Difference between revisions of "AP Statistics Curriculum 2007"

Jump to: navigation, search
(Chapter IV: Probability Distributions)
(93 intermediate revisions by 2 users not shown)
Line 1: Line 1:
This is a General Advanced-Placement (AP) Statistics Curriculum E-Book
#REDIRECT [[Probability and statistics EBook]]
==[[AP_Statistics_Curriculum_2007_Preface| Preface]]==
This is an Internet-based E-Book for advanced-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.
===[[AP_Statistics_Curriculum_2007_Format| Format]]===
Follow the instructions in [[AP_Statistics_Curriculum_2007_Format| this page]] to expand, revise or improve the materials in this E-Book.
==Chapter I: Introduction to Statistics==
===[[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?
===[[AP_Statistics_Curriculum_2007_IntroUses |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 [http://en.wikipedia.org/wiki/Logic principles of logic] allow us to disambiguate the obtained statistical inference.
===[[AP_Statistics_Curriculum_2007_IntroDesign | 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.)
===[[AP_Statistics_Curriculum_2007_IntroTools |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==
===[[AP_Statistics_Curriculum_2007_EDA_DataTypes |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.
===[[AP_Statistics_Curriculum_2007_EDA_Freq |Summarizing data with Frequency Tables ]]===
There are two important ways to describe a data set (sample from a population) - Graphs or Tables.
===[[AP_Statistics_Curriculum_2007_EDA_Pics |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.
===[[AP_Statistics_Curriculum_2007_EDA_Center |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).
===[[AP_Statistics_Curriculum_2007_EDA_Var |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.
===[[AP_Statistics_Curriculum_2007_EDA_Shape |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 [[AP_Statistics_Curriculum_2007_EDA_Pics |frequency plots, dot plots or stem and leaf displays]] may be helpful.
===[[AP_Statistics_Curriculum_2007_EDA_Statistics | Statistics]]===
Variables can be summarized using statistics - functions of data samples.
===[[AP_Statistics_Curriculum_2007_EDA_Plots | 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.
===[[AP_Statistics_Curriculum_2007_Prob_Basics |Fundamentals]]===
Some fundamental concepts of probability theory include random events, sampling, types of probabilities, event manipulations and axioms of probability.
===[[AP_Statistics_Curriculum_2007_Prob_Rules | 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.
===[[AP_Statistics_Curriculum_2007_Prob_Simul |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.
===[[AP_Statistics_Curriculum_2007_Prob_Count |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 of complex events.
==Chapter IV: Probability Distributions==
There are two basic types of processes that we observe in nature - discrete and continuous. We begine by discussing several important discrete random processes, their distributions, expectations, variances and applications. In the [[AP_Statistics_Curriculum_2007#Chapter_V:_Normal_Probability_Distribution | next chapter]], we will discuss their continuous counterparts.
===[[AP_Statistics_Curriculum_2007_Distrib_RV | Random Variables]]===
To simplify the calculations of probabilities, we will define the concept of a '''random variable''' which will allows ut to study uniformly various processes, using the same mathamatical and computational techniques.
===[[AP_Statistics_Curriculum_2007_Distrib_Binomial |Bernoulli & Binomial Experiments]]===
The Bernoulli and Binomial processes provide the simplest models for discrete random experiments. Here we also define the expectation and the variance for any discrete random variable or process.
===[[AP_Statistics_Curriculum_2007_Distrib_Dists |Geometric, HyperGeometric & Negative Binomial]]===
Overview TBD
===[[AP_Statistics_Curriculum_2007_Distrib_Poisson |Poisson Distribution]]===
Overview TBD
==Chapter V: Normal Probability Distribution==
===[[AP_Statistics_Curriculum_2007_Normal_Std |The Standard Normal Distribution]]===
Overview TBD
===[[AP_Statistics_Curriculum_2007_Normal_Prob |Nonstandard Normal Distribution: Finding Probabilities]]===
Overview TBD
===[[AP_Statistics_Curriculum_2007_Normal_Critical |Nonstandard Normal Distribution: Finding Scores (critical values)]]===
Overview TBD
==Chapter VI: Relations Between Distributions==
===[[AP_Statistics_Curriculum_2007_Limits_CLT |The Central Limit Theorem]]===
Overview TBD
===[[AP_Statistics_Curriculum_2007_Limits_LLN |Law of Large Numbers]]===
Overview TBD
===[[AP_Statistics_Curriculum_2007_Limits_Norm2Bin |Normal Distribution as Approximation to Binomial Distribution]]===
Overview TBD
===[[AP_Statistics_Curriculum_2007_Limits_Poisson2Bin |Poisson Approximation to Binomial Distribution]]===
Overview TBD
===[[AP_Statistics_Curriculum_2007_Limits_Bin2HyperG |Binomial Approximation to HyperGeometric]]===
Overview TBD
===[[AP_Statistics_Curriculum_2007_Limits_Norm2Poisson |Normal Approximation to Poisson]]===
Overview TBD
==Chapter VII: Estimates and Sample Sizes==
===[[AP_Statistics_Curriculum_2007_Estim_L_Mean |Estimating a Population Mean: Large Samples]]===
Overview TBD
===[[AP_Statistics_Curriculum_2007_Estim_S_Mean |Estimating a Population Mean: Small Samples]]===
Overview TBD
===[[AP_Statistics_Curriculum_2007_Estim_Proportion |Estimating a Population Proportion]]===
Overview TBD
===[[AP_Statistics_Curriculum_2007_Estim_Var |Estimating a Population Variance]]===
Overview TBD
==Chapter VIII: Hypothesis Testing==
===[[AP_Statistics_Curriculum_2007_Hypothesis_Basics |Fundamentals of Hypothesis Testing]]===
Overview TBD
===[[AP_Statistics_Curriculum_2007_Hypothesis_L_Mean |Testing a Claim about a Mean: Large Samples]]===
Overview TBD
===[[AP_Statistics_Curriculum_2007_Hypothesis_S_Mean |Testing a Claim about a Mean: Small Samples]]===
Overview TBD
===[[AP_Statistics_Curriculum_2007_Hypothesis_Proportion |Testing a Claim about a Proportion]]===
Overview TBD
===[[AP_Statistics_Curriculum_2007_Hypothesis_Var |Testing a Claim about a Standard Deviation or Variance]]===
Overview TBD
==Chapter IX: Inferences from Two Samples==
===[[AP_Statistics_Curriculum_2007_Infer_2Means_Dep |Inferences about Two Means: Dependent Samples]]===
Overview TBD
===[[AP_Statistics_Curriculum_2007_Infer_2Means_Indep |Inferences about Two Means: Independent and Large Samples]]===
Overview TBD
===[[AP_Statistics_Curriculum_2007_Infer_BiVar |Comparing Two Variances]]===
Overview TBD
===[[AP_Statistics_Curriculum_2007_Infer_2Means_S_Indep |Inferences about Two Means: Independent and Small Samples]]===
Overview TBD
===[[AP_Statistics_Curriculum_2007_Infer_2Proportions |Inferences about Two Proportions]]===
Overview TBD
==Chapter X: Correlation and Regression==
===[[AP_Statistics_Curriculum_2007_GLM_Corr |Correlation]]===
Overview TBD
===[[AP_Statistics_Curriculum_2007_GLM_Regress |Regression]]===
Overview TBD
===[[AP_Statistics_Curriculum_2007_GLM_Predict |Variation and Prediction Intervals]]===
Overview TBD
===[[AP_Statistics_Curriculum_2007_GLM_MultLin |Multiple Regression]]===
Overview TBD
==Chapter XI: Non-Parametric Inference==
===[[AP_Statistics_Curriculum_2007_NonParam_2MeansPair | Differences of Means of Two Paired Samples]]===
Overview TBD
===[[AP_Statistics_Curriculum_2007_NonParam_2MeansIndep | Differences of Means of Two Independent Samples]]===
Overview TBD
===[[AP_Statistics_Curriculum_2007_NonParam_2MedianPair | Differences of Medians of Two Paired Samples]]===
Overview TBD
===[[AP_Statistics_Curriculum_2007_NonParam_2MedianIndep | Differences of Medians of Two Independent Samples]]===
Overview TBD
===[[AP_Statistics_Curriculum_2007_NonParam_2PropIndep | Differences of Proportions of Two Independent Samples]]===
Overview TBD
===[[AP_Statistics_Curriculum_2007_NonParam_ANOVA | Differences of Means of Several Independent Samples]]===
Overview TBD
===[[AP_Statistics_Curriculum_2007_NonParam_VarIndep | Differences of Variances of Two Independent Samples]]===
Overview TBD
==Chapter XII: Multinomial Experiments and Contingency Tables==
===[[AP_Statistics_Curriculum_2007_Contingency_Fit |Multinomial Experiments: Goodness-of-Fit]]===
Overview TBD
===[[AP_Statistics_Curriculum_2007_Contingency_Indep |Contingency Tables: Independence and Homogeneity]]===
Overview TBD
==Chapter XIII: Statistical Process Control==
===[[AP_Statistics_Curriculum_2007_Control_MeanVar |Control Charts for Variation and Mean]]===
Overview TBD
===[[AP_Statistics_Curriculum_2007_Control_Attrib |Control Charts for Attributes]]===
Overview TBD
==Chapter XIV: Survival/Failure Analysis==
Overview TBD
==Chapter XV: Multivariate Statistical Analyses==
===[[AP_Statistics_Curriculum_2007_MultiVar_ANOVA | Multivariate Analysis of Variance]]===
Overview TBD
===[[AP_Statistics_Curriculum_2007_MultiVar_LinRegression | Multiple Linear Regression]]===
Overview TBD
===[[AP_Statistics_Curriculum_2007_MultiVar_Logistic | Logistic Regression]]===
Overview TBD
===[[AP_Statistics_Curriculum_2007_MultiVar_LogLinear | Log-Linear Regression]]===
Overview TBD
===[[AP_Statistics_Curriculum_2007_MultiVar_ANCOVA | Multivariate Analysis of Covariance]]===
Overview TBD
==Chapter XVI: Time Series Analysis==
Overview TBD
* SOCR Home page: http://www.socr.ucla.edu

Latest revision as of 22:59, 7 November 2008