Understandable Statistics correlated to the Advanced Placement Program Course Description for Statistics Prepared for Alabama CC2 6/2003 2003
Understandable Statistics 2003 correlated to the Advanced Placement Program Course Description for Statistics I. Exploring Data: Observing patterns and departures from patterns. Exploratory analysis of data makes use of graphical and numerical techniques to study patterns and departures from patterns. Emphasis should be place 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 Frequency Distributions and Histograms, 47-66; Dotplot, 66; Stem-and-Leaf Displays, 67-76; Using Technology: Applications, 85-87; Box-and-Whisker Plots, 129-137 2. Clusters and gaps Bar Graphs, Circle Graphs, and Time Plots, 36-47; Frequency Distributions and Histograms, 47-66 3. Outliers and other unusual features Bar Graphs, Circle Graphs, and Time Plots, 36-47; Frequency Distributions and Histograms, 47-66; Stem-and-Leaf Displays, 67-76; Box-and-Whisker Plots, 129-137 4. Shape Time Plots, 41-42; Distribution Shapes, 54, 85-87 B. Summarizing distributions of univariate data 1. Measuring center: median, mean Measures of Central Tendency: Mode, Median, Mean, 90-99 2. Measuring spread: range, interquartile range, standard deviation Measures of Variation, 99-114 1
3. Measuring position: quartiles, percentiles, standardized scores (z-scores) Percentiles, 124-128, 132-133; z Scores and Raw Scores, 289-290 4. Using boxplots Box-and-Whisker Plots, 129-137 5. The effect of changing units on summary measures Coefficient of Variation, 105-107 C. Comparing distributions of univariate data (dotplots, back-to-back stemplots, parallel boxplots) 1. Comparing center and spread: within group, between group variation Back-to-Back Stem Plots, 75-76; Using Technology: Comparing Histograms, 85; Mean and Standard Deviation of Grouped Data, 114-124; Comparing Box-and- Whisker Plots, 130-131, 133, 134-135; Using Technology, 146 2. Comparing clusters and gaps Dotplot, 66; Back-to-Back Stem Plot, 75-76 3. Comparing outliers and other unusual features Fences and Outliers, 131, 135; Using Technology, 146 4. Comparing shapes Distribution Shapes, 54 D. Exploring bivariate data 1. Analyzing patterns in scatterplots Introduction to Paired Data and Scatter Diagrams, 552-559 2. Correlation and linearity The Linear Correlation Coefficient, 580-595; Inferences Concerning Regression Parameters, 596-606 3. Least-squares regression line Linear Regression and Confidence Bounds for Prediction, 560-580 2
4. Residual plots, outliers, and influential points Residual Plot, 579-580; Outlier, 580; Influential Points, 627-628 5. Transformations to achieve linearity: logarithmic and power transformations Changing Scales, 559 E. Exploring categorical data: frequency tables 1. Marginal and joint frequencies for two-way tables Contingency Table, 637-638 2. Conditional relative frequencies and association Relative Frequency, 50-51; Relative Frequency as Probability, 150-151 3
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 Census, 20 2. Sample survey Sample Data, 5; Sample, 20; Surveys, 24-25 3. Experiment Experiments, 21-22, 153, 220-221 4. Observational study Observational Study, 21 B. Planning and conducting surveys 1. Characteristics of a well-designed and well-conducted survey Surveys, 24-25 2. Sample survey Sample Data, 5; Sample Statistical Survey, 20; Surveys, 24-25 3. Sources of bias in surveys Hidden bias, 24 4. Simple random sampling Simple Random Samples, 11-15 5. Stratified random sampling Stratified Sampling, 15-16 4
C. Planning and conducting experiments 1. Characteristics of a well-designed and well-conducted experiment Experiments and Observation, 21-23, 28; Binomial Experiment, 220-222; Experimental Design, 702-703 2. Treatments, control groups, experimental units, random assignments, and replication Randomized Two-Treatment Experiment, Control, and Replication, 22-23; Control Charts, 278-284 3. Sources of bias and confounding, including placebo effect and blinding Placebo, Double-Blind, Lurking or Confounding Variables, 22-23 4. Completely randomized design Completely Randomized Design, 702 5. Randomized block design, including matched pairs design Randomized Block Design, 703 D. Generalizability of results from observational studies, experimental studies, and surveys Descriptive and Inferential Statistics, 9; Generalizing Results, 25 5
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 What Is Probability?, 150-161; Using Technology: Demonstration of the Law of Large Numbers, 203 2. Addition rule, multiplication rule, conditional probability, and independence Some Probability Rules Compound Events, 161-181; Trees and Counting Techniques, 182-197; Bayes Theorem, A1-A4 3. Discrete random variables and their probability distributions, including binomial Introduction to Random Variables and Probability Distributions, 206-220 4. Simulation of probability distributions, including binomial and geometric Binomial Probabilities, 220-234; The Geometric and Poisson Probability Distributions, 246-260; Using Technology: Binomial Distributions, 269 5. Mean (expected value) and standard deviation of a random variable, and linear transformation of a random variable Introduction to Random Variables and Probability Distributions, 206-220; Additional Properties of the Binomial Distribution, 235-246 B. Combining independent random variables 1. Notion of independence versus dependence Linear Combinations of Independent Random Variables, 213-214, 219-220 2. Mean and standard deviation for sums and differences of independent random variables Linear Combinations of Independent Random Variables, 213-214, 219-220 C. The normal distribution 1. Properties of the normal distribution Graphs of Normal Probability Distributions, 272-288 6
2. Using tables of the normal distribution Standard Units and Areas Under the Standard Normal Distribution, 289-302; Areas of a Standard Normal Distribution, A26-A27 3. The normal distribution as a model for measurements Areas Under Any Normal Curve, 303-315; Normal Approximation to the Binomial Distribution, 316-324; Using Technology: Applications, 331-333 D. Sampling distributions 1. Sampling distribution of a sample proportion Sampling Distributions for Proportions, 353-364 2. Sampling distribution of a sample mean Sampling Distributions, 336-341 3. Central Limit Theorem The Central Limit Theorem, 341-353; Using Technology: Project Illustrating the Central Limit Theorem, 369-371 4. Sampling distribution of a difference between two independent sample proportions Estimating p 1 p 2, 428-431; Testing Difference of Proportions, 529-530, 539-540 5. Sampling distribution of a difference between two independent sample means Estimating µ 1 µ 2, 421-428; Testing Difference of Means, 520-529, 534-539 6. Simulation of sampling distributions Using Technology: Simulation, 548-549 7
IV. Statistical Inference: Confirming models Statistical inference guides the selection of appropriate models. A. Confidence intervals 1. The meaning of a confidence interval Confidence Interval, 379, 381-382 2. Large sample confidence interval for a proportion Confidence Interval for p, 403-412 3. Large sample confidence interval for a mean Confidence Interval for µ (Large Samples), 376-379, 395 4. Large sample confidence interval for a difference between two proportions Confidence Interval for p 1 p 2 (Large Samples), 428-439 5. Large sample confidence interval for a difference between two means (unpaired and paired) Confidence Interval for µ 1 µ 2 (Large Samples), 423-425, 431-439 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 Hypothesis Tests, 454-463; The P Value in Hypothesis Testing, 477-487 2. Large sample test for a proportion Tests Involving a Proportion, 498-505 3. Large sample test for a mean Test Involving the Mean µ (Large Samples), 463-477 4. Large sample test for a difference between two proportions Tests for Difference of Proportions, 529-541 8
5. Large sample test for a difference between two means (unpaired and paired) Tests Involving Paired Differences (Dependent Samples), 505-519; Testing Difference of Means for Large, Independent Samples, 520-524, 534-541 6. Chi-square test for goodness of fit, homogeneity of proportions, and independence (one- and two-way tables) Chi Square: Tests of Independence, 637-649; Chi Square: Goodness of Fit, 650-657; Testing and Estimating a Single Variance, 658-667; Testing Two Variances, 667-676 C. Special case of normally distributed data 1. t-distribution Estimating µ with Small Samples, 389-401 2. Single sample t procedures Tests Involving the Mean µ (Small Samples), 487-498 3. Two sample (independent and matched pairs) t procedures Tests Involving Paired Differences, 505-519; Testing Difference of Means for Small Samples, 525-529 4. Inference for the slope of least-squares regression line Linear Regression and Confidence Bounds for Prediction, 560-580; The Linear Correlation Coefficient, 580-596; Inferences Concerning Regression Parameters, 596-606; Multiple Regression, 607-624; Using Technology: Applications, 630-633 9