![]() ![]() As an example, let’s go back to the PURE study that we discussed in Chapter 1. When we summarize data, we are necessarily throwing away information, and one might plausibly object to this. 18.3.1 Positive predictive value and statistical significance.18.3 The reproducibility crisis in science.18.2 How science (sometimes) actually works.Criticize the model to make sure it fits properly 17.1.3 3: Prepare the data for analysis.17.1.2 2: Identify or collect the appropriate data.17.1.1 1: Specify your question of interest.17.1 The process of statistical modeling.16.4.3 Determining the number of factors.15.8.1 The paired t-test as a linear model.15.3.1 Effect sizes for comparing two means.15.1 Testing the value of a single mean.14.9.1 Estimating linear regression parameters.14.5 Criticizing our model and checking assumptions.14.4 Beyond linear predictors and outcomes.14.1.5 Quantifying goodness of fit of the model.14.1.4 Statistical tests for regression parameters.14.1.3 Standard errors for regression models.14.1.2 The relation between correlation and regression.13.7.1 Quantifying inequality: The Gini index.13.3.1 Hypothesis testing for correlations.13.2 Is income inequality related to hate crimes?.13.1 An example: Hate crimes and income inequality.12.7 Categorical analysis beyond the 2 X 2 table.12.3 Contingency tables and the two-way test.11.6.3 Assessing evidence for the null hypothesis.11.6.2 Bayes factors for statistical hypotheses.11.4.6 Maximum a posteriori (MAP) estimation.11.4.4 Computing the marginal likelihood.11.4 Estimating posterior distributions.11.3.4 Computing the marginal likelihood.11.2 Bayes’ theorem and inverse inference.10.1.5 Relation of confidence intervals to hypothesis tests.10.1.4 Computing confidence intervals using the bootstrap.10.1.3 Confidence intervals and sample size.10.1.2 Confidence intervals using the t distribution. ![]() 10.1.1 Confidence intervals using the normal distribution.10 Quantifying effects and designing studies.9.4 NHST in a modern context: Multiple testing.9.3.7 What does a significant result mean?.9.3.6 Step 6: Assess the “statistical significance” of the result.9.3.5 Step 5: Determine the probability of the observed result under the null hypothesis.9.3.4 Step 4: Fit a model to the data and compute a test statistic.9.3.2 Step 2: Specify the null and alternative hypotheses.9.3.1 Step 1: Formulate a hypothesis of interest.9.3 The process of null hypothesis testing.9.2 Null hypothesis statistical testing: An example.9.1 Null Hypothesis Statistical Testing (NHST).8.5 Using simulation for statistics: The bootstrap.6.7 Reversing a conditional probability: Bayes’ rule.6.5 Computing conditional probabilities from data.6.3.1 Cumulative probability distributions.5.11.1 Proof that the sum of errors from the Mean is zero.5.8 Using simulations to understand statistics.5.7 Variability: How well does the mean fit the data?.5.5.1 Summarizing data robustly using the median.4.2.1 Show the data and make them stand out.3.3 Idealized representations of distributions.2.2 Discrete versus continuous measurements. ![]()
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