AP Statistics Curriculum 2007 IntroVar

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==This is an Outline of a General Advance-Placement (AP) Statistics Curriculum==
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==[[ | General Advance-Placement (AP) Statistics Curriculum]] - Introduction to Statistics==
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===Outline===
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===The Nature of Data & Variation===
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Each topic discussed in the SOCR AP Curricumum should contain the following subsections:
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* '''Motivation/Problem''': A real data set and fundamental challenge.
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* '''Approach''': Models & strategies for solving the problem, data understanding & inference.
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* '''Model Validation''': Checking/affirming underlying assumptions.
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* '''Computational Resources''': Internet-based SOCR Tools (including offline resources, e.g., tables).
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* '''Examples''': computer simulations and real observed data.
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* '''Hands-on activities''': Step-by-step practice problems.
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===Introduction to Statistics===
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====[[AP_Statistics_Curriculum_2007_IntroVar | The Nature of Data & Variation]]====  
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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.
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.
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====Uses and Abuses of Statistics ====
 
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====Design of Experiments ====
 
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====Statistics with Calculators and Computers====
 
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===Describing, Exploring, and Comparing Data===
 
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====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 Position ====
 
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====Exploratory Data Analysis ====
 
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===Probability===
 
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====Fundamentals====
 
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====Addition Rule ====
 
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====Multiplication Rule ====
 
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====Probabilities through Simulations ====
 
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====Counting ====
 
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===Probability Distributions===
 
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====Random Variables ====
 
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====Bernoulli & Binomial Experiments ====
 
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====Geometric, HyperGeometric & Negative Binomial====
 
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====Mean, Variance, and Standard Deviation for the Binomial Distribution ====
 
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====Poisson Distribution====
 
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===Normal Probability Distributions===
 
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====The Standard Normal Distribution ====
 
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====Nonstandard Normal Distribution: Finding Probabilities ====
 
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====Nonstandard Normal Distributions: Finding Scores ====
 
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===Relations Between Distributions===
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For example, a UCLA study of Alzheimer’s disease*, analyzed the data of 31 MCI and 34 probable Alzheimer’s disease patients. The investigators made every attempt to control for as many variables as possible, yet, the demographic information they collected on the subjects contained unavoidable variation. The same study found variation in the MMSE cognitive scores even in the same subjects.
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====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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==References==
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* Apostolova LG, Dinov ID, Dutton RA, Hayashi KM, Toga AW, Cummings JL, Thompson PM. 3D comparison of hippocampal atrophy in amnestic mild cognitive impairment and Alzheimer's disease. Brain. 2006 Nov; 129(Pt 11):2867-73.
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===Estimates and Sample Sizes===
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====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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===Hypothesis Testing===
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====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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===Inferences from Two Samples===
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====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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===Correlation and Regression===
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====Correlation ====
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====Regression ====
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====Variation and Prediction Intervals ====
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====Multiple Regression ====
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===Multinomial Experiments and Contingency Tables===
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====Multinomial Experiments: Goodness-of-Fit ====
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====Contingency Tables: Independence and Homogeneity====
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===Statistical Process Control===
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====Control Charts for Variation and Mean ====
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====Control Charts for Attributes====
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<hr>
<hr>

Revision as of 23:01, 13 June 2007

[[ | General Advance-Placement (AP) Statistics Curriculum]] - 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.


For example, a UCLA study of Alzheimer’s disease*, analyzed the data of 31 MCI and 34 probable Alzheimer’s disease patients. The investigators made every attempt to control for as many variables as possible, yet, the demographic information they collected on the subjects contained unavoidable variation. The same study found variation in the MMSE cognitive scores even in the same subjects.



References

  • Apostolova LG, Dinov ID, Dutton RA, Hayashi KM, Toga AW, Cummings JL, Thompson PM. 3D comparison of hippocampal atrophy in amnestic mild cognitive impairment and Alzheimer's disease. Brain. 2006 Nov; 129(Pt 11):2867-73.



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