# AP Statistics Curriculum 2007

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

## Contents

- 1 Preface
- 2 Chapter I: Introduction to Statistics
- 3 Chapter II: Describing, Exploring, and Comparing Data
- 4 Chapter III: Probability
- 5 Chapter IV: Probability Distributions
- 6 Chapter V: Normal Probability Distributions
- 7 Chapter VI: Relations Between Distributions
- 8 Chapter VII: Estimates and Sample Sizes
- 9 Chapter VIII: Hypothesis Testing
- 10 Chapter IX: Inferences from Two Samples
- 11 Chapter X: Correlation and Regression
- 12 Chapter XI: Non-Parametric Inference
- 12.1 Differences of Means of Two Paired Samples
- 12.2 Differences of Means of Two Independent Samples
- 12.3 Differences of Medians of Two Paired Samples
- 12.4 Differences of Medians of Two Independent Samples
- 12.5 Differences of Proportions of Two Independent Samples
- 12.6 Differences of Means of Several Independent Samples
- 12.7 Differences of Variances of Two Independent Samples

- 13 Chapter XII: Multinomial Experiments and Contingency Tables
- 14 Chapter XIII: Statistical Process Control
- 15 Chapter XIV: Survival/Failure Analysis
- 16 Chapter XV: Multivariate Statistical Analyses
- 17 Chapter XVI: Time Series Analysis

## 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

### Summarizing data with Frequency Tables

Overview TBD

### Pictures of Data

Overview TBD

### Measures of Central Tendency

Overview TBD

### Measures of Variation

Overview TBD

### Measures of Shape

Overview TBD

### Graphs & Exploratory Data Analysis

## Chapter III: Probability

### Fundamentals

Overview TBD

### Addition & Multiplication Rules

Overview TBD

### Probabilities Through Simulations

Overview TBD

### Counting

Overview TBD

## Chapter IV: Probability Distributions

### Random Variables

Overview TBD

### Bernoulli & Binomial Experiments

Overview TBD

### Geometric, HyperGeometric & Negative Binomial

Overview TBD

### Poisson Distribution

Overview TBD

## Chapter V: Normal Probability Distributions

### The Standard Normal Distribution

Overview TBD

### Nonstandard Normal Distribution: Finding Probabilities

Overview TBD

### Nonstandard Normal Distributions: Finding Scores (critical values)

Overview TBD

## Chapter VI: Relations Between Distributions

### The Central Limit Theorem

Overview TBD

### Law of Large Numbers

Overview TBD

### Normal Distribution as Approximation to Binomial Distribution

Overview TBD

### Poisson Approximation to Binomial Distribution

Overview TBD

### Binomial Approximation to HyperGeometric

Overview TBD

### Normal Approximation to Poisson

Overview TBD

## Chapter VII: Estimates and Sample Sizes

### Estimating a Population Mean: Large Samples

Overview TBD

### Estimating a Population Mean: Small Samples

Overview TBD

### Estimating a Population Proportion

Overview TBD

### Estimating a Population Variance

Overview TBD

## Chapter VIII: Hypothesis Testing

### Fundamentals of Hypothesis Testing

Overview TBD

### Testing a Claim about a Mean: Large Samples

Overview TBD

### Testing a Claim about a Mean: Small Samples

Overview TBD

### Testing a Claim about a Proportion

Overview TBD

### Testing a Claim about a Standard Deviation or Variance

Overview TBD

## Chapter IX: Inferences from Two Samples

### Inferences about Two Means: Dependent Samples

Overview TBD

### Inferences about Two Means: Independent and Large Samples

Overview TBD

### Comparing Two Variances

Overview TBD

### Inferences about Two Means: Independent and Small Samples

Overview TBD

### Inferences about Two Proportions

Overview TBD

## Chapter X: Correlation and Regression

### Correlation

Overview TBD

### Regression

Overview TBD

### Variation and Prediction Intervals

Overview TBD

### Multiple Regression

Overview TBD

## Chapter XI: Non-Parametric Inference

### Differences of Means of Two Paired Samples

Overview TBD

### Differences of Means of Two Independent Samples

Overview TBD

### Differences of Medians of Two Paired Samples

Overview TBD

### Differences of Medians of Two Independent Samples

Overview TBD

### Differences of Proportions of Two Independent Samples

Overview TBD

### Differences of Means of Several Independent Samples

Overview TBD

### Differences of Variances of Two Independent Samples

Overview TBD

## Chapter XII: Multinomial Experiments and Contingency Tables

### Multinomial Experiments: Goodness-of-Fit

Overview TBD

### Contingency Tables: Independence and Homogeneity

Overview TBD

## Chapter XIII: Statistical Process Control

### Control Charts for Variation and Mean

Overview TBD

### Control Charts for Attributes

Overview TBD

## Chapter XIV: Survival/Failure Analysis

Overview TBD

## Chapter XV: Multivariate Statistical Analyses

### Multivariate Analysis of Variance

Overview TBD

### Multiple Linear Regression

Overview TBD

### Logistic Regression

Overview TBD

### Log-Linear Regression

Overview TBD

### Multivariate Analysis of Covariance

Overview TBD

## Chapter XVI: Time Series Analysis

Overview TBD

- SOCR Home page: http://www.socr.ucla.edu

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