Difference between revisions of "AP Statistics Curriculum 2007"

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==This is an Outline of a General Advance-Placement (AP) Statistics Curriculum==
 
==This is an Outline of a General Advance-Placement (AP) Statistics Curriculum==
  
===Outline===
+
===[[AP_Statistics_Curriculum_2007_Preface| Preface]]===
 
This is an Internet-based E-Book for advance-placement (AP) statistics educational curriculum. The e-book is initially developed by the UCLA [[SOCR | 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.
 
This is an Internet-based E-Book for advance-placement (AP) statistics educational curriculum. The e-book is initially developed by the UCLA [[SOCR | 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.
  
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Follow the instructions in [[AP_Statistics_Curriculum_2007_Format| this page]] to expand, revise or improve the materials in this e-book.
 
Follow the instructions in [[AP_Statistics_Curriculum_2007_Format| this page]] to expand, revise or improve the materials in this e-book.
  
===Introduction to Statistics===
+
===Chapter I: Introduction to Statistics===
 
====[[AP_Statistics_Curriculum_2007_IntroVar | The Nature of Data & Variation]]====  
 
====[[AP_Statistics_Curriculum_2007_IntroVar | 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?
 
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?
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Overview TBD
 
Overview TBD
 
   
 
   
===Describing, Exploring, and Comparing Data===
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===Chapter II: Describing, Exploring, and Comparing Data===
 
====[[AP_Statistics_Curriculum_2007_EDA_Freq |Summarizing data with Frequency Tables ]]====
 
====[[AP_Statistics_Curriculum_2007_EDA_Freq |Summarizing data with Frequency Tables ]]====
 
Overview TBD
 
Overview TBD
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====[[AP_Statistics_Curriculum_2007_EDA_Plots | Graphs & Exploratory Data Analysis]] ====
 
====[[AP_Statistics_Curriculum_2007_EDA_Plots | Graphs & Exploratory Data Analysis]] ====
 
   
 
   
===Probability===
+
===Chapter III: Probability===
 
====[[AP_Statistics_Curriculum_2007_Prob_Basics |Fundamentals]]====  
 
====[[AP_Statistics_Curriculum_2007_Prob_Basics |Fundamentals]]====  
 
Overview TBD
 
Overview TBD
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Overview TBD
 
Overview TBD
  
===Normal Probability Distributions===
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===Chapter IV: Normal Probability Distributions===
 
====[[AP_Statistics_Curriculum_2007_Normal_Std |The Standard Normal Distribution]] ====
 
====[[AP_Statistics_Curriculum_2007_Normal_Std |The Standard Normal Distribution]] ====
 
Overview TBD
 
Overview TBD
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Overview TBD
 
Overview TBD
  
===Relations Between Distributions===
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===Chapter V: Relations Between Distributions===
 
====[[AP_Statistics_Curriculum_2007_Limits_CLT |The Central Limit Theorem]] ====
 
====[[AP_Statistics_Curriculum_2007_Limits_CLT |The Central Limit Theorem]] ====
 
Overview TBD
 
Overview TBD
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Overview TBD
 
Overview TBD
 
   
 
   
===Estimates and Sample Sizes===
+
===Chapter VI: Estimates and Sample Sizes===
 
====[[AP_Statistics_Curriculum_2007_Estim_L_Mean |Estimating a Population Mean: Large Samples]] ====
 
====[[AP_Statistics_Curriculum_2007_Estim_L_Mean |Estimating a Population Mean: Large Samples]] ====
 
Overview TBD
 
Overview TBD
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Overview TBD
 
Overview TBD
 
   
 
   
===Hypothesis Testing===
+
===Chapter VII: Hypothesis Testing===
 
====[[AP_Statistics_Curriculum_2007_Hypothesis_Basics |Fundamentals of Hypothesis Testing]] ====
 
====[[AP_Statistics_Curriculum_2007_Hypothesis_Basics |Fundamentals of Hypothesis Testing]] ====
 
Overview TBD
 
Overview TBD
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Overview TBD
 
Overview TBD
 
   
 
   
===Inferences from Two Samples===
+
===Chapter VIII: Inferences from Two Samples===
 
====[[AP_Statistics_Curriculum_2007_Infer_2Means_Dep |Inferences about Two Means: Dependent Samples]] ====
 
====[[AP_Statistics_Curriculum_2007_Infer_2Means_Dep |Inferences about Two Means: Dependent Samples]] ====
 
Overview TBD
 
Overview TBD
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Overview TBD
 
Overview TBD
 
   
 
   
===Correlation and Regression===
+
===Chapter IX: Correlation and Regression===
 
====[[AP_Statistics_Curriculum_2007_GLM_Corr |Correlation]] ====
 
====[[AP_Statistics_Curriculum_2007_GLM_Corr |Correlation]] ====
 
Overview TBD
 
Overview TBD
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Overview TBD
 
Overview TBD
 
   
 
   
===Multinomial Experiments and Contingency Tables===
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===Chapter X: Multinomial Experiments and Contingency Tables===
 
====[[AP_Statistics_Curriculum_2007_Contingency_Fit |Multinomial Experiments: Goodness-of-Fit]] ====
 
====[[AP_Statistics_Curriculum_2007_Contingency_Fit |Multinomial Experiments: Goodness-of-Fit]] ====
 
Overview TBD
 
Overview TBD
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Overview TBD
 
Overview TBD
 
   
 
   
===Statistical Process Control===
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===Chapter XI: Statistical Process Control===
 
====[[AP_Statistics_Curriculum_2007_Control_MeanVar |Control Charts for Variation and Mean]] ====
 
====[[AP_Statistics_Curriculum_2007_Control_MeanVar |Control Charts for Variation and Mean]] ====
 
Overview TBD
 
Overview TBD

Revision as of 17:06, 19 June 2007

Contents

This is an Outline of a General Advance-Placement (AP) Statistics Curriculum

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)

Overview TBD

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




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