Chapter 13. Factorial ANOVA. Patrick Mair 2015 Psych Factorial ANOVA 0 / 19
|
|
- Carol Glenn
- 6 years ago
- Views:
Transcription
1 Chapter 13 Factorial ANOVA Patrick Mair 2015 Psych Factorial ANOVA 0 / 19
2 Today s Menu Now we extend our one-way ANOVA approach to two (or more) factors. Factorial ANOVA: two-way ANOVA, SS decomposition, interactions. Unbalanced designs. Factorial ANOVA through a linear model: simple effect analysis. Nonparametric approaches. Mixed ANOVA (between-within subject designs) Patrick Mair 2015 Psych Factorial ANOVA 1 / 19
3 Extension to Two Factors The data scenario for this unit is: Two or more categorical variables (factors). One metric variable (response). We are interested in which factors (or factor combinations) have an influence on the response variable. Patrick Mair 2015 Psych Factorial ANOVA 2 / 19
4 Effects in Two-Way ANOVA In a one-way ANOVA the only possible effect was due to the factor. Question: Do the response means differ across factor levels (groups)? In a two-way ANOVA with factors A and B we have: Main effect A: the means of Y differ across the levels of A Main effect B: the means of Y differ across the levels of B Interaction effect: the means of Y differ across combinations of A and B Patrick Mair 2015 Psych Factorial ANOVA 3 / 19
5 Honk Example In the t-test unit we looked for differences in the average honking frequency between a fancy BMW and a small Ford KA. Now: This time we use a different response variable: Duration until the first honk. We have two factors: car and gender. What we have is a 2 2 design (2 car categories, 2 gender categories). Note that we are not limited to binary factors. Research question: Do car type and/or gender influence the average honking duration? Patrick Mair 2015 Psych Factorial ANOVA 4 / 19
6 The F-test and Sum of Squares We have our well-known SS decomposition: SSTO = SSTR + SSE Now, the SSTR (based on deviation of the cell means from the grand mean) looks a little bit more complex: SSTR = SSTR A + SSTR B + SSTR A B with: SSTR A as the deviation of the A factor level mean from the grand mean. SSTR B as the deviation of the B factor level mean from the grand mean. SSTR AB = SSTO SSTR A SSTR B SSE. The F -statistics are based on these SS and the corresponding df. Patrick Mair 2015 Psych Factorial ANOVA 5 / 19
7 Assumptions Basically there are two assumptions in factorial ANOVA: For small samples, normal residuals/response within each factor combination. Variance homogeneity across factor combinations: Levene test. If possible, keep your design balanced (same number of observations within each factor combination). With unbalanced designs things are getting tricky in factorial ANOVA. More on that later. Patrick Mair 2015 Psych Factorial ANOVA 6 / 19
8 Main Effects Structures for the Honking Example Hypothetical main effect structures (means across groups) for our car example (dashed line male, solid line female). Null Model Main Effect Car BMW Ford BMW Ford Main Effect Sex Main Effect Car + Sex BMW Ford BMW Ford Patrick Mair 2015 Psych Factorial ANOVA 7 / 19
9 Interactions The interpretation of a two-way (or more) ANOVA depends on the interaction structure. If the interaction effect is significant, we need to look at the interaction plots and distinguish: 1) Ordinal interactions: even though significant, main effects interpretable. B A interaction A B interaction Means Factor B b1 b2 Means Factor A a1 a2 a1 a2 b1 b2 Factor A Factor B Patrick Mair 2015 Psych Factorial ANOVA 8 / 19
10 Interactions 2) Disordinal Interactions: if significant, main effects not interpretable. B A interaction A B interaction Means Factor B b1 b2 Means Factor A a1 a2 a1 a2 b1 b2 Factor A Factor B In this case we can go back to the interaction plot and interpret the interaction effect. Another possibility would be to define special contrasts and look at the effect of one factor at individual levels of the other factor (simple effect analysis). Patrick Mair 2015 Psych Factorial ANOVA 9 / 19
11 Interactions 3) Hybrid Interactions: if significant, main effect for B interpretable, main effect for A not. B A interaction A B interaction Means Factor B b1 b2 Means Factor A a1 a2 a1 a2 b1 b2 Factor A Factor B Patrick Mair 2015 Psych Factorial ANOVA 10 / 19
12 [ Factorial ANOVA ] Unbalanced Designs Patrick Mair 2015 Psych Factorial ANOVA 11 / 19
13 Unbalanced Designs An unbalanced design can occur: because of subject attrition, because the study is observational in nature and subjects were taken as they came. The main problem is that the factors lose their independence from one another. It then makes a difference in what order the factors are entered into the model formula. A quick and dirty way would be to try entering the factors in different orders to see how much of a difference this makes to the outcome of the analysis. Patrick Mair 2015 Psych Factorial ANOVA 12 / 19
14 Unbalanced Designs Different types of SS: Type I SS (sequential SS): Used by aov(), SSTR A SSTR B A SSTR AB A,B Type II SS: Implemented in Anova(), SSTR A B ; SSTR B A. It assumes no interaction, main effects are interpretable independently from each other. Type III SS: Implemented in Anova(), SSTR A B,AB ; SSTR B A,AB. This approach is therefore valid in the presence of significant interactions. 1 A few remarks: Note that the interaction effect doesn t change at all across the approaches. It is all about the main effects. Note that with unbalanced designs the parameter interpretation within the context of a linear model (design matrix) becomes difficult. There is lots of controversy/confusion in literature regarding how to formulate hypotheses, contrasts, and SS in unbalanced designs. Type II SS is the way to go if the interaction is not significant. If we have a significant interaction, we can t interpret the main effects anyway (except for ordinal and hybrid interactions). 1 But if we have disordinal significant interactions we shouldn t interpret the main effects anyway! Patrick Mair 2015 Psych Factorial ANOVA 13 / 19
15 [ Factorial ANOVA ] Linear Models Patrick Mair 2015 Psych Factorial ANOVA 14 / 19
16 Factorial ANOVA as Linear Models The design matrix principle is exactly the same as we ve seen so far. dummy coding (contr.treatment) effects coding (contr.sum) other special coding schemes such as Helmert, polynomial, etc. The interaction contrasts result from main-effects multiplication. Another nice implication of doing 2-way ANOVA through a linear model specification is that we can do a simple effect analysis in order to break down significant interactions. Patrick Mair 2015 Psych Factorial ANOVA 15 / 19
17 Extensions We ve already seen how painful interactions can be for two variables. Things become much worse for 3, 4, etc. and at some point it becomes uninterpretable. Keep the number of factors low, if possible! There is an example in the R code file for a 3-way ANOVA. Nonparametric approaches: For 2-way ANOVA the WRS2 package offers several options: 2-way ANOVA on trimmed means (t2way()) 2-way ANOVA on medians (med2way()) The nonparametric version is t3way() in the WRS2 package. Patrick Mair 2015 Psych Factorial ANOVA 16 / 19
18 [ Factorial ANOVA ] Mixed ANOVA Patrick Mair 2015 Psych Factorial ANOVA 17 / 19
19 Mixed ANOVA Let s now combine dependent measure ANOVA with standard between group ANOVA. This leads to a mixed ANOVA (aka split-plot design or between-within subjects ANOVA). We can fit these models through: classic between-within ANOVA: ezanova(). mixed effects models: greater flexibility (lme()) Nothing changes in terms of assumptions and interpretation. Robust alternatives are given in the WRS2 package by means of bwtrim(). Patrick Mair 2015 Psych Factorial ANOVA 18 / 19
20 Summary Today we have seen higher-order ANOVA models with possibly unbalanced designs: 2-way ANOVA, 3-way ANOVA, robust alternatives. Note that you can also use post-hoc tests. The glht() function in the multcomp package is pretty powerful. However, a more modern approach is to incorporate special hypotheses using design matrices. We also started elaborating on mixed ANOVA (between-within subjects) designs. Such settings will be extensively covered in the mixed-effects units. Readings due to Tues: Field Chapter 11 (ANCOVA). Patrick Mair 2015 Psych Factorial ANOVA 19 / 19
Introduction to Analysis of Variance (ANOVA) The Structural Model, The Summary Table, and the One- Way ANOVA
Introduction to Analysis of Variance (ANOVA) The Structural Model, The Summary Table, and the One- Way ANOVA Limitations of the t-test Although the t-test is commonly used, it has limitations Can only
More informationSetting up group models Part 1 NITP, 2011
Setting up group models Part 1 NITP, 2011 What is coming up Crash course in setting up models 1-sample and 2-sample t-tests Paired t-tests ANOVA! Mean centering covariates Identifying rank deficient matrices
More informationAnalysis of Variance. Copyright 2014 Pearson Education, Inc.
Analysis of Variance 12-1 Learning Outcomes Outcome 1. Understand the basic logic of analysis of variance. Outcome 2. Perform a hypothesis test for a single-factor design using analysis of variance manually
More informationANOVA - Implementation.
ANOVA - Implementation http://www.pelagicos.net/classes_biometry_fa17.htm Doing an ANOVA With RCmdr Categorical Variable One-Way ANOVA Testing a single Factor dose with 3 treatments (low, mid, high) Doing
More informationOne-factor ANOVA by example
ANOVA One-factor ANOVA by example 2 One-factor ANOVA by visual inspection 3 4 One-factor ANOVA H 0 H 0 : µ 1 = µ 2 = µ 3 = H A : not all means are equal 5 One-factor ANOVA but why not t-tests t-tests?
More informationLegendre et al Appendices and Supplements, p. 1
Legendre et al. 2010 Appendices and Supplements, p. 1 Appendices and Supplement to: Legendre, P., M. De Cáceres, and D. Borcard. 2010. Community surveys through space and time: testing the space-time interaction
More informationPLANNED ORTHOGONAL CONTRASTS
PLANNED ORTHOGONAL CONTRASTS Please note: This handout is useful background for the workshop, not what s covered in it. Basic principles for contrasts are the same in repeated measures. Planned orthogonal
More informationClass 23: Chapter 14 & Nested ANOVA NOTES: NOTES: NOTES:
Slide 1 Chapter 13: ANOVA for 2-way classifications (2 of 2) Fixed and Random factors, Model I, Model II, and Model III (mixed model) ANOVA Chapter 14: Unreplicated Factorial & Nested Designs Slide 2 HW
More informationFactorial Analysis of Variance
Factorial Analysis of Variance Overview of the Factorial ANOVA Factorial ANOVA (Two-Way) In the context of ANOVA, an independent variable (or a quasiindependent variable) is called a factor, and research
More informationUnit 4: Inference for numerical variables Lecture 3: ANOVA
Unit 4: Inference for numerical variables Lecture 3: ANOVA Statistics 101 Thomas Leininger June 10, 2013 Announcements Announcements Proposals due tomorrow. Will be returned to you by Wednesday. You MUST
More informationOne-way ANOVA: round, narrow, wide
5/4/2009 9:19:18 AM Retrieving project from file: 'C:\DOCUMENTS AND SETTINGS\BOB S\DESKTOP\RJS\COURSES\MTAB\FIRSTBASE.MPJ' ========================================================================== This
More informationNCSS Statistical Software
Chapter 256 Introduction This procedure computes summary statistics and common non-parametric, single-sample runs tests for a series of n numeric, binary, or categorical data values. For numeric data,
More informationRunning head: DATA ANALYSIS AND INTERPRETATION 1
Running head: DATA ANALYSIS AND INTERPRETATION 1 Data Analysis and Interpretation Final Project Vernon Tilly Jr. University of Central Oklahoma DATA ANALYSIS AND INTERPRETATION 2 Owners of the various
More informationCitation for published version (APA): Canudas Romo, V. (2003). Decomposition Methods in Demography Groningen: s.n.
University of Groningen Decomposition Methods in Demography Canudas Romo, Vladimir IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite from it. Please
More informationStats 2002: Probabilities for Wins and Losses of Online Gambling
Abstract: Jennifer Mateja Andrea Scisinger Lindsay Lacher Stats 2002: Probabilities for Wins and Losses of Online Gambling The objective of this experiment is to determine whether online gambling is a
More informationy ) s x x )(y i (x i r = 1 n 1 s y Statistics Lecture 7 Exploring Data , y 2 ,y n (x 1 ),,(x n ),(x 2 ,y 1 How two variables vary together
Statistics 111 - Lecture 7 Exploring Data Numerical Summaries for Relationships between Variables Administrative Notes Homework 1 due in recitation: Friday, Feb. 5 Homework 2 now posted on course website:
More informationNavigate to the golf data folder and make it your working directory. Load the data by typing
Golf Analysis 1.1 Introduction In a round, golfers have a number of choices to make. For a particular shot, is it better to use the longest club available to try to reach the green, or would it be better
More informationWeek 7 One-way ANOVA
Week 7 One-way ANOVA Objectives By the end of this lecture, you should be able to: Understand the shortcomings of comparing multiple means as pairs of hypotheses. Understand the steps of the ANOVA method
More informationChapter 2: ANOVA and regression. Caroline Verhoeven
Chapter 2: ANOVA and regression Caroline Verhoeven Table of contents 1 ANOVA One-way ANOVA Repeated measures ANOVA Two-way ANOVA 2 Regression Simple linear regression Multiple regression 3 Conclusion Caroline
More informationEXPLORING MOTIVATION AND TOURIST TYPOLOGY: THE CASE OF KOREAN GOLF TOURISTS TRAVELLING IN THE ASIA PACIFIC. Jae Hak Kim
EXPLORING MOTIVATION AND TOURIST TYPOLOGY: THE CASE OF KOREAN GOLF TOURISTS TRAVELLING IN THE ASIA PACIFIC Jae Hak Kim Thesis submitted for the degree of Doctor of Philosophy at the University of Canberra
More informationFactorial ANOVA Problems
Factorial ANOVA Problems Q.1. In a 2-Factor ANOVA, measuring the effects of 2 factors (A and B) on a response (y), there are 3 levels each for factors A and B, and 4 replications per treatment combination.
More informationTaking Your Class for a Walk, Randomly
Taking Your Class for a Walk, Randomly Daniel Kaplan Macalester College Oct. 27, 2009 Overview of the Activity You are going to turn your students into an ensemble of random walkers. They will start at
More informationAnalysis of recent swim performances at the 2013 FINA World Championship: Counsilman Center, Dept. Kinesiology, Indiana University
Analysis of recent swim performances at the 2013 FINA World Championship: initial confirmation of the rumored current. Joel M. Stager 1, Andrew Cornett 2, Chris Brammer 1 1 Counsilman Center, Dept. Kinesiology,
More informationa) List and define all assumptions for multiple OLS regression. These are all listed in section 6.5
Prof. C. M. Dalton ECN 209A Spring 2015 Practice Problems (After HW1, HW2, before HW3) CORRECTED VERSION Question 1. Draw and describe a relationship with heteroskedastic errors. Support your claim with
More informationBBS Fall Conference, 16 September Use of modeling & simulation to support the design and analysis of a new dose and regimen finding study
BBS Fall Conference, 16 September 211 Use of modeling & simulation to support the design and analysis of a new dose and regimen finding study Didier Renard Background (1) Small molecule delivered by lung
More informationAnnouncements. Lecture 19: Inference for SLR & Transformations. Online quiz 7 - commonly missed questions
Announcements Announcements Lecture 19: Inference for SLR & Statistics 101 Mine Çetinkaya-Rundel April 3, 2012 HW 7 due Thursday. Correlation guessing game - ends on April 12 at noon. Winner will be announced
More informationAnnouncements. % College graduate vs. % Hispanic in LA. % College educated vs. % Hispanic in LA. Problem Set 10 Due Wednesday.
Announcements Announcements UNIT 7: MULTIPLE LINEAR REGRESSION LECTURE 1: INTRODUCTION TO MLR STATISTICS 101 Problem Set 10 Due Wednesday Nicole Dalzell June 15, 2015 Statistics 101 (Nicole Dalzell) U7
More informationHitting with Runners in Scoring Position
Hitting with Runners in Scoring Position Jim Albert Department of Mathematics and Statistics Bowling Green State University November 25, 2001 Abstract Sportscasters typically tell us about the batting
More informationN. Abid 2 and M. Idrissi 1 ABSTRACT
SCRS//. ANALYSIS OF THE SIZE STRUCTURE AND LENGTH-WEIGHT RELATIONSHIPS OF SWORDFISH (Xiphias gladius) CAUGHT BY THE MOROCCAN DRIFTNET FISHERY IN THE MEDITERRANEAN SEA DURING 7. N. Abid and M. Idrissi 1
More informationSport statistics: how to assemble your team elivian.nl high quality, poorly written update history current(v2.1):7-oct-16, original(v1):13-sep-14
Sport statistics: how to assemble your team elivian.nl high quality, poorly written update history current(v2.1):7-oct-16, original(v1):13-sep-14 If you ve ever tried to make a selection team for any sport,
More informationBiostatistics & SAS programming
Biostatistics & SAS programming Kevin Zhang March 6, 2017 ANOVA 1 Two groups only Independent groups T test Comparison One subject belongs to only one groups and observed only once Thus the observations
More informationMRI-2: Integrated Simulation and Safety
MRI-2: Integrated Simulation and Safety Year 3 2 nd Quarterly Report Submitted by: Dr. Essam Radwan, P.E. (PI), Ahmed.Radwan@ucf.edu Dr. Hatem Abou-Senna, P.E., habousenna@ucf.edu Dr. Mohamed Abdel-Aty,
More informationDISMAS Evaluation: Dr. Elizabeth C. McMullan. Grambling State University
DISMAS Evaluation 1 Running head: Project Dismas Evaluation DISMAS Evaluation: 2007 2008 Dr. Elizabeth C. McMullan Grambling State University DISMAS Evaluation 2 Abstract An offender notification project
More informationBIOL 101L: Principles of Biology Laboratory
BIOL 101L: Principles of Biology Laboratory Sampling populations To understand how the world works, scientists collect, record, and analyze data. In this lab, you will learn concepts that pertain to these
More informationA Combined Recruitment Index for Demersal Juvenile Cod in NAFO Divisions 3K and 3L
NAFO Sci. Coun. Studies, 29: 23 29 A Combined Recruitment Index for Demersal Juvenile Cod in NAFO Divisions 3K and 3L David C. Schneider Ocean Sciences Centre, Memorial University St. John's, Newfoundland,
More informationName May 3, 2007 Math Probability and Statistics
Name May 3, 2007 Math 341 - Probability and Statistics Long Exam IV Instructions: Please include all relevant work to get full credit. Encircle your final answers. 1. An article in Professional Geographer
More information1. OVERVIEW OF METHOD
1. OVERVIEW OF METHOD The method used to compute tennis rankings for Iowa girls high school tennis http://ighs-tennis.com/ is based on the Elo rating system (section 1.1) as adopted by the World Chess
More informationData Set 7: Bioerosion by Parrotfish Background volume of bites The question:
Data Set 7: Bioerosion by Parrotfish Background Bioerosion of coral reefs results from animals taking bites out of the calcium-carbonate skeleton of the reef. Parrotfishes are major bioerosion agents,
More informationA few things to remember about ANOVA
A few things to remember about ANOVA 1) The F-test that is performed is always 1-tailed. This is because your alternative hypothesis is always that the between group variation is greater than the within
More informationMultilevel Models for Other Non-Normal Outcomes in Mplus v. 7.11
Multilevel Models for Other Non-Normal Outcomes in Mplus v. 7.11 Study Overview: These data come from a daily diary study that followed 41 male and female college students over a six-week period to examine
More informationGLMM standardisation of the commercial abalone CPUE for Zones A-D over the period
GLMM standardisation of the commercial abalone for Zones A-D over the period 1980 2015 Anabela Brandão and Doug S. Butterworth Marine Resource Assessment & Management Group (MARAM) Department of Mathematics
More informationCHAP Summary 8 TER 155
CHAPTER 8 Summary 155 SUMMARY Feral horses are social animals, which have adopted early predator detection and flight as their prime defence mechanisms. They rely on survival strategies centered on the
More informationNBA TEAM SYNERGY RESEARCH REPORT 1
NBA TEAM SYNERGY RESEARCH REPORT 1 NBA Team Synergy and Style of Play Analysis Karrie Lopshire, Michael Avendano, Amy Lee Wang University of California Los Angeles June 3, 2016 NBA TEAM SYNERGY RESEARCH
More informationCOMPLETING THE RESULTS OF THE 2013 BOSTON MARATHON
COMPLETING THE RESULTS OF THE 2013 BOSTON MARATHON Dorit Hammerling 1, Matthew Cefalu 2, Jessi Cisewski 3, Francesca Dominici 2, Giovanni Parmigiani 2,4, Charles Paulson 5, Richard Smith 1,6 1 Statistical
More informationGuidelines for Applying Multilevel Modeling to the NSCAW Data
Guidelines for Applying Multilevel Modeling to the NSCAW Data by Sharon Christ, Paul Biemer and Christopher Wiesen Odum Institute for Research in Social Science May 2007 Summary. This document is intended
More informationCase Processing Summary. Cases Valid Missing Total N Percent N Percent N Percent % 0 0.0% % % 0 0.0%
GET FILE='C:\Users\acantrell\Desktop\demo5.sav'. DATASET NAME DataSet1 WINDOW=FRONT. EXAMINE VARIABLES=PASSYDSPG RUSHYDSPG /PLOT BOXPLOT HISTOGRAM /COMPARE GROUPS /STATISTICS DESCRIPTIVES /CINTERVAL 95
More informationConfidence Interval Notes Calculating Confidence Intervals
Confidence Interval Notes Calculating Confidence Intervals Calculating One-Population Mean Confidence Intervals for Quantitative Data It is always best to use a computer program to make these calculations,
More informationDriv e accu racy. Green s in regul ation
LEARNING ACTIVITIES FOR PART II COMPILED Statistical and Measurement Concepts We are providing a database from selected characteristics of golfers on the PGA Tour. Data are for 3 of the players, based
More informationCompetition Jumping Horses: Effects of Age, Sex and Breed on the Fei/Wbfsh World Ranking
Competition Jumping Horses: Effects of Age, Sex and Breed on the Fei/Wbfsh World Ranking Anca ROMAN-POPOVICI *, Dan SUMOVSCHI, Ioan GÎLCĂ Faculty of Animal Science, University of Agricultural Science and
More informationMGB 203B Homework # LSD = 1 1
MGB 0B Homework # 4.4 a α =.05: t = =.05 LSD = α /,n k t.05, 7 t α /,n k MSE + =.05 700 + = 4.8 n i n j 0 0 i =, j = 8.7 0.4 7. i =, j = 8.7.7 5.0 i =, j = 0.4.7. Conclusion: µ differs from µ and µ. b
More informationBoston Marathon Data. Instructor: G. William Schwert
APS 425 Fall 2015 Boston Marathon Data Instructor: G. William Schwert 585-275-2470 schwert@schwert.ssb.rochester.edu Winning Times in Marathon Sports records are often interesting because they reflect
More information1. The data below gives the eye colors of 20 students in a Statistics class. Make a frequency table for the data.
1. The data below gives the eye colors of 20 students in a Statistics class. Make a frequency table for the data. Green Blue Brown Blue Blue Brown Blue Blue Blue Green Blue Brown Blue Brown Brown Blue
More informationClassroom Tips and Techniques: The Partial-Fraction Decomposition. Robert J. Lopez Emeritus Professor of Mathematics and Maple Fellow Maplesoft
Classroom Tips and Techniques: The Partial-Fraction Decomposition Robert J. Lopez Emeritus Professor of Mathematics and Maple Fellow Maplesoft Introduction Students typically meet the algebraic technique
More informationPaper prepared by the Secretariat
COMMISSION FOURTEENTH REGULAR SESSION Manila, Philippines 3 7 December 2017 REFERENCE DOCUMENT FOR REVIEW OF CMM 2005-03 AND FOR THE DEVELOPMENT OF HARVEST STRATEGIES UNDER CMM 2014-06 North Pacific Albacore
More informationDistancei = BrandAi + 2 BrandBi + 3 BrandCi + i
. Suppose that the United States Golf Associate (USGA) wants to compare the mean distances traveled by four brands of golf balls when struck by a driver. A completely randomized design is employed with
More informationMajor League Baseball Offensive Production in the Designated Hitter Era (1973 Present)
Major League Baseball Offensive Production in the Designated Hitter Era (1973 Present) Jonathan Tung University of California, Riverside tung.jonathanee@gmail.com Abstract In Major League Baseball, there
More informationEmpirical Example II of Chapter 7
Empirical Example II of Chapter 7 1. We use NBA data. The description of variables is --- --- --- storage display value variable name type format label variable label marr byte %9.2f =1 if married wage
More informationLab 11: Introduction to Linear Regression
Lab 11: Introduction to Linear Regression Batter up The movie Moneyball focuses on the quest for the secret of success in baseball. It follows a low-budget team, the Oakland Athletics, who believed that
More informationExample 1: One Way ANOVA in MINITAB
Example : One Way ANOVA in MINITAB A consumer group wants to compare a new brand of wax (Brand-X) to two leading brands (Sureglow and Microsheen) in terms of Effectiveness of wax. Following data is collected
More informationESP 178 Applied Research Methods. 2/26/16 Class Exercise: Quantitative Analysis
ESP 178 Applied Research Methods 2/26/16 Class Exercise: Quantitative Analysis Introduction: In summer 2006, my student Ted Buehler and I conducted a survey of residents in Davis and five other cities.
More informationSession 2: Introduction to Multilevel Modeling Using SPSS
Session 2: Introduction to Multilevel Modeling Using SPSS Exercise 1 Description of Data: exerc1 This is a dataset from Kasia Kordas s research. It is data collected on 457 children clustered in schools.
More informationIn my left hand I hold 15 Argentine pesos. In my right, I hold 100 Chilean
Chapter 6 Meeting Standards and Standings In This Chapter How to standardize scores Making comparisons Ranks in files Rolling in the percentiles In my left hand I hold 15 Argentine pesos. In my right,
More informationSTT 315 Section /19/2014
Name: PID: A STT 315 Section 101 05/19/2014 Quiz 1A 50 minutes 1. A survey by an electric company contains questions on the following: Age of household head, Gender of household head and use of electric
More informationChapter 9: Hypothesis Testing for Comparing Population Parameters
Chapter 9: Hypothesis Testing for Comparing Population Parameters Hypothesis testing can address many di erent types of questions. We are not restricted to looking at the estimated value of a single population
More informationSafety at Intersections in Oregon A Preliminary Update of Statewide Intersection Crash Rates
Portland State University PDXScholar Civil and Environmental Engineering Master's Project Reports Civil and Environmental Engineering 2015 Safety at Intersections in Oregon A Preliminary Update of Statewide
More informationSample Final Exam MAT 128/SOC 251, Spring 2018
Sample Final Exam MAT 128/SOC 251, Spring 2018 Name: Each question is worth 10 points. You are allowed one 8 1/2 x 11 sheet of paper with hand-written notes on both sides. 1. The CSV file citieshistpop.csv
More informationEvaluation of Regression Approaches for Predicting Yellow Perch (Perca flavescens) Recreational Harvest in Ohio Waters of Lake Erie
Evaluation of Regression Approaches for Predicting Yellow Perch (Perca flavescens) Recreational Harvest in Ohio Waters of Lake Erie QFC Technical Report T2010-01 Prepared for: Ohio Department of Natural
More informationarxiv: v1 [stat.ap] 18 Nov 2018
Modeling Baseball Outcomes as Higher-Order Markov Chains Jun Hee Kim junheek1@andrew.cmu.edu Department of Statistics & Data Science, Carnegie Mellon University arxiv:1811.07259v1 [stat.ap] 18 Nov 2018
More informationGuide to Computing Minitab commands used in labs (mtbcode.out)
Guide to Computing Minitab commands used in labs (mtbcode.out) A full listing of Minitab commands can be found by invoking the HELP command while running Minitab. A reference card, with listing of available
More informationSelect Boxplot -> Multiple Y's (simple) and select all variable names.
One Factor ANOVA in Minitab As an example, we will use the data below. A study looked at the days spent in the hospital for different regions of the United States. Can the company reject the claim the
More informationANALYSIS OF THE DOMINATING POWER OF SERVICE RECEPTION IN VOLLEYBALL IN DIFFERENT LEVELS OF COMPETITIONS
ANALYSIS OF THE DOMINATING POWER OF SERVICE RECEPTION IN VOLLEYBALL IN DIFFERENT LEVELS OF COMPETITIONS 1 SANJIB GHOSH 2 DR. MAHESH SWETA 1 Research scholar, department of Physical Education, Visva-Bharati,
More informationBuilding an NFL performance metric
Building an NFL performance metric Seonghyun Paik (spaik1@stanford.edu) December 16, 2016 I. Introduction In current pro sports, many statistical methods are applied to evaluate player s performance and
More informationAnalyses of the Scoring of Writing Essays For the Pennsylvania System of Student Assessment
Analyses of the Scoring of Writing Essays For the Pennsylvania System of Student Assessment Richard Hill The National Center for the Improvement of Educational Assessment, Inc. April 4, 2001 Revised--August
More informationOnline Companion to Using Simulation to Help Manage the Pace of Play in Golf
Online Companion to Using Simulation to Help Manage the Pace of Play in Golf MoonSoo Choi Industrial Engineering and Operations Research, Columbia University, New York, NY, USA {moonsoo.choi@columbia.edu}
More informationAverage Runs per inning,
Home Team Scoring Advantage in the First Inning Largely Due to Time By David W. Smith Presented June 26, 2015 SABR45, Chicago, Illinois Throughout baseball history, the home team has scored significantly
More informationDIFFERENCES BETWEEN THE WINNING AND DEFEATED FEMALE HANDBALL TEAMS IN RELATION TO THE TYPE AND DURATION OF ATTACKS
DIFFERENCES BETWEEN THE WINNING AND DEFEATED FEMALE HANDBALL TEAMS IN RELATION TO THE TYPE AND DURATION OF ATTACKS Katarina OHNJEC, Dinko VULETA, Lidija BOJIĆ-ĆAĆIĆ Faculty of Kinesiology, University of
More informationStaking plans in sports betting under unknown true probabilities of the event
Staking plans in sports betting under unknown true probabilities of the event Andrés Barge-Gil 1 1 Department of Economic Analysis, Universidad Complutense de Madrid, Spain June 15, 2018 Abstract Kelly
More information5.1 Introduction. Learning Objectives
Learning Objectives 5.1 Introduction Statistical Process Control (SPC): SPC is a powerful collection of problem-solving tools useful in achieving process stability and improving capability through the
More informationTitle: Modeling Crossing Behavior of Drivers and Pedestrians at Uncontrolled Intersections and Mid-block Crossings
Title: Modeling Crossing Behavior of Drivers and Pedestrians at Uncontrolled Intersections and Mid-block Crossings Objectives The goal of this study is to advance the state of the art in understanding
More informationChapter 12 Practice Test
Chapter 12 Practice Test 1. Which of the following is not one of the conditions that must be satisfied in order to perform inference about the slope of a least-squares regression line? (a) For each value
More informationDesign of Experiments Example: A Two-Way Split-Plot Experiment
Design of Experiments Example: A Two-Way Split-Plot Experiment A two-way split-plot (also known as strip-plot or split-block) design consists of two split-plot components. In industry, these designs arise
More informationAddendum to SEDAR16-DW-22
Addendum to SEDAR16-DW-22 Introduction Six king mackerel indices of abundance, two for each region Gulf of Mexico, South Atlantic, and Mixing Zone, were constructed for the SEDAR16 data workshop using
More informationDescriptive Statistics. Dr. Tom Pierce Department of Psychology Radford University
Descriptive Statistics Dr. Tom Pierce Department of Psychology Radford University Descriptive statistics comprise a collection of techniques for better understanding what the people in a group look like
More informationIs lung capacity affected by smoking, sport, height or gender. Table of contents
Sample project This Maths Studies project has been graded by a moderator. As you read through it, you will see comments from the moderator in boxes like this: At the end of the sample project is a summary
More informationLecture 16: Chapter 7, Section 2 Binomial Random Variables
Lecture 16: Chapter 7, Section 2 Binomial Random Variables!Definition!What if Events are Dependent?!Center, Spread, Shape of Counts, Proportions!Normal Approximation Cengage Learning Elementary Statistics:
More information(JUN10SS0501) General Certificate of Education Advanced Level Examination June Unit Statistics TOTAL.
Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Examiner s Initials Statistics Unit Statistics 5 Friday 18 June 2010 General Certificate of Education Advanced
More informationWhy We Should Use the Bullpen Differently
Why We Should Use the Bullpen Differently A look into how the bullpen can be better used to save runs in Major League Baseball. Andrew Soncrant Statistics 157 Final Report University of California, Berkeley
More informationThe final set in a tennis match: four years at Wimbledon 1
Published as: Journal of Applied Statistics, Vol. 26, No. 4, 1999, 461-468. The final set in a tennis match: four years at Wimbledon 1 Jan R. Magnus, CentER, Tilburg University, the Netherlands and Franc
More informationOREGON DEPARTMENT OF FISH AND WILDLIFE SUMMARY OF COUGAR POPULATION MODEL AND EFFECTS OF LETHAL CONTROL
OREGON DEPARTMENT OF FISH AND WILDLIFE SUMMARY OF COUGAR POPULATION MODEL ODFW is authorized to reduce human-cougar conflict, livestock depredation, and benefit native ungulate populations through the
More informationSurface Texture Gage study in the qs-stat Measurement System Analysis Module
study in the qs-stat Measurement System Analysis Module Q-DAS Library Living Documentation Last edited: 11/22/2004 Version: EB C:\Documents and Settings\Ellen Fassbeck\My Documents \My Temp Files\GMPT\TC\GMPT
More informationCHAPTER ANALYSIS AND INTERPRETATION Average total number of collisions for a try to be scored
CHAPTER 8 8.1 ANALYSIS AND INTERPRETATION As mentioned in the previous chapter, four key components have been identified as indicators of the level of significance of dominant collisions when evaluating
More information(c) The hospital decided to collect the data from the first 50 patients admitted on July 4, 2010.
Math 155, Test 1, 18 October 2011 Name: Instructions. This is a closed-book test. You may use a calculator (but not a cell phone). Make sure all cell-phones are put away and that the ringer is off. Show
More informationPressured Applied by the Emergency/Israeli Bandage
Pressured Applied by the Emergency/Israeli Bandage By Charles S. Lessard, Ph.D. Nolan Shipman, M.D. Amanda Bickham Jasper Butler 9 December 2007 1 Introduction At the request of Performance Systems, this
More informationIDENTIFICATION OF WIND SEA AND SWELL EVENTS AND SWELL EVENTS PARAMETERIZATION OFF WEST AFRICA. K. Agbéko KPOGO-NUWOKLO
Workshop: Statistical models of the metocean environment for engineering uses IDENTIFICATION OF WIND SEA AND SWELL EVENTS AND SWELL EVENTS PARAMETERIZATION OFF WEST AFRICA K. Agbéko KPOGO-NUWOKLO IFREMER-
More informationPradiptaArdiPrastowo Sport Science. SebelasMaret University. Indonesia
The Influence of the Volley Ball Serve Training Methods to the Overhand Serve Skills from Gender Consideration (An Experiment Research using the Near Target to Far Target and the Far Target to Nearer Target
More informationCS 7641 A (Machine Learning) Sethuraman K, Parameswaran Raman, Vijay Ramakrishnan
CS 7641 A (Machine Learning) Sethuraman K, Parameswaran Raman, Vijay Ramakrishnan Scenario 1: Team 1 scored 200 runs from their 50 overs, and then Team 2 reaches 146 for the loss of two wickets from their
More informationThis file is part of the following reference:
This file is part of the following reference: Hancock, Timothy Peter (2006) Multivariate consensus trees: tree-based clustering and profiling for mixed data types. PhD thesis, James Cook University. Access
More informationJournal of Quantitative Analysis in Sports Manuscript 1039
An Article Submitted to Journal of Quantitative Analysis in Sports Manuscript 1039 A Simple and Flexible Rating Method for Predicting Success in the NCAA Basketball Tournament Brady T. West University
More informationPackage STI. August 19, Index 7. Compute the Standardized Temperature Index
Package STI August 19, 2015 Type Package Title Calculation of the Standardized Temperature Index Version 0.1 Date 2015-08-18 Author Marc Fasel [aut, cre] Maintainer Marc Fasel A set
More informationMJA Rev 10/17/2011 1:53:00 PM
Problem 8-2 (as stated in RSM Simplified) Leonard Lye, Professor of Engineering and Applied Science at Memorial University of Newfoundland contributed the following case study. It is based on the DOE Golfer,
More information