Statistics Essentials for Dummies

Statistics Essentials For Dummies (9781119590309) was previously published as Statistics Essentials For Dummies (9780470618394). While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product.

Statistics Essentials For Dummies not only provides students enrolled in Statistics I with an excellent high-level overview of key concepts, but it also serves as a reference or refresher for students in upper-level statistics courses. Free of review and ramp-up material, Statistics Essentials For Dummies sticks to the point, with content focused on key course topics only. It provides discrete explanations of essential concepts taught in a typical first semester college-level statistics course, from odds and error margins to confidence intervals and conclusions. This guide is also a perfect reference for parents who need to review critical statistics concepts as they help high school students with homework assignments, as well as for adult learners headed back into the classroom who just need a refresher of the core concepts.

The Essentials For Dummies Series
Dummies is proud to present our new series, The Essentials For Dummies. Now students who are prepping for exams, preparing to study new material, or who just need a refresher can have a concise, easy-to-understand review guide that covers an entire course by concentrating solely on the most important concepts. From algebra and chemistry to grammar and Spanish, our expert authors focus on the skills students most need to succeed in a subject.

Deborah J. Rumsey, PhD, is an Auxiliary Professor and Statistics Education Specialist at The Ohio State University. She is the author of Statistics For Dummies, Statistics II For Dummies, Statistics Workbook For Dummies, and Probability For Dummies.

Introduction 1

About This Book 1

Conventions Used in This Book 2

Foolish Assumptions 2

Icons Used in This Book 2

Where to Go from Here 3

Chapter 1: Statistics in a Nutshell 5

Designing Studies 5

Surveys 5

Experiments 6

Collecting Data 7

Selecting a good sample 7

Avoiding bias in your data 8

Describing Data 8

Descriptive statistics 8

Charts and graphs 9

Analyzing Data 10

Making Conclusions 10

Chapter 2: Descriptive Statistics 13

Types of Data 13

Counts and Percents 14

Measures of Center 15

Measures of Variability 17

Percentiles 18

Finding a percentile 19

Interpreting percentiles 20

The Five-Number Summary 21

Chapter 3: Charts and Graphs 23

Pie Charts 23

Bar Graphs 24

Time Charts 26

Histograms 27

Making a histogram 27

Interpreting a histogram 29

Evaluating a histogram 30

Boxplots 31

Making a boxplot 31

Interpreting a boxplot 32

Chapter 4: The Binomial Distribution 35

Characteristics of a Binomial 35

Checking the binomial conditions step by step 36

Non-binomial examples 36

Finding Binomial Probabilities Using the Formula 38

Finding Probabilities Using the Binomial Table 40

Finding probabilities when p ≤ 050 40

Finding probabilities when p > 050 41

Finding probabilities for X greater-than, less-than, or between two values 42

The Expected Value and Variance of the Binomial 43

Chapter 5: The Normal Distribution 45

Basics of the Normal Distribution 45

The Standard Normal (Z) Distribution 46

Finding Probabilities for X 48

Finding X for a Given Probability 51

Normal Approximation to the Binomial 53

Chapter 6: Sampling Distributions and the Central Limit Theorem 55

Sampling Distributions 55

The mean of a sampling distribution 56

Standard error of a sampling distribution 57

Sample size and standard error 58

Population standard deviation and standard error 60

The shape 60

Finding Probabilities for x̄ 62

The Sampling Distribution of the Sample Proportion 63

What proportion of students need math help? 64

Finding Probabilities for p 66

Chapter 7: Confidence Intervals 69

Making Your Best Guesstimate 69

The Goal: Small Margin of Error 71

Choosing a Confidence Level 72

Factoring in the Sample Size 73

Counting on Population Variability 75

Confidence Interval for a Population Mean 76

Confidence Interval for a Population Proportion 77

Confidence Interval for the Difference of Two Means 78

Confidence Interval for the Difference of Two Proportions 80

Interpreting Confidence Intervals 81

Spotting Misleading Confidence Intervals 84

Chapter 8: Hypothesis Tests 87

Doing a Hypothesis Test 87

Identifying what you’re testing 88

Setting up the hypotheses 88

Finding sample statistics 90

Standardizing the evidence: The test statistic 90

Weighing the evidence and making decisions: p-values 91

General steps for a hypothesis test 94

Testing One Population Mean 94

Testing One Population Proportion 96

Comparing Two Population Means 97

Testing the Mean Difference: Paired Data 99

Testing Two Population Proportions 102

You Could Be Wrong: Errors in Hypothesis Testing 104

A false alarm: Type-1 error 104

A missed detection: Type-2 error 105

Chapter 9: The t-Distribution 107

Basics of the t-Distribution 107

Understanding the t-Table 108

t-Distributions and Hypothesis Tests 109

Finding critical values 110

Finding p-values 110

t-Distributions and Confidence Intervals 111

Chapter 10: Correlation and Regression 113

Picturing the Relationship with a Scatterplot 113

Making a scatterplot 114

Interpreting a scatterplot 114

Measuring Relationships Using the Correlation 115

Calculating the correlation 115

Interpreting the correlation 117

Properties of the correlation 118

Finding the Regression Line 118

Which is X and which is Y? 119

Checking the conditions 119

Understanding the equation 119

Finding the slope 120

Finding the y-intercept 121

Interpreting the slope and y-intercept 121

Making Predictions 124

Avoid Extrapolation! 124

Correlation Doesn’t Necessarily Mean Cause-and-Effect 125

Chapter 11: Two-Way Tables 127

Organizing and Interpreting a Two-Way Table 127

Defining the outcomes 128

Setting up the rows and columns 128

Inserting the numbers 129

Finding the row, column, and grand totals 129

Finding Probabilities within a Two-Way Table 130

Figuring joint probabilities 130

Calculating marginal probabilities 131

Finding conditional probabilities 132

Checking for Independence 134

Chapter 12: A Checklist for Samples and Surveys 137

The Target Population is Well Defined 138

The Sample Matches the Target Population 138

The Sample is Randomly Selected 139

The Sample Size is Large Enough 139

Nonresponse is Minimized 140

The importance of following up 140

Anonymity versus confidentiality 141

The Survey is of the Right Type 142

Questions are Well Worded 142

The Timing is Appropriate 143

Personnel are Well Trained 143

Proper Conclusions are Made 144

Chapter 13: A Checklist for Judging Experiments 147

Experiments versus Observational Studies 147

Criteria for a Good Experiment 148

Inspect the Sample Size 148

Small samples — small conclusions 148

Original versus final sample size 149

Examine the Subjects 149

Check for Random Assignments 150

Gauge the Placebo Effect 150

Identify Confounding Variables 151

Assess Data Quality 152

Check out the Analysis 153

Scrutinize the Conclusions 153

Overstated results 154

Ad-hoc explanations 154

Generalizing beyond the scope 154

Chapter 14: Ten Common Statistical Mistakes 155

Misleading Graphs 155

Pie charts 156

Bar graphs 156

Time charts 156

Histograms 157

Biased Data 157

No Margin of Error 158

Nonrandom Samples 158

Missing Sample Sizes 159

Misinterpreted Correlations 159

Confounding Variables 160

Botched Numbers 161

Selectively Reporting Results 161

The Almighty Anecdote 162

Appendix: Tables for Reference 163

Index 171

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