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What is included with this book?
Introduction | p. 1 |
About This Book | p. 1 |
Conventions Used in This Book | p. 2 |
Foolish Assumptions | p. 2 |
Icons Used in This Book | p. 3 |
Where to Go from Here | p. 3 |
Statistics in a Nutshell | p. 5 |
Designing Studies | p. 5 |
Surveys | p. 5 |
Experiments | p. 6 |
Collecting Data | p. 7 |
Selecting a good sample | p. 7 |
Avoiding bias in your data | p. 8 |
Describing Data | p. 8 |
Descriptive statistics | p. 8 |
Charts and graphs | p. 9 |
Analyzing Data | p. 10 |
Making Conclusions | p. 10 |
Descriptive Statistics | p. 13 |
Types of Data | p. 13 |
Counts and Percents | p. 14 |
Measures of Center | p. 15 |
Measures of Variability | p. 17 |
Percentiles | p. 19 |
Finding a percentile | p. 19 |
Interpreting percentiles | p. 20 |
The Five-Number Summary | p. 21 |
Charts and Graphs | p. 23 |
Pie Charts | p. 23 |
Bar Graphs | p. 24 |
Time Charts | p. 26 |
Histograms | p. 27 |
Making a histogram | p. 27 |
Interpreting a histogram | p. 29 |
The distribution of the data in a histogram | p. 29 |
Variability in the data from a histogram | p. 29 |
Center of the data from a histogram | p. 30 |
Evaluating a histogram | p. 30 |
Boxplots | p. 31 |
Making a boxplot | p. 31 |
Interpreting a boxplot | p. 32 |
Distribution of data in a boxplot | p. 32 |
Variability in a data set from a boxplot | p. 34 |
Center of the data from a boxplot | p. 34 |
The Binomial Distribution | p. 35 |
Characteristics of a Binomial | p. 35 |
Checking the binomial conditions step by step | p. 36 |
Non-binomial examples | p. 36 |
No fixed number of trials | p. 37 |
More than success or failure | p. 37 |
Probability of success (p) changes | p. 37 |
Trials are not independent | p. 38 |
Finding Binomial Probabilities Using the Formula | p. 38 |
Finding Probabilities Using the Binomial Table | p. 40 |
Finding probabilities when p ≤ 0.50 | p. 40 |
Finding probabilities when p > 0.50 | p. 41 |
Finding probabilities for X greater-than, less-than, or between two values | p. 42 |
The Expected Value and Variance of the Binomial | p. 43 |
The Normal Distribution | p. 45 |
Basics of the Normal Distribution | p. 45 |
The Standard Normal (Z) Distribution | p. 46 |
Finding Probabilities for X | p. 48 |
Finding X for a Given Probability | p. 51 |
Normal Approximation to the Binomial | p. 53 |
Sampling Distributions and the Central Limit Theorem | p. 55 |
Sampling Distributions | p. 55 |
The mean of sampling distribution | p. 57 |
The standard error of a sampling distribution | p. 57 |
Sample size and standard error | p. 58 |
Population standard deviation and standard error | p. 60 |
The shape | p. 61 |
Distribution of X is normal | p. 61 |
Distribution of X is unknown or not normal | p. 61 |
Finding Probabilities for X | p. 62 |
The Sampling Distribution of the Sample Proportion | p. 63 |
What proportion of students need math help? | p. 64 |
Finding Probabilities for p | p. 66 |
Confidence Intervals | p. 69 |
Making Your Best Guesstimate | p. 69 |
The Goal: Small Margin of Error | p. 71 |
Choosing a Confidence Level | p. 71 |
Factoring In the Sample Size | p. 73 |
Counting On Population Variability | p. 75 |
Confidence Interval for a Population Mean | p. 75 |
Confidence Interval for a Population Proportion | p. 77 |
Confidence Interval for the Difference of Two Means | p. 78 |
Confidence Interval for the Difference of Two Proportions | p. 80 |
Interpreting Confidence Intervals | p. 82 |
Spotting Misleading Confidence Intervals | p. 84 |
Hypothesis Tests | p. 87 |
Doing a Hypothesis Test | p. 87 |
Identifying what you're testing | p. 88 |
Setting up the hypotheses | p. 88 |
What's the alternative? | p. 88 |
Knowing which hypothesis is which | p. 89 |
Finding sample statistics | p. 90 |
Standardizing the evidence: the test statistic | p. 90 |
Weighing the evidence and making decisions: p-values | p. 91 |
Finding the p-value | p. 92 |
Interpreting a p-value | p. 93 |
General steps for a hypothesis test | p. 94 |
Testing One Population Mean | p. 94 |
Testing One Population Proportion | p. 96 |
Comparing Two Population Means | p. 97 |
Testing the Mean Difference: Paired Data | p. 99 |
Testing Two Population Proportions | p. 102 |
You Could Be Wrong: Errors in Hypothesis Testing | p. 104 |
A false alarm: Type-1 error | p. 105 |
A missed detection: Type-2 error | p. 105 |
The t-distribution | p. 107 |
Basics of the t-Distribution | p. 107 |
Understanding the t-Table | p. 108 |
t-distributions and Hypothesis Tests | p. 109 |
Finding critical values | p. 110 |
Finding p-values | p. 110 |
t-distributions and Confidence Intervals | p. 112 |
Correlation and Regression | p. 113 |
Picturing the Relationship with a Scatterplot | p. 113 |
Making a scatterplot | p. 114 |
Interpreting a scatterplot | p. 114 |
Measuring Relationships Using the Correlation | p. 115 |
Calculating the correlation | p. 116 |
Interpreting the correlation | p. 117 |
Properties of the correlation | p. 118 |
Finding the Regression Line | p. 119 |
Which is X and which is Y? | p. 119 |
Checking the conditions | p. 119 |
Understanding the equation | p. 120 |
Finding the slope | p. 121 |
Finding the y-intercept | p. 121 |
Interpreting the slope and y-intercept | p. 122 |
Interpreting the slope | p. 122 |
Interpreting the y-intercept | p. 123 |
The best-fitting line for the crickets | p. 123 |
Making Predictions | p. 124 |
Avoid Extrapolation! | p. 125 |
Correlation Doesn't Necessarily Mean Cause-and-Effect | p. 125 |
Two-Way Tables | p. 127 |
Organizing and Interpreting a Two-way Table | p. 127 |
Defining the outcomes | p. 128 |
Setting up the rows and columns | p. 128 |
Inserting the numbers | p. 129 |
Finding the row, column, and grand totals | p. 130 |
Finding Probabilities within a Two-Way Table | p. 131 |
Figuring joint probabilities | p. 31 |
Calculating marginal probabilities | p. 131 |
Finding conditional probabilities | p. 132 |
Checking for Independence | p. 134 |
A Checklist for Samples and Surveys | p. 137 |
The Target Population is Well Defined | p. 138 |
The Sample Matches the Target Population | p. 138 |
The Sample Is Randomly Selected | p. 139 |
The Sample Size Is Large Enough | p. 139 |
Nonresponse Is Minimized | p. 140 |
The importance of following up | p. 140 |
Anonymity versus confidentiality | p. 141 |
The Survey Is of the Right Type | p. 142 |
Questions Are Well Worded | p. 142 |
The Timing Is Appropriate | p. 143 |
Personnel Are Well Trained | p. 143 |
Proper Conclusions Are Made | p. 144 |
A Checklist for Judging Experiments | p. 147 |
Experiments versus Observational Studies | p. 147 |
Criteria for a Good Experiment | p. 148 |
Inspect the Sample Size | p. 148 |
Small samples - small conclusions | p. 148 |
Original versus final sample size | p. 149 |
Examine the Subjects | p. 149 |
Check for Random Assignments | p. 150 |
Gauge the Placebo Effect | p. 150 |
Identify Confounding Variables | p. 151 |
Assess Data Quality | p. 152 |
Check Out the Analysis | p. 152 |
Scrutinize the Conclusions | p. 153 |
Overstated results | p. 153 |
Ad-hoc explanations | p. 154 |
Generalizing beyond the scope | p. 154 |
Ten Common Statistical Mistakes | p. 155 |
Misleading Graphs | p. 155 |
Pie charts | p. 155 |
Bar graphs | p. 156 |
Time charts | p. 156 |
Histograms | p. 157 |
Biased Data | p. 157 |
No Margin of Error | p. 158 |
Nonrandom Samples | p. 158 |
Missing Sample Sizes | p. 159 |
Misinterpreted Correlations | p. 159 |
Confounding Variables | p. 160 |
Botched Numbers | p. 160 |
Selectively Reporting Results | p. 161 |
The Almighty Anecdote | p. 162 |
Appendix: Tables for Reference | p. 163 |
Index | p. 171 |
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