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 x 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
