SALINE AREA SCHOOLS
COURSE OUTCOMES
ADVANCED PLACEMENT STATISTICS
| Advanced Placement Statistics is a one-semester course designed to deepen the students' understanding of basic statistics and to include the advanced level topics needed to succeed on the A.P. examination. Many of the initial outcomes reflect the knowledge base obtained in the prerequisite course Statistics. These outcomes are repeated in order to provide the appropriate review and theoretical foundation to pursue the more difficult topics. |
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I. Explore Data: Observe Patterns and Departures from Patterns Exploratory analysis of data makes use of graphical and numerical techniques to study patterns and departures from patterns. Emphasis is placed on interpreting information from graphical and numerical displays and summaries. A. Interpret Graphical Displays of Distributions of Univariate Data (Dotplot, Stemplot, Histogram, Cumulative Frequency Plot) 1. Center and spread 2. Clusters and gaps 3. Outliers and other unusual features 4. Shape B. Summarize Distributions of Univariate Data 1. Measure center: median and mean 2. Measure spread: range, interquartile range, standard deviation 3. Measure position: quartiles, percentiles, standardized scores (z-scores) 4. Use boxplots 5. Observe the effect of changing units on summary measures C. Compare Distributions of Univariate Data (Dotplots, Back-to-Back Stemplots, Parallel Boxplots) 1. Compare center and spread: within group, between group variation 2. Compare clusters and gaps 3. Compare outliers and other unusual features 4. Compare shapes D. Explore Bivariate Data 1. Analyze patterns in scatterplots 2. Correlation and linearity 3. Least-squares regression line 4. Residual plots, outliers, and influential points E. Explore Categorical Data: Frequency Tables 1. Marginal and joint frequencies for two-way tables 2. Conditional relative frequencies and association
II. Plan a Study: Decide what and how to measure Data is 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. Compare of Methods of Data Collection 1. Census 2. Sample survey 3. Experiment 4. Observational study B. Plan and Conduct Surveys 1. Characteristics of a well-designed and well-conducted survey 2. Sources of bias in survey 3. Simple and stratified random sampling C. Plan and Conduct Experiments 1. Characteristics of a well-designed and well-conducted experiment 2. Treatments, control groups, experimental units, random assignments, and replication 3. Sources of bias and confounding 4. Completely randomized design 5. Randomized block design, including matched pairs design D. Generalize Results from Observational Studies, Experiments and Surveys
III. Anticipate Patterns: Produce Models Using Probability Theory and Simulation Probability is the tool used for anticipating what the distribution of data looks like under a given model. A. View Probability as Relative Frequency/ Empirical Approach to Probability 1. "Law of large numbers" concept 2. Addition rule, multiplication rule, conditional probability and independence 3. Discrete random variables and their probability distributions 4. Simulation of probability distributions, including geometric and binomial 5. Mean (expected value) and standard deviation of a random variable B. Combining Independent Random Variables 1. Notion of independence versus dependence 2. Mean and standard deviation for sums and differences of independent random variables C. Understand the Normal Distribution 1. Properties of the normal distribution 2. Using tables of the normal distribution 3. The normal distribution as a model for measurements D. Analyze Sampling Distributions 1. Sampling distribution of a sample proportion 2. Sampling distribution of a sample mean 3. Central Limit Theorem
IV. Use Statistical Inference: Confirming Models Statistical inference guides the selection of appropriate models. A. Understand Confidence Intervals 1. The meaning of a confidence interval 2. Large sample confidence interval for a proportion 3. Large sample confidence interval for a mean 4. Large sample confidence interval for a difference between two proportions 5. Large sample confidence interval for a difference between two means (paired and unpaired) B. Use Tests of Significance 1. Logic of significance testing, null and alternative hypotheses; p-values; one-and two-sided tests; 2. Type I and Type II errors; concept of power 3. Large sample test for a proportion 4. Large sample test for a mean 5. Large sample test for a difference between two proportions 6. Large sample test for a difference between two means (paired and unpaired) 7. Chi-square test for goodness of fit, homogeneity of proportions, and independence C. Special Cases of Normally Distributed Data 1. The t-distribution 2. Single sample t procedures 3. Two sample (independent and matched pairs) t procedures 4. Inference for slope of least squares line |