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.