Correlations

Stats: Modeling the World, 2nd Edition AP® Edition ©2007

Bock, Velleman, De Veaux

Correlated to: Advanced Placement® (AP®) Statistics Standards (Grades 9–12)

I. Exploring Data: Describing patterns and departures from patterns

Chapters 2–10

A. Constructing and interpreting graphical displays of distributions of univariate data (dotplot, stemplot, histogram, cumulative frequency plot)
1. Center and spread Ch 4, 5
2. Clusters and gaps Ch 4
3. Outliers and other unusual features Ch 4, 5
4. Shape Ch 4
B. Summarizing distributions of univariate data
1. Measuring center: median, mean Ch 5
2. Measuring spread: range, interquartile range, standard deviation Ch 5
3. Measuring position: quartiles, percentiles, standardized scores (z-scores) Ch 5, 6
4. Using boxplots Ch 5
5. The effect of changing units on summary measures Ch 6
C. Comparing distributions of univariate data (dotplots, back-to back stemplots, parallel boxplots)
1. Comparing center and spread: within group, between group variation Ch 4, 5
2. Comparing clusters and gaps Ch 4
3. Comparing outliers and other unusual features Ch 4, 5
4. Comparing shapes Ch 4
D. Exploring bivariate data
1. Analyzing patterns in scatterplots Ch 7
2. Correlation and linearity Ch 7
3. Least-squares regression line Ch 8
4. Residual plots, outliers, and influential points Ch 8, 9
5. Transformations to achieve linearity: logarithmic and power transformations Ch 10
E. Exploring categorical data
1. Frequency tables and bar charts Ch 3
2. Marginal and joint frequencies for two-way tables Ch 3
3. Conditional relative frequencies and association Ch 3
4. Comparing distributions using bar charts Ch 3

II. Sampling and Experimentation: Planning and conducting a study

Chapters 12, 13

A. Overview of methods of data collection
1. Census Ch 12
2. Sample survey Ch 12
3. Experiment Ch 13
4. Observational study Ch 13
B. Planning and conducting surveys
1. Characteristics of a well-designed and well-conducted survey Ch 12
2. Populations, samples, and random selection Ch 12
3. Sources of bias in surveys Ch 12
4. Sampling methods, including simple random sampling, stratified random sampling, and cluster sampling Ch 12
C. Planning and conducting experiments
1. Characteristics of a well-designed and well-conducted experiment Ch 13
2. Treatments, control groups, experimental units, random assignments, and replication Ch 13
3. Sources of bias and confounding, including placebo effect and blinding Ch 13
4. Completely randomized design Ch 13
5. Randomized block design, including matched pairs design Ch 13
D. Generalizability of results and types of conclusions that can be drawn from observational studies, experiments, and surveys Ch 12, 13

III. Anticipating Patterns: Exploring random phenomena using probability and simulation

Chapters 6, 11, 14–18, 22–24, 26

A. Probability
1. Interpreting probability, including long-run relative frequency interpretation Ch 14
2. "Law of large numbers" concept Ch 14
3. Addition rule, multiplication rule, conditional probability, and independence Ch 14, 15
4. Discrete random variables and their probability distributions, including binomial and geometric Ch 16, 17
5. Simulation of random behavior and probability distributions Ch 11, 16, 17
6. Mean (expected value) and standard deviation of a random variable, and linear transformation of a random variable Ch 14
B. Combining independent random variables
1. Notion of independence versus dependence Ch 16
2. Mean and standard deviation for sums and differences of independent random variables Ch 16
C. The normal distribution
1. Properties of the normal distribution Ch 6
2. Using tables of the normal distribution Ch 6
3. The normal distribution as a model for measurements Ch 6
D. Sampling distributions
1. Sampling distribution of a sample proportion Ch 18
2. Sampling distribution of a sample mean Ch 18
3. Central Limit Theorem Ch 18
4. Sampling distribution of a difference between two independent sample proportions Ch 22
5. Sampling distribution of a difference between two independent sample means Ch 24
6. Simulation of sampling distributions Ch 11, 18
7. t-distribution Ch 23
8. Chi-square distribution Ch 26

IV. Statistical Inference: Estimating population parameters and testing hypotheses

Chapters 18–27

A. Estimation (point estimators and confidence intervals)
1. Estimating population parameters and margins of error Ch 19, 22–25, 27
2. Properties of point estimators, including unbiasedness and variability Ch 18, 19, 23
3. Logic of confidence intervals, meaning of confidence level and confidence intervals, and properties of confidence intervals Ch 19
4. Large sample confidence interval for a proportion Ch 19
5. Large sample confidence interval for a difference between two proportions Ch 22
6. Confidence interval for a mean Ch 23
7. Confidence interval for a difference between two means (unpaired and paired) Ch 24, 25
8. Confidence interval for the slope of a least-squares regression line Ch 27
B. Tests of significance
1. Logic of significance testing, null and alternative hypotheses; p-values; one- and two-sided tests; concepts of Type I and Type II errors; concept of power Ch 20, 21
2. Large sample test for a proportion Ch 20
3. Large sample test for a difference between two proportions Ch 22
4. Test for a mean Ch 23
5. Test for a difference between two means (unpaired and paired) Ch 24, 25
6. Chi-square test for goodness of fit, homogeneity of proportions, and independence (one- and two-way tables) Ch 26
7. Test for the slope of a least-squares regression line Ch 27

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