# 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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