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−  This is a General AdvancedPlacement (AP) Statistics Curriculum EBook
 +  #REDIRECT [[Probability and statistics EBook]] 
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−  ==[[AP_Statistics_Curriculum_2007_Preface Preface]]==
 
−  This is an Internetbased EBook for advancedplacement (AP) statistics educational curriculum. The EBook 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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−  ===[[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 EBook.
 
−   
−  ==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 closedform 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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−  ===[[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 longtime 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.
 
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−  ===[[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.)
 
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−  ===[[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.
 
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−  ==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.
 
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−  ===[[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.
 
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−  ===[[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.
 
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−  ===[[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).
 
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−  ===[[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.
 
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−  ===[[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.
 
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−  ===[[AP_Statistics_Curriculum_2007_EDA_Statistics  Statistics]]===
 
−  Variables can be summarized using statistics  functions of data samples.
 
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−  ===[[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.
 
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−  ==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.
 
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−  ===[[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.
 
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−  ===[[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.
 
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−  ===[[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.
 
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−  ===[[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 countingbased estimation of probabilities of complex events.
 
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−  ==Chapter IV: Probability Distributions==
 
−  ===[[AP_Statistics_Curriculum_2007_Distrib_RV  Random Variables]]===
 
−  Overview TBD
 
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−  ===[[AP_Statistics_Curriculum_2007_Distrib_Binomial Bernoulli & Binomial Experiments]]===
 
−  Overview TBD
 
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−  ===[[AP_Statistics_Curriculum_2007_Distrib_Dists Geometric, HyperGeometric & Negative Binomial]]===
 
−  Overview TBD
 
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−  ===[[AP_Statistics_Curriculum_2007_Distrib_Poisson Poisson Distribution]]===
 
−  Overview TBD
 
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−  ==Chapter V: Normal Probability Distribution==
 
−  ===[[AP_Statistics_Curriculum_2007_Normal_Std The Standard Normal Distribution]]===
 
−  Overview TBD
 
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−  ===[[AP_Statistics_Curriculum_2007_Normal_Prob Nonstandard Normal Distribution: Finding Probabilities]]===
 
−  Overview TBD
 
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−  ===[[AP_Statistics_Curriculum_2007_Normal_Critical Nonstandard Normal Distribution: Finding Scores (critical values)]]===
 
−  Overview TBD
 
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−  ==Chapter VI: Relations Between Distributions==
 
−  ===[[AP_Statistics_Curriculum_2007_Limits_CLT The Central Limit Theorem]]===
 
−  Overview TBD
 
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−  ===[[AP_Statistics_Curriculum_2007_Limits_LLN Law of Large Numbers]]===
 
−  Overview TBD
 
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−  ===[[AP_Statistics_Curriculum_2007_Limits_Norm2Bin Normal Distribution as Approximation to Binomial Distribution]]===
 
−  Overview TBD
 
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−  ===[[AP_Statistics_Curriculum_2007_Limits_Poisson2Bin Poisson Approximation to Binomial Distribution]]===
 
−  Overview TBD
 
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−  ===[[AP_Statistics_Curriculum_2007_Limits_Bin2HyperG Binomial Approximation to HyperGeometric]]===
 
−  Overview TBD
 
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−  ===[[AP_Statistics_Curriculum_2007_Limits_Norm2Poisson Normal Approximation to Poisson]]===
 
−  Overview TBD
 
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−  ==Chapter VII: Estimates and Sample Sizes==
 
−  ===[[AP_Statistics_Curriculum_2007_Estim_L_Mean Estimating a Population Mean: Large Samples]]===
 
−  Overview TBD
 
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−  ===[[AP_Statistics_Curriculum_2007_Estim_S_Mean Estimating a Population Mean: Small Samples]]===
 
−  Overview TBD
 
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−  ===[[AP_Statistics_Curriculum_2007_Estim_Proportion Estimating a Population Proportion]]===
 
−  Overview TBD
 
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−  ===[[AP_Statistics_Curriculum_2007_Estim_Var Estimating a Population Variance]]===
 
−  Overview TBD
 
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−  ==Chapter VIII: Hypothesis Testing==
 
−  ===[[AP_Statistics_Curriculum_2007_Hypothesis_Basics Fundamentals of Hypothesis Testing]]===
 
−  Overview TBD
 
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−  ===[[AP_Statistics_Curriculum_2007_Hypothesis_L_Mean Testing a Claim about a Mean: Large Samples]]===
 
−  Overview TBD
 
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−  ===[[AP_Statistics_Curriculum_2007_Hypothesis_S_Mean Testing a Claim about a Mean: Small Samples]]===
 
−  Overview TBD
 
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−  ===[[AP_Statistics_Curriculum_2007_Hypothesis_Proportion Testing a Claim about a Proportion]]===
 
−  Overview TBD
 
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−  ===[[AP_Statistics_Curriculum_2007_Hypothesis_Var Testing a Claim about a Standard Deviation or Variance]]===
 
−  Overview TBD
 
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−  ==Chapter IX: Inferences from Two Samples==
 
−  ===[[AP_Statistics_Curriculum_2007_Infer_2Means_Dep Inferences about Two Means: Dependent Samples]]===
 
−  Overview TBD
 
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−  ===[[AP_Statistics_Curriculum_2007_Infer_2Means_Indep Inferences about Two Means: Independent and Large Samples]]===
 
−  Overview TBD
 
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−  ===[[AP_Statistics_Curriculum_2007_Infer_BiVar Comparing Two Variances]]===
 
−  Overview TBD
 
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−  ===[[AP_Statistics_Curriculum_2007_Infer_2Means_S_Indep Inferences about Two Means: Independent and Small Samples]]===
 
−  Overview TBD
 
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−  ===[[AP_Statistics_Curriculum_2007_Infer_2Proportions Inferences about Two Proportions]]===
 
−  Overview TBD
 
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−  ==Chapter X: Correlation and Regression==
 
−  ===[[AP_Statistics_Curriculum_2007_GLM_Corr Correlation]]===
 
−  Overview TBD
 
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−  ===[[AP_Statistics_Curriculum_2007_GLM_Regress Regression]]===
 
−  Overview TBD
 
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−  ===[[AP_Statistics_Curriculum_2007_GLM_Predict Variation and Prediction Intervals]]===
 
−  Overview TBD
 
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−  ===[[AP_Statistics_Curriculum_2007_GLM_MultLin Multiple Regression]]===
 
−  Overview TBD
 
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−  ==Chapter XI: NonParametric Inference==
 
−  ===[[AP_Statistics_Curriculum_2007_NonParam_2MeansPair  Differences of Means of Two Paired Samples]]===
 
−  Overview TBD
 
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−  ===[[AP_Statistics_Curriculum_2007_NonParam_2MeansIndep  Differences of Means of Two Independent Samples]]===
 
−  Overview TBD
 
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−  ===[[AP_Statistics_Curriculum_2007_NonParam_2MedianPair  Differences of Medians of Two Paired Samples]]===
 
−  Overview TBD
 
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−  ===[[AP_Statistics_Curriculum_2007_NonParam_2MedianIndep  Differences of Medians of Two Independent Samples]]===
 
−  Overview TBD
 
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−  ===[[AP_Statistics_Curriculum_2007_NonParam_2PropIndep  Differences of Proportions of Two Independent Samples]]===
 
−  Overview TBD
 
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−  ===[[AP_Statistics_Curriculum_2007_NonParam_ANOVA  Differences of Means of Several Independent Samples]]===
 
−  Overview TBD
 
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−  ===[[AP_Statistics_Curriculum_2007_NonParam_VarIndep  Differences of Variances of Two Independent Samples]]===
 
−  Overview TBD
 
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−  ==Chapter XII: Multinomial Experiments and Contingency Tables==
 
−  ===[[AP_Statistics_Curriculum_2007_Contingency_Fit Multinomial Experiments: GoodnessofFit]]===
 
−  Overview TBD
 
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−  ===[[AP_Statistics_Curriculum_2007_Contingency_Indep Contingency Tables: Independence and Homogeneity]]===
 
−  Overview TBD
 
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−  ==Chapter XIII: Statistical Process Control==
 
−  ===[[AP_Statistics_Curriculum_2007_Control_MeanVar Control Charts for Variation and Mean]]===
 
−  Overview TBD
 
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−  ===[[AP_Statistics_Curriculum_2007_Control_Attrib Control Charts for Attributes]]===
 
−  Overview TBD
 
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−  ==Chapter XIV: Survival/Failure Analysis==
 
−  Overview TBD
 
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−  ==Chapter XV: Multivariate Statistical Analyses==
 
−  ===[[AP_Statistics_Curriculum_2007_MultiVar_ANOVA  Multivariate Analysis of Variance]]===
 
−  Overview TBD
 
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−  ===[[AP_Statistics_Curriculum_2007_MultiVar_LinRegression  Multiple Linear Regression]]===
 
−  Overview TBD
 
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−  ===[[AP_Statistics_Curriculum_2007_MultiVar_Logistic  Logistic Regression]]===
 
−  Overview TBD
 
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−  ===[[AP_Statistics_Curriculum_2007_MultiVar_LogLinear  LogLinear Regression]]===
 
−  Overview TBD
 
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−  ===[[AP_Statistics_Curriculum_2007_MultiVar_ANCOVA  Multivariate Analysis of Covariance]]===
 
−  Overview TBD
 
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−  ==Chapter XVI: Time Series Analysis==
 
−  Overview TBD
 
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−  <hr>
 
−  * SOCR Home page: http://www.socr.ucla.edu
 
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−  {{translatepageName=http://wiki.stat.ucla.edu/socr/index.php?title=AP_Statistics_Curriculum_2007}}
 