STATISTICS for DECISION-MAKERS. P. Richard Hahn
|
|
- Hubert Norris
- 7 years ago
- Views:
Transcription
1 STATISTICS for DECISION-MAKERS P. Richard Hahn
2 Statistics for Decision-Makers COPYRIGHT P. RICHARD HAHN ISBN INFO ISBN 13: ALL RIGHTS RESERVED i
3 Contents Contents ii I Core Concepts 6 1 Exploiting statistical patterns 9 How to predict well on average. 1.1 Basic probability Random variables Expected value (averages) Expected utility maximization Bayes rule: refining your reference set The best linear predictor Learning statistical patterns from data 11 How to make data-driven predictions. 2.1 Empirical distributions vs. "true" distributions Estimand, estimator, estimate Empirical utility maximization ii
4 3 Assessing sampling variability 13 How to judge the reliability of a data-driven prediction rule. 3.1 Sampling variation and sampling distributions Null hypotheses Permutation tests Boot-strapping Over-fitting and regularization II Linear prediction 14 4 Linear regression 17 Finding trend lines in data. 4.1 Estimating the best linear predictor Least-squares R-squared Confidence intervals (and hypothesis tests) Data transformations Multiple linear regression 19 Finding linear trends when there are multiple factors. 5.1 R-squared with more than one predictor Interactions Logistic regression 21 How to predict binary outcomes. 6.1 Link functions Classification rules Odds ratios and log-odds iii
5 III Beyond prediction 22 7 Experimental design 25 Guidelines for data collection. 7.1 Controlled randomized experiments Power calculation Controlling for confounding Coping with sampling bias 27 How policy evaluation differs from straight prediction. 8.1 Natural experiments" and instrumental variables Regression discontinuity design Causal regret analysis 29 How to make sense of statistical information for one-time decisions. iv
6 Preface This book aims to communicate core ideas from probability and statistics distributions, expected value, conditional probability, sampling variability and sampling bias towards the goal of making practical use of statistical data. Readers of this book should not expect to come away with a technical understanding of how to apply modern data analytic methods to massive databases. What I do hope to deliver is a clear picture of how such methods work on a conceptual level, a flavor of the variety of situations where they might profitably be applied, and a useful mental vocabulary for thinking about the various data streams you interact with on a daily basis in your work and your life. While there is a proliferation of books documenting that individuals and institutions are using data to guide their decisions, this book aims to fill a gap in explaining the basic logic behind how exactly data ought to inform our decision making. 1
7
8 Outline This book is divided into three parts, each with three chapters. Part one presents the foundational concepts underpinning statistical data analysis. The first chapter concerns what to do when you need to make a decision based on uncertain information. Our prototypical decision will be a prediction of some sort. (Later we will consider more general decision-making scenarios.) The classic example of an applied prediction scenario would be picking stocks. You have to make a decision which stocks to pick and the eventual payoff will depend on some future outcome. The key idea of this first chapter is the idea of an average. When making predictions in random environments, you can t hope to be right every time, so you have to think about selecting strategies that lead to good average performance. Accordingly, defining what average means is important. This first chapter is essentially a primer on the basic ideas of probability, which is a language for describing patterns which emerge when one looks at many random events in aggregate. Chapter two is about how to find patterns that allow 3
9 you to characterize randomness (more specifically, probability distributions) in processes you might care about. The whole idea of an average presumes that even random events have some structure. For example, although which specific people happen to die in car crashes in Illinois in a given year is essentially random, the total number of motor vehicle fatalities might be relatively stable from year to year. In the first chapter, we pretend such features are know to us at the outset. The second chapter turns to the problem of determining such patterns directly from data. The chapter closes by introducing the notion of a linear prediction rule, which is a powerful technique for describing relationships between two quantities such as the price of gas in a country and that country s unemployment rate which hold approximately. The third chapter focuses on determining how much we should trust the patterns we find in data. For example, it might seem like higher gas price associates strongly with high unemployment, but is the pattern we observe real, or just a fluke? Part two covers linear regression, which refers to the process of finding linear prediction rules from observed data. This method is the workhorse of applied statistical analysis. This section includes a chapter on how to find linear prediction rules when there are multiple factors influencing the outcome we are trying to predict (multiple linear regression), as well as a chapter that extends the basic method to predicting yes/no outcomes such as who is going to win a (two-party) election or tonight s Bulls- Pacers game or whether or not a given patient has diabetes. Part three looks at how to extend these ideas beyond the pure prediction setting, where we might be interested in policy/managerial interventions. It turns out that a whole separate set of delicate issues crop up when we want to mess with the system we re studying (such as the econ- 4
10 omy) rather than just passively make predictions about it. Things also get more subtle when we try to apply statistical reasoning to one-shot decisions, such as what diet you should stick to if you re pregnant. Unlike an investing strategy, most people won t face such a decision enough times to make the statistical information a reliable guide to future outcomes. Note to the reader Two more things. First, this book has formulas and equations here and there. I empathize with the anxiety that formulas provoke in a lot of folks. (A pet peeve of mine is when formulas are used to impress rather than to express ideas clearly and compactly.) With this common aversion in mind, I ve tried to keep my equations and symbols and such to a bare minimum, but it turns out that minimum in this case is not none. So I encourage you to face this hurdle with the knowledge that sticking with it will pay dividends. Achieving a comfort with mathematical notation is challenging in much the same way that learning to play the piano or speak a foreign language is challenging, and is similarly worthwhile. Second, this is not a textbook. It is a chatty guided tour through the key ideas underpinning data analysis for decision-making. My selection of topics, choice of examples and ordering of material are all in service of a narrative designed to make the case that statistical data analysis is 1) broadly useful and 2) not rocket science. So while much of the material will overlap with a more traditional statistics text, do not be alarmed if the territory seems markedly different from what you expected or have seen previously in a statistics book. 5
Sample Size and Power in Clinical Trials
Sample Size and Power in Clinical Trials Version 1.0 May 011 1. Power of a Test. Factors affecting Power 3. Required Sample Size RELATED ISSUES 1. Effect Size. Test Statistics 3. Variation 4. Significance
More informationFairfield Public Schools
Mathematics Fairfield Public Schools AP Statistics AP Statistics BOE Approved 04/08/2014 1 AP STATISTICS Critical Areas of Focus AP Statistics is a rigorous course that offers advanced students an opportunity
More informationOrganizing Your Approach to a Data Analysis
Biost/Stat 578 B: Data Analysis Emerson, September 29, 2003 Handout #1 Organizing Your Approach to a Data Analysis The general theme should be to maximize thinking about the data analysis and to minimize
More informationAssociation Between Variables
Contents 11 Association Between Variables 767 11.1 Introduction............................ 767 11.1.1 Measure of Association................. 768 11.1.2 Chapter Summary.................... 769 11.2 Chi
More informationProblem of the Month: Fair Games
Problem of the Month: The Problems of the Month (POM) are used in a variety of ways to promote problem solving and to foster the first standard of mathematical practice from the Common Core State Standards:
More informationExample: Boats and Manatees
Figure 9-6 Example: Boats and Manatees Slide 1 Given the sample data in Table 9-1, find the value of the linear correlation coefficient r, then refer to Table A-6 to determine whether there is a significant
More informationAnalysis of Variance ANOVA
Analysis of Variance ANOVA Overview We ve used the t -test to compare the means from two independent groups. Now we ve come to the final topic of the course: how to compare means from more than two populations.
More informationBeating the MLB Moneyline
Beating the MLB Moneyline Leland Chen llxchen@stanford.edu Andrew He andu@stanford.edu 1 Abstract Sports forecasting is a challenging task that has similarities to stock market prediction, requiring time-series
More informationImplementing Portfolio Management: Integrating Process, People and Tools
AAPG Annual Meeting March 10-13, 2002 Houston, Texas Implementing Portfolio Management: Integrating Process, People and Howell, John III, Portfolio Decisions, Inc., Houston, TX: Warren, Lillian H., Portfolio
More informationWeight of Evidence Module
Formula Guide The purpose of the Weight of Evidence (WoE) module is to provide flexible tools to recode the values in continuous and categorical predictor variables into discrete categories automatically,
More informationUSES OF CONSUMER PRICE INDICES
USES OF CONSUMER PRICE INDICES 2 2.1 The consumer price index (CPI) is treated as a key indicator of economic performance in most countries. The purpose of this chapter is to explain why CPIs are compiled
More informationStats 202 Data Analysis Project Winter 2016
Stats 202 Data Analysis Project Winter 2016 1 Learning Objectives The learning goals of the Stats 202 data analysis project are Formulate clear scientific research questions; Explore public data sources
More informationSome Essential Statistics The Lure of Statistics
Some Essential Statistics The Lure of Statistics Data Mining Techniques, by M.J.A. Berry and G.S Linoff, 2004 Statistics vs. Data Mining..lie, damn lie, and statistics mining data to support preconceived
More informationSample Size Issues for Conjoint Analysis
Chapter 7 Sample Size Issues for Conjoint Analysis I m about to conduct a conjoint analysis study. How large a sample size do I need? What will be the margin of error of my estimates if I use a sample
More informationMicrosoft Azure Machine learning Algorithms
Microsoft Azure Machine learning Algorithms Tomaž KAŠTRUN @tomaz_tsql Tomaz.kastrun@gmail.com http://tomaztsql.wordpress.com Our Sponsors Speaker info https://tomaztsql.wordpress.com Agenda Focus on explanation
More informationDecision Making under Uncertainty
6.825 Techniques in Artificial Intelligence Decision Making under Uncertainty How to make one decision in the face of uncertainty Lecture 19 1 In the next two lectures, we ll look at the question of how
More informationThe Partnership for the Assessment of College and Careers (PARCC) Acceptance Policy Adopted by the Illinois Council of Community College Presidents
The Partnership for the Assessment of College and Careers (PARCC) Acceptance Policy Adopted by the Illinois Council of Community College Presidents This policy was developed with the support and endorsement
More informationSession 7 Bivariate Data and Analysis
Session 7 Bivariate Data and Analysis Key Terms for This Session Previously Introduced mean standard deviation New in This Session association bivariate analysis contingency table co-variation least squares
More informationStatistics 3202 Introduction to Statistical Inference for Data Analytics 4-semester-hour course
Statistics 3202 Introduction to Statistical Inference for Data Analytics 4-semester-hour course Prerequisite: Stat 3201 (Introduction to Probability for Data Analytics) Exclusions: Class distribution:
More informationProspect Theory Ayelet Gneezy & Nicholas Epley
Prospect Theory Ayelet Gneezy & Nicholas Epley Word Count: 2,486 Definition Prospect Theory is a psychological account that describes how people make decisions under conditions of uncertainty. These may
More informationStatistics in Retail Finance. Chapter 2: Statistical models of default
Statistics in Retail Finance 1 Overview > We consider how to build statistical models of default, or delinquency, and how such models are traditionally used for credit application scoring and decision
More informationThat s Not Fair! ASSESSMENT #HSMA20. Benchmark Grades: 9-12
That s Not Fair! ASSESSMENT # Benchmark Grades: 9-12 Summary: Students consider the difference between fair and unfair games, using probability to analyze games. The probability will be used to find ways
More informationPart 2: Analysis of Relationship Between Two Variables
Part 2: Analysis of Relationship Between Two Variables Linear Regression Linear correlation Significance Tests Multiple regression Linear Regression Y = a X + b Dependent Variable Independent Variable
More informationQualitative Analysis Vs. Quantitative Analysis 06/16/2014 1
Qualitative Analysis Vs. Quantitative Analysis 06/16/2014 1 What s the Difference? Qualitative adjustments are purely relative (inferior, similar and superior). Quantitative adjustments use specific numbers
More informationNonparametric statistics and model selection
Chapter 5 Nonparametric statistics and model selection In Chapter, we learned about the t-test and its variations. These were designed to compare sample means, and relied heavily on assumptions of normality.
More informationCOLUMBIA UNIVERSITY IN THE CITY OF NEW YORK DEPARTMENT OF INDUSTRIAL ENGINEERING AND OPERATIONS RESEARCH
Course: IEOR 4575 Business Analytics for Operations Research Lectures MW 2:40-3:55PM Instructor Prof. Guillermo Gallego Office Hours Tuesdays: 3-4pm Office: CEPSR 822 (8 th floor) Textbooks and Learning
More informationExample: Credit card default, we may be more interested in predicting the probabilty of a default than classifying individuals as default or not.
Statistical Learning: Chapter 4 Classification 4.1 Introduction Supervised learning with a categorical (Qualitative) response Notation: - Feature vector X, - qualitative response Y, taking values in C
More informationThe Cross-Sectional Study:
The Cross-Sectional Study: Investigating Prevalence and Association Ronald A. Thisted Departments of Health Studies and Statistics The University of Chicago CRTP Track I Seminar, Autumn, 2006 Lecture Objectives
More informationStudy Guide for the Final Exam
Study Guide for the Final Exam When studying, remember that the computational portion of the exam will only involve new material (covered after the second midterm), that material from Exam 1 will make
More informationIntroduction to Fixed Effects Methods
Introduction to Fixed Effects Methods 1 1.1 The Promise of Fixed Effects for Nonexperimental Research... 1 1.2 The Paired-Comparisons t-test as a Fixed Effects Method... 2 1.3 Costs and Benefits of Fixed
More informationA. General Rules and Conditions: 1) This plan conforms to the regulations of the general frame of the program of graduate studies.
Study Plan for M.B.A in Banking and Finance applied from 2003/2004-2008/2009 A. General Rules and Conditions: 1) This plan conforms to the regulations of the general frame of the program of graduate studies.
More informationCopyright 2013 The National Council of Teachers of Mathematics, Inc. www.nctm.org. All rights reserved. This material may not be copied or
A W weet Copyright 203 The National Council of Teachers of Mathematics, Inc. www.nctm.org. All rights reserved. This material may not be copied or distributed electronically or in any other format without
More informationFDU-Vancouver Bachelor of Science in Business Administration International Business Concentration Course Descriptions
FDU-Vancouver Bachelor of Science in Business Administration International Business Concentration Course Descriptions Business Foundational Courses General Education DSCI 1234 Mathematics for Business
More informationHYPOTHESIS TESTING: CONFIDENCE INTERVALS, T-TESTS, ANOVAS, AND REGRESSION
HYPOTHESIS TESTING: CONFIDENCE INTERVALS, T-TESTS, ANOVAS, AND REGRESSION HOD 2990 10 November 2010 Lecture Background This is a lightning speed summary of introductory statistical methods for senior undergraduate
More informationVirtual Child Written Project Assignment. Four-Assignment Version of Reflective Questions
Virtual Child Written Project Assignment Four-Assignment Version of Reflective Questions Virtual Child Report (Assignment) 1: Infants and Toddlers (20 points) Choose 7 or 8 questions whose total point
More informationIn mathematics, there are four attainment targets: using and applying mathematics; number and algebra; shape, space and measures, and handling data.
MATHEMATICS: THE LEVEL DESCRIPTIONS In mathematics, there are four attainment targets: using and applying mathematics; number and algebra; shape, space and measures, and handling data. Attainment target
More informationTwo Correlated Proportions (McNemar Test)
Chapter 50 Two Correlated Proportions (Mcemar Test) Introduction This procedure computes confidence intervals and hypothesis tests for the comparison of the marginal frequencies of two factors (each with
More informationECON 459 Game Theory. Lecture Notes Auctions. Luca Anderlini Spring 2015
ECON 459 Game Theory Lecture Notes Auctions Luca Anderlini Spring 2015 These notes have been used before. If you can still spot any errors or have any suggestions for improvement, please let me know. 1
More informationData Analysis, Research Study Design and the IRB
Minding the p-values p and Quartiles: Data Analysis, Research Study Design and the IRB Don Allensworth-Davies, MSc Research Manager, Data Coordinating Center Boston University School of Public Health IRB
More informationNew Work Item for ISO 3534-5 Predictive Analytics (Initial Notes and Thoughts) Introduction
Introduction New Work Item for ISO 3534-5 Predictive Analytics (Initial Notes and Thoughts) Predictive analytics encompasses the body of statistical knowledge supporting the analysis of massive data sets.
More informationA spreadsheet Approach to Business Quantitative Methods
A spreadsheet Approach to Business Quantitative Methods by John Flaherty Ric Lombardo Paul Morgan Basil desilva David Wilson with contributions by: William McCluskey Richard Borst Lloyd Williams Hugh Williams
More informationAcquisition Lesson Plan for the Concept, Topic or Skill---Not for the Day
Acquisition Lesson Plan Concept: Linear Systems Author Name(s): High-School Delaware Math Cadre Committee Grade: Ninth Grade Time Frame: Two 45 minute periods Pre-requisite(s): Write algebraic expressions
More informationSummary of important mathematical operations and formulas (from first tutorial):
EXCEL Intermediate Tutorial Summary of important mathematical operations and formulas (from first tutorial): Operation Key Addition + Subtraction - Multiplication * Division / Exponential ^ To enter a
More informationMultiple Regression: What Is It?
Multiple Regression Multiple Regression: What Is It? Multiple regression is a collection of techniques in which there are multiple predictors of varying kinds and a single outcome We are interested in
More informationModule 223 Major A: Concepts, methods and design in Epidemiology
Module 223 Major A: Concepts, methods and design in Epidemiology Module : 223 UE coordinator Concepts, methods and design in Epidemiology Dates December 15 th to 19 th, 2014 Credits/ECTS UE description
More informationData quality and metadata
Chapter IX. Data quality and metadata This draft is based on the text adopted by the UN Statistical Commission for purposes of international recommendations for industrial and distributive trade statistics.
More informationThe importance of graphing the data: Anscombe s regression examples
The importance of graphing the data: Anscombe s regression examples Bruce Weaver Northern Health Research Conference Nipissing University, North Bay May 30-31, 2008 B. Weaver, NHRC 2008 1 The Objective
More informationMaster of Science in Marketing Analytics (MSMA)
Master of Science in Marketing Analytics (MSMA) COURSE DESCRIPTION The Master of Science in Marketing Analytics program teaches students how to become more engaged with consumers, how to design and deliver
More information13: Additional ANOVA Topics. Post hoc Comparisons
13: Additional ANOVA Topics Post hoc Comparisons ANOVA Assumptions Assessing Group Variances When Distributional Assumptions are Severely Violated Kruskal-Wallis Test Post hoc Comparisons In the prior
More informationLOGISTIC REGRESSION ANALYSIS
LOGISTIC REGRESSION ANALYSIS C. Mitchell Dayton Department of Measurement, Statistics & Evaluation Room 1230D Benjamin Building University of Maryland September 1992 1. Introduction and Model Logistic
More informationCorrelational Research. Correlational Research. Stephen E. Brock, Ph.D., NCSP EDS 250. Descriptive Research 1. Correlational Research: Scatter Plots
Correlational Research Stephen E. Brock, Ph.D., NCSP California State University, Sacramento 1 Correlational Research A quantitative methodology used to determine whether, and to what degree, a relationship
More informationA Statistical Analysis of Popular Lottery Winning Strategies
CS-BIGS 4(1): 66-72 2010 CS-BIGS http://www.bentley.edu/csbigs/vol4-1/chen.pdf A Statistical Analysis of Popular Lottery Winning Strategies Albert C. Chen Torrey Pines High School, USA Y. Helio Yang San
More informationCircuits and Boolean Expressions
Circuits and Boolean Expressions Provided by TryEngineering - Lesson Focus Boolean logic is essential to understanding computer architecture. It is also useful in program construction and Artificial Intelligence.
More informationX X X a) perfect linear correlation b) no correlation c) positive correlation (r = 1) (r = 0) (0 < r < 1)
CORRELATION AND REGRESSION / 47 CHAPTER EIGHT CORRELATION AND REGRESSION Correlation and regression are statistical methods that are commonly used in the medical literature to compare two or more variables.
More informationLearning Example. Machine learning and our focus. Another Example. An example: data (loan application) The data and the goal
Learning Example Chapter 18: Learning from Examples 22c:145 An emergency room in a hospital measures 17 variables (e.g., blood pressure, age, etc) of newly admitted patients. A decision is needed: whether
More informationNEW ZEALAND INJURY PREVENTION STRATEGY SERIOUS INJURY OUTCOME INDICATORS
NEW ZEALAND INJURY PREVENTION STRATEGY SERIOUS INJURY OUTCOME INDICATORS 166 MOTOR VEHICLE CRASHES IN NEW ZEALAND 2012 CONTENTS TABLES Table 1 New Zealand Injury Prevention Strategy serious outcome indicators
More informationCurrent Standard: Mathematical Concepts and Applications Shape, Space, and Measurement- Primary
Shape, Space, and Measurement- Primary A student shall apply concepts of shape, space, and measurement to solve problems involving two- and three-dimensional shapes by demonstrating an understanding of:
More informationA Little Set Theory (Never Hurt Anybody)
A Little Set Theory (Never Hurt Anybody) Matthew Saltzman Department of Mathematical Sciences Clemson University Draft: August 21, 2013 1 Introduction The fundamental ideas of set theory and the algebra
More informationConstructing a TpB Questionnaire: Conceptual and Methodological Considerations
Constructing a TpB Questionnaire: Conceptual and Methodological Considerations September, 2002 (Revised January, 2006) Icek Ajzen Brief Description of the Theory of Planned Behavior According to the theory
More informationEST.03. An Introduction to Parametric Estimating
EST.03 An Introduction to Parametric Estimating Mr. Larry R. Dysert, CCC A ACE International describes cost estimating as the predictive process used to quantify, cost, and price the resources required
More informationAcknowledgments. Data Mining with Regression. Data Mining Context. Overview. Colleagues
Data Mining with Regression Teaching an old dog some new tricks Acknowledgments Colleagues Dean Foster in Statistics Lyle Ungar in Computer Science Bob Stine Department of Statistics The School of the
More informationBayesian probability theory
Bayesian probability theory Bruno A. Olshausen arch 1, 2004 Abstract Bayesian probability theory provides a mathematical framework for peforming inference, or reasoning, using probability. The foundations
More informationResearch Methods & Experimental Design
Research Methods & Experimental Design 16.422 Human Supervisory Control April 2004 Research Methods Qualitative vs. quantitative Understanding the relationship between objectives (research question) and
More information2016 ERCOT System Planning Long-Term Hourly Peak Demand and Energy Forecast December 31, 2015
2016 ERCOT System Planning Long-Term Hourly Peak Demand and Energy Forecast December 31, 2015 2015 Electric Reliability Council of Texas, Inc. All rights reserved. Long-Term Hourly Peak Demand and Energy
More informationSimple Regression Theory II 2010 Samuel L. Baker
SIMPLE REGRESSION THEORY II 1 Simple Regression Theory II 2010 Samuel L. Baker Assessing how good the regression equation is likely to be Assignment 1A gets into drawing inferences about how close the
More informationPurchase Conversions and Attribution Modeling in Online Advertising: An Empirical Investigation
Purchase Conversions and Attribution Modeling in Online Advertising: An Empirical Investigation Author: TAHIR NISAR - Email: t.m.nisar@soton.ac.uk University: SOUTHAMPTON UNIVERSITY BUSINESS SCHOOL Track:
More informationMATH ADVISEMENT GUIDE
MATH ADVISEMENT GUIDE Recommendations for math courses are based on your placement results, degree program and career interests. Placement score: MAT 001 or MAT 00 You must complete required mathematics
More informationCase Studies. Dewayne E Perry ENS 623 perry@mail.utexas.edu
Case Studies Dewayne E Perry ENS 623 perry@mail.utexas.edu Adapted from Perry, Sim & Easterbrook,Case Studies for Software Engineering, ICSE 2004 Tutorial 1 What is a case study? A case study is an empirical
More informationLogNormal stock-price models in Exams MFE/3 and C/4
Making sense of... LogNormal stock-price models in Exams MFE/3 and C/4 James W. Daniel Austin Actuarial Seminars http://www.actuarialseminars.com June 26, 2008 c Copyright 2007 by James W. Daniel; reproduction
More informationReview of Fundamental Mathematics
Review of Fundamental Mathematics As explained in the Preface and in Chapter 1 of your textbook, managerial economics applies microeconomic theory to business decision making. The decision-making tools
More informationCHAPTER 2 Estimating Probabilities
CHAPTER 2 Estimating Probabilities Machine Learning Copyright c 2016. Tom M. Mitchell. All rights reserved. *DRAFT OF January 24, 2016* *PLEASE DO NOT DISTRIBUTE WITHOUT AUTHOR S PERMISSION* This is a
More informationUntangling F9 terminology
Untangling F9 terminology Welcome! This is not a textbook and we are certainly not trying to replace yours! However, we do know that some students find some of the terminology used in F9 difficult to understand.
More informationDecision Analysis. Here is the statement of the problem:
Decision Analysis Formal decision analysis is often used when a decision must be made under conditions of significant uncertainty. SmartDrill can assist management with any of a variety of decision analysis
More informationDIGITAL MEDIA MEASUREMENT FRAMEWORK SUMMARY Last updated April 2015
DIGITAL MEDIA MEASUREMENT FRAMEWORK SUMMARY Last updated April 2015 DIGITAL MEDIA MEASUREMENT FRAMEWORK SUMMARY Digital media continues to grow exponentially in Canada. Multichannel video content delivery
More informationInference for two Population Means
Inference for two Population Means Bret Hanlon and Bret Larget Department of Statistics University of Wisconsin Madison October 27 November 1, 2011 Two Population Means 1 / 65 Case Study Case Study Example
More informationRisk, Return and Market Efficiency
Risk, Return and Market Efficiency For 9.220, Term 1, 2002/03 02_Lecture16.ppt Student Version Outline 1. Introduction 2. Types of Efficiency 3. Informational Efficiency 4. Forms of Informational Efficiency
More informationSTANDARD. Risk Assessment. Supply Chain Risk Management: A Compilation of Best Practices
A S I S I N T E R N A T I O N A L Supply Chain Risk Management: Risk Assessment A Compilation of Best Practices ANSI/ASIS/RIMS SCRM.1-2014 RA.1-2015 STANDARD The worldwide leader in security standards
More informationWorking with whole numbers
1 CHAPTER 1 Working with whole numbers In this chapter you will revise earlier work on: addition and subtraction without a calculator multiplication and division without a calculator using positive and
More informationThe first three steps in a logistic regression analysis with examples in IBM SPSS. Steve Simon P.Mean Consulting www.pmean.com
The first three steps in a logistic regression analysis with examples in IBM SPSS. Steve Simon P.Mean Consulting www.pmean.com 2. Why do I offer this webinar for free? I offer free statistics webinars
More informationThe Predictive Data Mining Revolution in Scorecards:
January 13, 2013 StatSoft White Paper The Predictive Data Mining Revolution in Scorecards: Accurate Risk Scoring via Ensemble Models Summary Predictive modeling methods, based on machine learning algorithms
More informationUnit 12 Logistic Regression Supplementary Chapter 14 in IPS On CD (Chap 16, 5th ed.)
Unit 12 Logistic Regression Supplementary Chapter 14 in IPS On CD (Chap 16, 5th ed.) Logistic regression generalizes methods for 2-way tables Adds capability studying several predictors, but Limited to
More informationInternational Statistical Institute, 56th Session, 2007: Phil Everson
Teaching Regression using American Football Scores Everson, Phil Swarthmore College Department of Mathematics and Statistics 5 College Avenue Swarthmore, PA198, USA E-mail: peverso1@swarthmore.edu 1. Introduction
More information*&6( 0DWKHPDWLFV,QWURGXFWLRQ
2;)25 23(1 *&6( 0DWKHPDWLFV,QWURGXFWLRQ Maths GCSE Welcome to your Mathematics GCSE course! This introduction contains all the information you need to be able to start your course, and you can also use
More informationCreating, Solving, and Graphing Systems of Linear Equations and Linear Inequalities
Algebra 1, Quarter 2, Unit 2.1 Creating, Solving, and Graphing Systems of Linear Equations and Linear Inequalities Overview Number of instructional days: 15 (1 day = 45 60 minutes) Content to be learned
More informationStatistics 2014 Scoring Guidelines
AP Statistics 2014 Scoring Guidelines College Board, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks of the College Board. AP Central is the official online home
More informationComparison of frequentist and Bayesian inference. Class 20, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom
Comparison of frequentist and Bayesian inference. Class 20, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom 1 Learning Goals 1. Be able to explain the difference between the p-value and a posterior
More informationBusiness and Economics Applications
Business and Economics Applications Most of the word problems you do in math classes are not actually related to real life. Textbooks try to pretend they are by using real life data, but they do not use
More informationNORTHWESTERN UNIVERSITY Department of Statistics. Fall 2012 Statistics 210 Professor Savage INTRODUCTORY STATISTICS FOR THE SOCIAL SCIENCES
NORTHWESTERN UNIVERSITY Department of Statistics Fall 2012 Statistics 210 Professor Savage INTRODUCTORY STATISTICS FOR THE SOCIAL SCIENCES Instructor: Professor Ian Savage 330 Andersen Hall, 847-491-8241,
More informationName Class Date. In the space provided, write the letter of the description that best matches the term or phrase.
Skills Worksheet Concept Review MATCHING In the space provided, write the letter of the description that best matches the term or phrase. 1. control group 2. prediction 3. physical model 4. risk 5. conceptual
More informationresearch/scientific includes the following: statistical hypotheses: you have a null and alternative you accept one and reject the other
1 Hypothesis Testing Richard S. Balkin, Ph.D., LPC-S, NCC 2 Overview When we have questions about the effect of a treatment or intervention or wish to compare groups, we use hypothesis testing Parametric
More informationCredit Risk Analysis Using Logistic Regression Modeling
Credit Risk Analysis Using Logistic Regression Modeling Introduction A loan officer at a bank wants to be able to identify characteristics that are indicative of people who are likely to default on loans,
More informationUnit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression
Unit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression Objectives: To perform a hypothesis test concerning the slope of a least squares line To recognize that testing for a
More informationCOMP6053 lecture: Relationship between two variables: correlation, covariance and r-squared. jn2@ecs.soton.ac.uk
COMP6053 lecture: Relationship between two variables: correlation, covariance and r-squared jn2@ecs.soton.ac.uk Relationships between variables So far we have looked at ways of characterizing the distribution
More informationR Simulations: Monty Hall problem
R Simulations: Monty Hall problem Monte Carlo Simulations Monty Hall Problem Statistical Analysis Simulation in R Exercise 1: A Gift Giving Puzzle Exercise 2: Gambling Problem R Simulations: Monty Hall
More informationSection 14 Simple Linear Regression: Introduction to Least Squares Regression
Slide 1 Section 14 Simple Linear Regression: Introduction to Least Squares Regression There are several different measures of statistical association used for understanding the quantitative relationship
More informationDepth-of-Knowledge Levels for Four Content Areas Norman L. Webb March 28, 2002. Reading (based on Wixson, 1999)
Depth-of-Knowledge Levels for Four Content Areas Norman L. Webb March 28, 2002 Language Arts Levels of Depth of Knowledge Interpreting and assigning depth-of-knowledge levels to both objectives within
More informationTotal Credits for Diploma of Interior Design and Decoration 63
Diploma of Interior Design and Decoration programme Code: MSF50213 Program Description The BHCK Diploma of Interior design and Decoration provides the skills and knowledge required to perform design and
More informationThe 2014 Ultimate Career Guide
The 2014 Ultimate Career Guide Contents: 1. Explore Your Ideal Career Options 2. Prepare For Your Ideal Career 3. Find a Job in Your Ideal Career 4. Succeed in Your Ideal Career 5. Four of the Fastest
More informationDealing with Missing Data
Dealing with Missing Data Roch Giorgi email: roch.giorgi@univ-amu.fr UMR 912 SESSTIM, Aix Marseille Université / INSERM / IRD, Marseille, France BioSTIC, APHM, Hôpital Timone, Marseille, France January
More information