Correlations

Stats: Modeling the World ©2004

Bock, Velleman, De Veaux

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

SE = Student Edition
TE = Teacher Edition

I. EXPLORING DATA

Exploratory analysis of data makes use of graphical and numerical techniques to study patterns and departures from patterns. Emphasis should be placed on interpreting information from graphical and numerical displays and summaries.

A. Interpreting graphical displays of distributions of univariate data (dotplot, stemplot, histogram, cumulative frequency plot)
1. Center and spread	SE/TE: 39–44
2. Clusters and gaps	SE/TE: 41–42, 233
3. Outliers and other unusual features	SE/TE: 41–42, 61–62, 117–122
4. Shape	SE/TE: 39–43
B. Summarizing distributions of univariate data
1. Measuring center: median, mean	SE/TE: 57–65
2. Measuring spread: range, interquartile range, standard deviation	SE/TE: 60–67, 83–84
3. Measuring position: quartiles, percentiles, standardized scores (z-scores)	SE/TE: 84–92, 387–388, 427–430
4. Using boxplots	SE/TE: 60–61, 70–72
5. The effect of changing units on summary measures	SE/TE: 45–46, 98–99
C. Comparing distributions of univariate data (dotplots, back-to-back stemplots, parallel boxplots)
1. Comparing center and spread: within group, between group variation	SE/TE: 38–43, 67–70
2. Comparing clusters and gaps	SE/TE: 41–42, 233
3. Comparing outliers and other unusual features	SE/TE: 41–42, 61–62, 117–122
4. Comparing shapes	SE/TE: 39–40
D. Exploring bivariate data
1. Analyzing patterns in scatterplots	SE/TE: 115–123
2. Correlation and linearity	SE/TE: 119–123, 125, 130, 139–140
3. Least-squares regression line	SE/TE: 139–142, 547–551, 553–556
4. Residual plots, outliers, and influential points	SE/TE: 138, 167–169, 174
5. Transformations to achieve linearity: logarithmic and power transformations	SE/TE: 45–46, 190–193
E. Exploring categorical data: frequency tables
1. Marginal and joint frequencies for two-way tables	SE/TE: 17–23
2. Conditional relative frequencies and association	SE/TE: 21–22, 37, 276, 292–293

II. PLANNING A STUDY: DECIDING WHAT AND HOW TO MEASURE

Data must be collected according to a well-developed plan if valid information on a conjecture is to be obtained. This plan includes clarifying the question and deciding upon a method of data collection and analysis.

A. Overview of methods of data collection
1. Census	SE/TE: 229–230
2. Sample survey	SE/TE: 227–240
3. Experiment	SE/TE: 246–262
4. Observational study	SE/TE: 246–247, 260
B. Planning and conducting surveys
1. Characteristics of a well-designed and well-conducted survey	SE/TE: 227–234
2. Populations, samples, and random selection	SE/TE: 229–234
3. Sources of bias in surveys	SE/TE: 227, 235, 238–242
4. Simple random sampling	SE/TE: 228, 231–235
5. Stratified random sampling	SE/TE: 232, 241
C. Planning and conducting experiments
1. Characteristics of a well-designed and well-conducted experiment	SE/TE: 248–251
2. Treatments, control groups, experimental units, random assignments, and replication	SE/TE: 231–232, 247–249, 254
3. Sources of bias and confounding, including placebo effect and blinding	SE/TE: 239–242, 254–255, 258–260
4. Completely randomized design	SE/TE: 247–251
5. Randomized block design, including matched pairs design	SE/TE: 250, 256–257, 492, 499–500
D. Generalizability of results from observational studies, experimental studies, and surveys

III. ANTICIPATING PATTERNS: PRODUCING MODELS USING PROBABILITY THEORY AND SIMULATION

Probability is the tool used for anticipating what the distribution of data should look like under a given model.

A. Probability as relative frequency
1. "Law of large numbers" concept	SE/TE: 276–277
2. Addition rule, multiplication rule, conditional probability, and independence	SE/TE: 291–297, 300–304
3. Discrete random variables and their probability distributions, including binomial	SE/TE: 309–313, 316–319, 329–332
4. Simulation of probability distributions, including binomial and geometric	SE/TE: 218–221, 327–332
5. Mean (expected value) and standard deviation of a random variable, and linear transformation of a random variable	SE/TE: 139–140, 311–315
B. Combining independent random variables
1. Notion of independence versus dependence	SE/TE: 119–120, 295–297
2. Mean and standard deviation for sums and differences of independent random variables	SE/TE: 85–86, 316–318, 320
C. The normal distribution
1. Properties of the normal distribution	SE/TE: 83–89
2. Using tables of the normal distribution	SE/TE: 91–95, Table in SE A70–73; Table in TE A104
3. The normal distribution as a model for measurements	SE/TE: 83–86, 96–98, 349–350
D. Sampling distributions
1. Sampling distribution of a sample proportion	SE/TE: 347–350
2. Sampling distribution of a sample mean	SE/TE: 352–354, 358
3. Central Limit Theorem	SE/TE: 354–357
4. Sampling distribution of a difference between two independent sample proportions	SE/TE: 347–360, 365–377
5. Sampling distribution of a difference between two independent sample means	SE/TE: 352–354
6. Simulation of sampling distributions	SE/TE: 352–354

IV. STATISTICAL INFERENCE: CONFIRMING MODELS

Statistical inference guides the selection of appropriate models.

A. Confidence intervals
1. The meaning of a confidence interval	SE/TE: 366–371
2. Large sample confidence interval for a proportion	SE/TE: 371–376
3. Large sample confidence interval for a mean	SE/TE: 449–454
4. Large sample confidence interval for a difference between two proportions	SE/TE: 424–430
5. Large sample confidence interval for a difference between two means (unpaired and paired)	SE/TE: 466–477, 491–498
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	SE/TE: 383–390, 392–396, 404–405, 409–414
2. Large sample test for a proportion	SE/TE: 350–355
3. Large sample test for a mean	SE/TE: 358–361
4. Large sample test for a difference between two proportions	SE/TE: 421–425, 428–432
5. Large sample test for a difference between two means (unpaired and paired)	SE/TE: 466–477, 491–498
6. Chi-square test for goodness of fit, homogeneity of proportions, and independence (one- and two-way tables)	SE/TE: 521–524, 527–530, 532–538; Table in SE A73; Table in TE A107
C. Special case of normally distributed data
1. t-distribution	SE/TE: 443–446
2. Single sample t procedures	SE/TE: 452–457
3. Two sample (independent and matched pairs) t procedures	SE/TE: 466–477, 491–499
4. Inference for the slope of least-squares regression line	SE/TE: 139–144, 547–551, 553–556