Preface |
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xxv |
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What makes the Book Unique? |
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Which Chapters are Essential? |
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Part A Introducing Statistics |
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1 Statistics and Probability are not Intuitive |
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3 |
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We Tend to Jump to Conclusions |
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We Tend to Be Overconfident |
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We See Patterns in Random Data |
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We Don't Realize that Coincidences are Common |
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We Don't Expect Variability to Depend on Sample Size |
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We Have Incorrect Intuitive Feelings about Probability |
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We Find It Hard to Combine Probabilities |
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We Don't Do Bayesian Calculations Intuitively |
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We are Fooled by Multiple Comparisons |
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We Tend to Ignore Alternative Explanations |
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We are Fooled By Regression to the Mean |
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We Let Our Biases Determine How We Interpret Data |
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We Crave Certainty, but Statistics Offers Probabilities |
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Term Introduced in this Chapter |
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2 The Complexities of Probability |
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14 |
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Probability as Long-Term Frequency |
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Probability as Strength of Belief |
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Calculations With Probabilities Can be Easier If You Switch to Calculating with Whole Numbers |
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Common Mistakes: Probability |
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Probability in Statistics |
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Terms Introduced in this Chapter |
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3 From Sample to Population |
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24 |
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Sampling from a Population |
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Multiple Levels of Sampling |
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What if Your Sample is the Entire Population? |
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Terms Introduced in this Chapter |
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Part B Introducing Confidence Intervals |
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4 Confidence Interval of a Proportion |
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31 |
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Data Expressed as Proportions |
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The Binomial Distribution: From Population to Sample |
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Example: Free Throws in Basketball |
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Assumptions: Confidence Interval of a Proportion |
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What Does 95% Confidence Really Mean? |
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Are You Quantifying the Event You Care About? |
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Calculating the CI of a Proportion |
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Ambiguity if the Proportion is 0% or 100% |
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An Alternative Approach: Bayesian Credible Intervals |
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Common Mistakes: CI of a Proportion |
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Terms Introduced in this Chapter |
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5 Confidence Interval of Survival Data |
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46 |
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Calculating Percentage Survival at Various Times |
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Graphing Survival Curves with Confidence Bands |
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Summarizing Survival Curves |
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Assumptions: Survival Analysis |
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Terms Introduced in this Chapter |
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6 Confidence Interval of Counted Data (Poisson Distribution) |
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55 |
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Assumptions: Poisson Distribution |
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Confidence Intervals Based on Poisson Distributions |
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How to Calculate the Poisson CI |
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The Advantage of Counting for Longer Time Intervals (Or in Larger Volumes) |
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Term Introduced in this Chapter |
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Part C Continuous Variables |
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7 Graphing Continuous Data |
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63 |
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Lingo: Terms Used to Explain Variability |
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Graphing Data to Show Variation |
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Terms Introduced in this Chapter |
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75 |
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Not Quite as Distinct as They Seem |
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Terms Introduced in this Chapter |
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80 |
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Interpreting a Standard Deviation |
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How it Works: Calculating SD |
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Situations in Which n Can Seem Ambiguous |
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Other Ways to Quantify and Display Variability |
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Terms Introduced in this Chapter |
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10 The Gaussian Distribution |
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89 |
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The Nature of The Gaussian Distribution |
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SD and the Gaussian Distribution |
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The Standard Normal Distribution |
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The Normal Distribution does not Define Normal Limits |
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Why The Gaussian Distribution is so Central to Statistical Theory |
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Terms Introduced in this Chapter |
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11 The Lognormal Distribution and Geometric Mean |
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95 |
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The Origin of a Lognormal Distribution |
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Common Mistakes: Lognormal Distributions |
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Terms Introduced in this Chapter |
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12 Confidence Interval of a Mean |
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101 |
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Interpreting A CI of a Mean |
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What Values Determine the CI of a Mean? |
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Assumptions: CI of a Mean |
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How to Calculate the CI of a Mean |
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More about Confidence Intervals |
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Terms Introduced in this Chapter |
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13 The Theory of Confidence Intervals |
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110 |
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CI of a Mean Via the t Distribution |
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CI of a Mean Via Resampling |
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CI of a Proportion Via Resampling |
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CI of a Proportion Via Binomial Distribution |
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Terms Introduced in this Chapter |
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118 |
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Which Kind of Error Bar Should I Plot? |
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The Appearance of Error Bars |
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How are SD and Sem Related to Sample Size? |
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Common Mistakes: Error Bars |
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Terms Introduced in this Chapter |
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Part D P Values and Statistical Significance |
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129 |
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Example 2: Antibiotics on Surgical Wounds |
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Example 3: Angioplasty and Myocardial Infarction |
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Why P Values are Confusing |
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One- Or Two-Tailed P Value? |
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P Values are Not Very Reproducible |
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There is much more to Statistics than P Values |
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Common Mistakes: P Values |
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Terms Introduced in this Chapter |
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16 Statistical Significance and Hypothesis Testing |
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145 |
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Statistical Hypothesis Testing |
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Analogy: Innocent Until Proven Guilty |
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Extremely Significant? Borderline Significant? |
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Lingo: Type I and Type II Errors |
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Tradeoffs When Choosing a Significance Level |
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What Significance Level Should You Choose? |
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Interpreting A CI, A P Value, and A Hypothesis Test |
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Statistical Significance vs. Scientific Significance |
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Common Mistakes: Statistical Hypothesis Testing |
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Terms Defined in this Chapter |
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17 Comparing Groups with Confidence Intervals and P Values |
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157 |
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CIS and Statistical Hypothesis Testing are Closely Related |
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Four Examples with CIS, P Values, and Conclusion about Statistical Significance |
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18 Interpreting a Result that is Statistically Significant |
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165 |
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Seven Explanations for Results that are "Statistically Significant" |
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How Frequently do Type I Errors (False Positives) Occur? |
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The Prior Probability Influences the FPRP (A Bit of Bayes) |
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Accounting for Prior Probability Informally |
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The Relationship Between Sample Size and P Values |
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Terms Introduced in this Chapter |
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19 Interpreting a Result that is not Statistically Significant |
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179 |
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Five Explanations For "Not Statistically Significant" Results |
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"Not Significantly Different" does not Mean "No Difference" |
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Example: a2-Adrenergic Receptors on Platelets |
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Example: Fetal Ultrasounds |
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What if the P Value is Really High? |
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186 |
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What is Statistical Power? |
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Distinguishing Power From Beta and the False Discovery Rate |
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An Analogy to Understand Statistical Power |
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Power of the Two Example Studies |
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When does It Make Sense to Compute Power? |
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Terms Introduced in this Chapter |
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21 Testing For Equivalence or Noninferiority |
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193 |
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Equivalence must be Defined Scientifically, not Statistically |
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If the Mean is Within the Equivalence Zone |
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If the Mean is Outside of the Equivalence Zone |
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Applying the Usual Approach of Statistical Hypothesis Testing to Testing for Equivalence |
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Common Mistakes: Testing for Equivalence |
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Terms Introduced in this Chapter |
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Part E Challenges in Statistics |
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22 Multiple Comparisons Concepts |
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203 |
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The Problem of Multiple Comparisons |
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Correcting for Multiple Comparisons is not Always Needed |
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The Traditional Approach to Correcting for Multiple Comparisons |
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Correcting for Multiple Comparisons with the False Discovery Rate |
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Comparing the Two Methods of Correcting for Multiple Comparisons |
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Terms Introduced in this Chapter |
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23 The Ubiquity of Multiple Comparisons |
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214 |
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Multiple Comparisons in Many Contexts |
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When are Multiple Comparisons Data Torture or P-Hacking? |
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How to Cope with Multiple Comparisons |
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Terms Introduced in this Chapter |
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224 |
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The Gaussian Distribution is an Unreachable Ideal |
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What A Gaussian Distribution Really Looks Like |
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Alternatives to Assuming a Gaussian Distribution |
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Common Mistakes: Normality Tests |
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Terms Introduced in this Chapter |
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232 |
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The Need for Outlier Tests |
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Five Questions to Ask before Testing for Outliers |
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Is It Legitimate to Remove Outliers? |
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An Alternative: Robust Statistical Tests |
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Common Mistakes: Outlier Tests |
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Terms Introduced in this Chapter |
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26 Choosing a Sample Size |
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239 |
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An Alternative Way to think about Sample Size Calculations |
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Interpreting a Sample Size Statement |
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Calculating the Predicted FPRP as Part of Interpreting a Sample Size Statement |
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Complexities when Computing Sample Size |
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Other Approaches to Choosing Sample Size |
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Common Mistakes: Sample Size |
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Terms Introduced in this Chapter |
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Part F Statistical Tests |
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263 |
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Example: Apixaban for Treatment of Thromboembolism |
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Comparing Observed and Expected Proportions |
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Common Mistakes: Comparing Proportions |
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Terms Introduced in this Chapter |
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273 |
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Example: Does a Cholera Vaccine Work? |
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Example: Isotretinoin and Bowel Disease |
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Example: Genome-Wide Association Studies |
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How are Controls Defined? |
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Common Mistakes: Case-Control Studies |
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Terms Introduced in this Chapter |
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29 Comparing Survival Curves |
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284 |
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Assumptions when Comparing Survival Curves |
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Comparing Two Survival Curves |
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Why Not Just Compare Mean or Median Survival Time: Five-Year Survival? |
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Terms Introduced in this Chapter |
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30 Comparing Two Means: Unpaired t Test |
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294 |
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Interpreting Results from an Unpaired t Test |
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Assumptions: Unpaired t Test |
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The Assumption of Equal Variances |
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Overlapping Error Bars and the t Test |
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How It Works: Unpaired t Test |
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Common Mistakes: Unpaired t Test |
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Terms Introduced in this Chapter |
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31 Comparing Two Paired Groups |
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306 |
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When to Use Special Tests for Paired Data |
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Interpreting Results from a Paired t Test |
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McNemar's Test for a Paired Case-Control Study |
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Common Mistakes: Paired t Test |
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Terms Introduced in this Chapter |
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318 |
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Introducing the Correlation Coefficient |
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How It Works: Calculating the Correlation Coefficient |
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Common Mistakes: Correlation |
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Terms Introduced in this Chapter |
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Part G Fitting Models to Data |
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33 Simple Linear Regression |
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331 |
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The Goals of Linear Regression |
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Linear Regression Results |
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Assumptions: Linear Regression |
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Comparison of Linear Regression and Correlation |
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Common Mistakes: Linear Regression |
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Terms Introduced in this Chapter |
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350 |
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Lingo: Models, Parameters, and Variables |
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The Linear Regression Model |
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Other Models and other Kinds of Regression |
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Terms Introduced in this Chapter |
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357 |
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Comparing Models is a Major Part of Statistics |
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Linear Regression as a Comparison of Models |
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Unpaired t Test Recast as Comparing the Fit of Two Models |
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Common Mistakes: Comparing Models |
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Terms Introduced in this Chapter |
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366 |
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Introducing Nonlinear Regression |
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An Example of Nonlinear Regression |
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Nonlinear Regression Results |
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How Nonlinear Regression Works |
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Assumptions: Nonlinear Regression |
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Tips for Understanding Models |
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Learn More About Nonlinear Regression |
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Common Mistakes: Nonlinear Regression |
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Terms Introduced in this Chapter |
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378 |
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Goals of Multivariable Regression |
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An Example of Multiple Linear Regression |
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Automatic Variable Selection |
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Sample Size for Multiple Regression |
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More Advanced Issues with Multiple Regression |
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Common Mistakes: Multiple Regression |
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Terms Introduced in this Chapter |
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38 Logistic and Proportional Hazards Regression |
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395 |
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Proportional Hazards Regression |
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Assumptions: Logistic Regression |
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Common Mistakes: Logistic Regression |
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Terms Introduced in this Chapter |
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Part H The Rest of Statistics |
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407 |
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Comparing the Means of Three or More Groups |
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Assumptions: One-Way Anova |
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How It Works: One-Way Anova |
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Repeated-Measures One Way Anova |
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An Example of Two-Way Anova |
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Repeated Measures Two-way Anova |
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Terms Introduced in this Chapter |
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40 Multiple Comparison Tests after Anova |
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418 |
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Multiple Comparison Tests for the Example Data |
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The Logic Of Multiple Comparisons Tests |
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Other Multiple Comparisons Tests |
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How It Works: Multiple Comparisons Tests |
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When Are Multiple Comparisons Tests Not Needed? |
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Common Mistakes: Multiple Comparisons |
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Terms Introduced in this Chapter |
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431 |
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Nonparametric Tests Based on Ranks |
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The Advantages and Disadvantages of Nonparametric Tests |
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Choosing Between Parametric and Nonparametric Tests: Does It Matter? |
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Sample Size for Nonparametric Tests |
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Nonparametric Tests that Analyze Values (Not Ranks) |
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Common Mistakes: Nonparametric Tests |
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Terms Introduced in this Chapter |
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42 Sensitivity, Specificity, and Receiver Operating Characteristic Curves |
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442 |
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Definitions of Sensitivity and Specificity |
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The Predictive Value of a Test |
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Receiver-Operating Characteristic (ROC) Curves |
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Terms Introduced in this Chapter |
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452 |
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Introducing Meta-Analysis |
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Results from a Meta-Analysis |
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Meta-Analysis of Individual Participant Data |
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Assumptions of Meta-Analysis |
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Common Mistakes: Meta-Analysis |
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Terms Introduced in this Chapter |
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Part I Putting It All Together |
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44 The Key Concepts of Statistics |
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463 |
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Term Introduced in this Chapter |
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45 Statistical Traps to Avoid |
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468 |
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Trap #1: Focusing on P Values and Statistical Significance Rather than Effect Size |
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Trap #2: Testing Hypotheses Suggested by the Data |
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Trap #3: Analyzing Without a Plan-"P-Hacking" |
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Trap #4: Making a Conclusion about Causation When the Data Only Show Correlation |
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Trap #5: Overinterpreting Studies that Measure a Proxy or Surrogate Outcome |
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Trap #6: Overinterpreting Data from an Observational Study |
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Trap #7: Making Conclusions about Individuals when the Data Were only Collected for Groups |
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Trap #8: Focusing Only on Means Without asking about Variability or Unusual Values |
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Trap #9: Comparing Statistically Significant with Not Statistically Significant |
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Trap #10: Missing Important Findings Because Data Combine Populations |
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Trap #11: Invalid Multiple Regression Analyses as a Result of an Omitted Variable |
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Trap #13: Mixing Up the Significance Level with the FPRP |
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Trap #14: Not Recognizing How Common False Positive Findings are |
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Trap #15: Not Realizing How Likely it is that a "Significant" Conclusion From a Speculative Experiment is a False Positive |
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Trap #16: Not Realizing That Many Published Studies have Little Statistical Power |
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Trap #17: Trying to Detect Small Signals When there is Lots of Noise |
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Trap #18: Unnecessary Dichotomizing |
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Trap #19: Inflating Sample Size by Pseudoreplication |
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Terms Introduced in this Chapter |
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487 |
(15) |
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The Case of the Eight Naked IC50S |
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Statistical Significance by Cheating |
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Using a t Test That Doesn't Assume Equal SDs |
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Unpaired t Test as Linear or Nonlinear Regression |
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Nonparametric Mann-Whitney Test |
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Just Report the Last Confirmatory Experiment? |
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Comparing the Logarithms of IC50 Values |
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Sample Size Calculations Revisited |
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Is it Ok to Switch Analysis Methods? |
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The Usefulness of Simulations |
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47 Statistics and Reproducibility |
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502 |
(9) |
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The Repoducibility Crisis |
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Many Analyses are Biased to Inflate the Effect Size |
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Even Perfectly Performed Experiments are Less Reproducible than Most Expect |
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48 Checklists for Reporting Statistical Methods and Results |
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511 |
(6) |
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Reporting Methods Used for Data Analysis |
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Reporting Statistical Results |
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Part J Appendices |
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517 |
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Appendix A: Statistics with Graphpad |
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Appendix B: Statistics with Excel |
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Appendix C: Statistics with R |
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Appendix D: Values of the t Distribution Needed to Compute CIs |
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Appendix E: A Review of Logarithms |
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Appendix F: Choosing a Statistical Test |
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Appendix G: Problems and Answers |
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References |
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Index |
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548 |
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