AP Statistics Curriculum 2007
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Revision as of 18:26, 20 June 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
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
Probability Distributions
Random Variables
Overview TBD
Bernoulli & Binomial Experiments
Overview TBD
Geometric, HyperGeometric & Negative Binomial
Overview TBD
Poisson Distribution
Overview TBD
Chapter IV: 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 V: 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 VI: 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 VII: 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 VIII: 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 IX: Correlation and Regression
Correlation
Overview TBD
Regression
Overview TBD
Variation and Prediction Intervals
Overview TBD
Multiple Regression
Overview TBD
Chapter X: Multinomial Experiments and Contingency Tables
Multinomial Experiments: Goodness-of-Fit
Overview TBD
Contingency Tables: Independence and Homogeneity
Overview TBD
Chapter XI: Statistical Process Control
Control Charts for Variation and Mean
Overview TBD
Control Charts for Attributes
Overview TBD
- SOCR Home page: http://www.socr.ucla.edu
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