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| Introduction | |
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| About This Book | |
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| Conventions Used in This Book | |
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| Foolish Assumptions | |
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| Icons Used in This Book | |
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| Where to Go from Here | |
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| Statistics in a Nutshell | |
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| Designing Studies | |
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| Surveys | |
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| Experiments | |
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| Collecting Data | |
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| Selecting a good sample | |
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| Avoiding bias in your data | |
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| Describing Data | |
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| Descriptive statistics | |
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| Charts and graphs | |
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| Analyzing Data | |
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| Making Conclusions | |
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| Descriptive Statistics | |
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| Types of Data | |
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| Counts and Percents | |
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| Measures of Center | |
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| Measures of Variability | |
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| Percentiles | |
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| Finding a percentile | |
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| Interpreting percentiles | |
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| The Five-Number Summary | |
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| Charts and Graphs | |
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| Pie Charts | |
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| Bar Graphs | |
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| Time Charts | |
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| Histograms | |
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| Making a histogram | |
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| Interpreting a histogram | |
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| The distribution of the data in a histogram | |
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| Variability in the data from a histogram | |
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| Center of the data from a histogram | |
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| Evaluating a histogram | |
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| Boxplots | |
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| Making a boxplot | |
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| Interpreting a boxplot | |
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| Distribution of data in a boxplot | |
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| Variability in a data set from a boxplot | |
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| Center of the data from a boxplot | |
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| The Binomial Distribution | |
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| Characteristics of a Binomial | |
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| Checking the binomial conditions step by step | |
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| Non-binomial examples | |
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| No fixed number of trials | |
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| More than success or failure | |
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| Probability of success (p) changes | |
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| Trials are not independent | |
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| Finding Binomial Probabilities Using the Formula | |
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| Finding Probabilities Using the Binomial Table | |
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| Finding probabilities when p ≤ 0.50 | |
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| Finding probabilities when p > 0.50 | |
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| Finding probabilities for X greater-than, less-than, or between two values | |
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| The Expected Value and Variance of the Binomial | |
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| The Normal Distribution | |
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| Basics of the Normal Distribution | |
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| The Standard Normal (Z) Distribution | |
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| Finding Probabilities for X | |
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| Finding X for a Given Probability | |
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| Normal Approximation to the Binomial | |
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| Sampling Distributions and the Central Limit Theorem | |
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| Sampling Distributions | |
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| The mean of sampling distribution | |
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| The standard error of a sampling distribution | |
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| Sample size and standard error | |
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| Population standard deviation and standard error | |
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| The shape | |
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| Distribution of X is normal | |
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| Distribution of X is unknown or not normal | |
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| Finding Probabilities for X | |
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| The Sampling Distribution of the Sample Proportion | |
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| What proportion of students need math help? | |
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| Finding Probabilities for p | |
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| Confidence Intervals | |
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| Making Your Best Guesstimate | |
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| The Goal: Small Margin of Error | |
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| Choosing a Confidence Level | |
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| Factoring In the Sample Size | |
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| Counting On Population Variability | |
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| Confidence Interval for a Population Mean | |
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| Confidence Interval for a Population Proportion | |
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| Confidence Interval for the Difference of Two Means | |
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| Confidence Interval for the Difference of Two Proportions | |
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| Interpreting Confidence Intervals | |
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| Spotting Misleading Confidence Intervals | |
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| Hypothesis Tests | |
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| Doing a Hypothesis Test | |
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| Identifying what you're testing | |
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| Setting up the hypotheses | |
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| What's the alternative? | |
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| Knowing which hypothesis is which | |
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| Finding sample statistics | |
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| Standardizing the evidence: the test statistic | |
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| Weighing the evidence and making decisions: p-values | |
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| Finding the p-value | |
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| Interpreting a p-value | |
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| General steps for a hypothesis test | |
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| Testing One Population Mean | |
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| Testing One Population Proportion | |
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| Comparing Two Population Means | |
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| Testing the Mean Difference: Paired Data | |
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| Testing Two Population Proportions | |
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| You Could Be Wrong: Errors in Hypothesis Testing | |
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| A false alarm: Type-1 error | |
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| A missed detection: Type-2 error | |
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| The t-distribution | |
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| Basics of the t-Distribution | |
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| Understanding the t-Table | |
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| t-distributions and Hypothesis Tests | |
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| Finding critical values | |
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| Finding p-values | |
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| t-distributions and Confidence Intervals | |
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| Correlation and Regression | |
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| Picturing the Relationship with a Scatterplot | |
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| Making a scatterplot | |
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| Interpreting a scatterplot | |
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| Measuring Relationships Using the Correlation | |
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| Calculating the correlation | |
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| Interpreting the correlation | |
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| Properties of the correlation | |
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| Finding the Regression Line | |
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| Which is X and which is Y? | |
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| Checking the conditions | |
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| Understanding the equation | |
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| Finding the slope | |
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| Finding the y-intercept | |
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| Interpreting the slope and y-intercept | |
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| Interpreting the slope | |
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| Interpreting the y-intercept | |
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| The best-fitting line for the crickets | |
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| Making Predictions | |
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| Avoid Extrapolation! | |
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| Correlation Doesn't Necessarily Mean Cause-and-Effect | |
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| Two-Way Tables | |
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| Organizing and Interpreting a Two-way Table | |
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| Defining the outcomes | |
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| Setting up the rows and columns | |
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| Inserting the numbers | |
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| Finding the row, column, and grand totals | |
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| Finding Probabilities within a Two-Way Table | |
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| Figuring joint probabilities | |
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| Calculating marginal probabilities | |
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| Finding conditional probabilities | |
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| Checking for Independence | |
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| A Checklist for Samples and Surveys | |
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| The Target Population is Well Defined | |
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| The Sample Matches the Target Population | |
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| The Sample Is Randomly Selected | |
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| The Sample Size Is Large Enough | |
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| Nonresponse Is Minimized | |
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| The importance of following up | |
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| Anonymity versus confidentiality | |
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| The Survey Is of the Right Type | |
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| Questions Are Well Worded | |
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| The Timing Is Appropriate | |
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| Personnel Are Well Trained | |
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| Proper Conclusions Are Made | |
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| A Checklist for Judging Experiments | |
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| Experiments versus Observational Studies | |
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| Criteria for a Good Experiment | |
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| Inspect the Sample Size | |
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| Small samples - small conclusions | |
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| Original versus final sample size | |
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| Examine the Subjects | |
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| Check for Random Assignments | |
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| Gauge the Placebo Effect | |
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| Identify Confounding Variables | |
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| Assess Data Quality | |
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| Check Out the Analysis | |
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| Scrutinize the Conclusions | |
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| Overstated results | |
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| Ad-hoc explanations | |
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| Generalizing beyond the scope | |
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| Ten Common Statistical Mistakes | |
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| Misleading Graphs | |
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| Pie charts | |
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| Bar graphs | |
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| Time charts | |
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| Histograms | |
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| Biased Data | |
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| No Margin of Error | |
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| Nonrandom Samples | |
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| Missing Sample Sizes | |
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| Misinterpreted Correlations | |
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| Confounding Variables | |
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| Botched Numbers | |
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| Selectively Reporting Results | |
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| The Almighty Anecdote | |
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| Appendix: Tables for Reference | |
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| Index | |