126
Alternative Hypothesis 126
7.2 Hypothesis Testing Issues 127
Test Statistic 127
Practical Significance Versus Statistical Significance 128
7.3 Decision-Making Risks 129
Type I Error 129
Type II Error 129
Risk Trade-Off 130
7.4 Performing Hypothesis Testing 130
Thep-Value Approach to Hypothesis Testing 131
p-Value 131
7.5 Types of Hypothesis Tests 132
Number of Groups 132
Relationship Stated in Alternative Hypothesis H 132
1
Type of Variable 132
One-Minute Summary 133
Test Yourself 133
Answers to Test Yourself Questions 135
References 135