AP Statistics Curriculum 2007

This is a General Advanced-Placement (AP) Statistics Curriculum E-Book

Preface

This is an Internet-based E-Book for advanced-placement (AP) statistics educational curriculum. The E-Book is initially developed by the UCLA Statistics Online Computational Resource (SOCR), however, any statistics instructor, researcher or educator is encouraged to contribute to this effort and improve the content of these learning materials.

Format

Follow the instructions in this page to expand, revise or improve the materials in this E-Book.

Chapter I: Introduction to Statistics

The Nature of Data & Variation

No mater how controlled the environment, the protocol or the design, virtually any repeated measurement, observation, experiment, trial, study or survey is bound to generate data that varies because of intrinsic (internal to the system) or extrinsic (due to the ambient environment) effects. How many natural processes or phenomena in real life can we describe that have an exact mathematical closed-form description and are completely deterministic? How do we model the rest of the processes that are unpredictable and have random characteristics?

Uses and Abuses of Statistics

Statistics is the science of variation, randomness and chance. As such, statistics is different from other sciences, where the processes being studied obey exact deterministic mathematical laws. Statistics provides quantitative inference represented as long-time probability values, confidence or prediction intervals, odds, chances, etc., which may ultimately be subjected to varying interpretations. The phrase Uses and Abuses of Statistics refers to the notion that in some cases statistical results may be used as evidence to seemingly opposite theses. However, most of the time, common principles of logic allow us to disambiguate the obtained statistical inference.

Design of Experiments

Design of experiments is the blueprint for planning a study or experiment, performing the data collection protocol and controlling the study parameters for accuracy and consistency. Data, or information, is typically collected in regard to a specific process or phenomenon being studied to investigate the effects of some controlled variables (independent variables or predictors) on other observed measurements (responses or dependent variables). Both types of variables are associated with specific observational units (living beings, components, objects, materials, etc.)

Statistics with Tools (Calculators and Computers)

All methods for data analysis, understanding or visualization are based on models that often have compact analytical representations (e.g., formulas, symbolic equations, etc.) Model are used to study processes theoretically. Empirical validations of the utility of models is achieved by plugging in data and actually testing the models. This validation step may be done manually, by computing the model prediction or model inference from recorded measurements. This however is possible by hand only for small number of observations (<10). In practice, we write (or use existent) algorithms and computer programs that automate these calculations for better efficiency, accuracy and consistency in applying models to larger datasets.

Chapter II: Describing, Exploring, and Comparing Data

Types of Data

There are two important concepts in any data analysis - population and sample. Each of these may generate data of two major types - quantitative or qualitative measurements.

Summarizing data with Frequency Tables

There are two important ways to describe a data set (sample from a population) - Graphs or Tables.

Pictures of Data

There are many different ways to display and graphically visualize data. These graphical techniques facilitate the udenrstanding of the dataset and enable the selection of an appropriate statistical methodology for the analysis of the data.

Measures of Central Tendency

There are three main features of data that are always critical in uderstanding and intepreting data distributions - Shape, Center and Spread.

Measures of Variation

Overview TBD

Measures of Shape

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Chapter III: Probability

Fundamentals

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Addition & Multiplication Rules

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Probabilities Through Simulations

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Counting

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Chapter IV: Probability Distributions

Random Variables

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Bernoulli & Binomial Experiments

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Geometric, HyperGeometric & Negative Binomial

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Poisson Distribution

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Chapter V: Normal Probability Distribution

The Standard Normal Distribution

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Nonstandard Normal Distribution: Finding Probabilities

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Nonstandard Normal Distribution: Finding Scores (critical values)

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Chapter VI: Relations Between Distributions

The Central Limit Theorem

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Law of Large Numbers

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Normal Distribution as Approximation to Binomial Distribution

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Poisson Approximation to Binomial Distribution

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Binomial Approximation to HyperGeometric

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Normal Approximation to Poisson

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Chapter VII: Estimates and Sample Sizes

Estimating a Population Mean: Large Samples

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Estimating a Population Mean: Small Samples

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Estimating a Population Proportion

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Estimating a Population Variance

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Chapter VIII: Hypothesis Testing

Fundamentals of Hypothesis Testing

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Testing a Claim about a Mean: Large Samples

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Testing a Claim about a Mean: Small Samples

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Testing a Claim about a Proportion

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Testing a Claim about a Standard Deviation or Variance

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Chapter IX: Inferences from Two Samples

Inferences about Two Means: Dependent Samples

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Inferences about Two Means: Independent and Large Samples

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Comparing Two Variances

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Inferences about Two Means: Independent and Small Samples

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Inferences about Two Proportions

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Chapter X: Correlation and Regression

Correlation

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Regression

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Variation and Prediction Intervals

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Multiple Regression

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Chapter XI: Non-Parametric Inference

Differences of Means of Two Paired Samples

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Differences of Means of Two Independent Samples

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Differences of Medians of Two Paired Samples

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Differences of Medians of Two Independent Samples

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Differences of Proportions of Two Independent Samples

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Differences of Means of Several Independent Samples

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Differences of Variances of Two Independent Samples

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Chapter XII: Multinomial Experiments and Contingency Tables

Multinomial Experiments: Goodness-of-Fit

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Contingency Tables: Independence and Homogeneity

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Chapter XIII: Statistical Process Control

Control Charts for Variation and Mean

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Control Charts for Attributes

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Chapter XIV: Survival/Failure Analysis

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Chapter XV: Multivariate Statistical Analyses

Multivariate Analysis of Variance

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Multiple Linear Regression

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Logistic Regression

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Log-Linear Regression

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Multivariate Analysis of Covariance

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Chapter XVI: Time Series Analysis

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