AP Statistics Curriculum 2007
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===[[AP_Statistics_Curriculum_2007_Prob_Count |Counting]]=== | ===[[AP_Statistics_Curriculum_2007_Prob_Count |Counting]]=== | ||
| - | There are many useful counting principles to compute the number of ways that certain arrangements of objects can be formed. This allows counting-based estimation of probabilities fo complex events. | + | There are many useful counting principles (including permutations and combinations) to compute the number of ways that certain arrangements of objects can be formed. This allows counting-based estimation of probabilities fo complex events. |
==Chapter IV: Probability Distributions== | ==Chapter IV: Probability Distributions== | ||
Revision as of 18:57, 29 January 2008
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.) Models are used to study processes theoretically. Empirical validations of the utility of models are 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 understanding 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 populations (or sample data) that are always critical in understanding and interpreting their distributions - Center, Spread and Shape. The main measures of centrality are mean, median and mode(s).
Measures of Variation
There are many measures of (population or sample) spread, e.g., the range, the variance, the standard deviation, mean absolute deviation, etc. These are used to assess the dispersion or variation in the population.
Measures of Shape
The shape of a distribution can usually be determined by just looking at a histogram of a (representative) sample from that population frequency plots, dot plots or stem and leaf displays may be helpful.
Statistics
Variables can be summarized using statistics - functions of data samples.
Graphs & Exploratory Data Analysis
Graphical visualization and interrogation of data are critical components of any reliable method for statistical modeling, analysis and interpretation of data.
Chapter III: Probability
Probability is important in many studies and disciplines because measurements, observations and findings are often influenced by variation. In addition, probability theory provides the theoretical groundwork for statistical inference.
Fundamentals
Some fundamental concepts of probability theory include random events, sampling, types of probabilities, event manipulations and axioms of probability.
Rules for Computing Probabilities
There are many important rule for computing probabilities of composite events. These include conditional probability, statistical independence, multiplication and addition rules, the law of total probability and the Bayesian rule.
Probabilities Through Simulations
Many experimental setting require probability computations of complex events. Such calculations may be carried out exactly, using theoretical models, or approximately, using estimation or simulations.
Counting
There are many useful counting principles (including permutations and combinations) to compute the number of ways that certain arrangements of objects can be formed. This allows counting-based estimation of probabilities fo complex events.
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 Distribution
The Standard Normal Distribution
Overview TBD
Nonstandard Normal Distribution: Finding Probabilities
Overview TBD
Nonstandard Normal Distribution: 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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