AP Statistics Curriculum 2007

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

Preface

This is an Internet-based E-Book for advance-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

Summarizing data with Frequency Tables

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Pictures of Data

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Measures of Central Tendency

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Measures of Variation

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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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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 IV: Normal Probability Distributions

The Standard Normal Distribution

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Nonstandard Normal Distribution: Finding Probabilities

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Nonstandard Normal Distributions: Finding Scores (critical values)

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Chapter V: 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 VI: 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 VII: 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 VIII: 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 IX: 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: Multinomial Experiments and Contingency Tables

Multinomial Experiments: Goodness-of-Fit

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Contingency Tables: Independence and Homogeneity

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Chapter XII: Statistical Process Control

Control Charts for Variation and Mean

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Control Charts for Attributes

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Chapter XV: Time Series Analysis

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