# Analyzing Intervention Effects: Multilevel & Other Approaches. Simplest Intervention Design. Better Design: Have Pretest

Save this PDF as:
Size: px
Start display at page:

Download "Analyzing Intervention Effects: Multilevel & Other Approaches. Simplest Intervention Design. Better Design: Have Pretest"

## Transcription

1 Analyzing Intervention Effects: Multilevel & Other Approaches Joop Hox Methodology & Statistics, Utrecht Simplest Intervention Design R X Y E Random assignment Experimental + Control group Analysis: t - test - Y C 2 Better Design: Have Pretest R Y 1E X Y 2E Y 1C - Y 2C Random assignment Experimental + Control group Pretest + Posttest Why Better? Analysis? 3 1

2 Why is Pretest/Posttest Better? Much larger power But depends on analysis Imagine effect: 4 Analysis Possibilities Covariance analysis (ancova) highest power t -Test on difference scores less power Interaction in 2-way analysis of variance (manova) less power 5 How Much Power? Example: assume posttest only Effect size is medium: Cohen s d = 0.5 Sample size is = 50 Alpha = 0.05, test is two-sided Power of t - test is

3 How Much Power? Example: assume pretest-posttest d = 0.5, N = = 50, α = 0.05 Power depends on correlation pretestposttest, which is typically high Assume r = 0.3 (Cohen: medium) Power of ancova - test is 0.46 Assume r = 0.5 (Cohen: high) Power of ancova - test is How Much Power? Same example: pretest-posttest, r = 0.6 Power of ancova - test is 0.57 Power of t - test on difference scores (assume equal variances) is 0.49 (t - test on posttest was 0.41) 8 How Much Power? Same example: pretest-posttest, r = 0.6 Power of ancova - test is 0.57 Power of interaction test in manova (interaction pre/posttest with exp/con) is 0.49 (t - test on posttest was 0.41) 9 3

4 How Much Power? Power of ancova - test is 0.57 Power t - test on difference scores 0.49 Power of interaction test in manova 0.49 Same hypothesis is tested, thus power is in general about equal But difference scores much simpler 10 Still Better Design: Have Pretest and Two Posttests R Y 1E X Y 2E Y 3E First posttest immediately after intervention: effect Second posttest much later: retention Y 1C - Y 2C Y 3C Best analysis: covariance analysis on posttests, separately or simultaneous 11 Why Multilevel Analysis? If your data have a grouping structure Interventions in organizations e.g. anti-smoking campaign in school classes, intervention done at class level If you have a panel design with substantial dropout It is not unusual to loose 25% at each wave 12 4

5 If Data Are Grouped Assume t-test, with natural groups (e.g. compare two intact schools) Significance test very biased! Dependence given by intraclass correlation Formal α = 0.05, but the actual alpha is larger! n per intraclass correlation group If You Have Panel Dropout SPSS ancova & manova completely handle random: dropout by casewise deletion do you really Cases with missings anywhere believe that? are deleted Minor disadvantage: waste of power Major disadvantage: assumes dropout is completely at random 14 Why Multilevel Analysis If your data do not have a grouping structure If your longitudinal study has negligible dropout Say at most 5% (Little & Rubin, 1987) Multilevel analysis has no advantages Use (m)anova with pretest as covariate 15 5

6 Example Intervention Data Experimental/Control group Pretest/Posttest: N = 2 25, r = 0.6 Part of data file: file: example.sav 16 Anova on Intervention Data 17 Anova on Intervention Data SPSS - output: 18 6

7 However If your data have a grouping structure and / or If you have a panel design with substantial dropout You need multilevel analysis! 19 Multilevel Data Three level data structure Groups at may have different sizes Response variable at lowest level Explanatory variables at all levels Model assumes sampling at all levels 20 Longitudinal Data As Multilevel Six persons measured on up to four occasions Levels are occasion level, and person level We can mix time variant (occasion level) and time invariant (person level) predictors Note that missing occasions are no problem 21 7

8 The Multilevel Regression Model: the Lowest (Individual) Level Ordinary regression, one explanatory variable X: Y i = β 0 + β 1 X i + e i β 0 intercept, β 1 regression slope, e i residual error term In multilevel regression, at the lowest level: Y ij = β 0j + β 1j X ij + e ij β 0j intercept, β 1j regression slope, e ij residual error subscript i for individuals, j for groups each group has its own intercept coefficient β 0j and its own slope coefficient β 1j Intercept and slope coefficients vary across the groups, hence the term random coefficient model 22 The Multilevel Regression Model: the Second (Group) Level At the lowest level: Y ij = β 0j + β 1j X ij + e ij Intercept and slope coefficients vary across the groups We predict intercept and slope with a second level regression model: β 0j = γ 00 + γ 01 Z j + u 0j β 1j = γ 10 + γ 11 Z j + u 1j γ 00 and γ 01 are the intercept and slope to predict β 0j from Z j, with u 0j the residual error term γ 10 and γ 11 are the intercept and slope to predict ß 1j from Z j, with u 1j the residual error term Coefficients γ do not vary across groups 23 The Multilevel Regression Model: Single Equation Version At the lowest (individual) level we have Y ij = β 0j + β 1j X ij + e ij and at the second (group) level β 0j = γ 00 + γ 01 Z j + u 0j β 1j = γ 10 + γ 11 Z j + u 1j Combining (substitution and rearranging terms) gives Y ij = γ 00 + γ 10 X ij + γ 01 Z j + γ 11 Z j X ij + u 1j X ij + u 0j + e ij Looks like an ordinary regression model with complicated error terms 24 8

9 The Multilevel Regression Model: Single Equation Version Y ij = [γ 00 + γ 10 X ij + γ 01 Z j + γ 11 Z j X ij ] + [u 1j X ij + u 0j + e ij ] This equation has two distinct parts [γ 00 + γ 10 X ij + γ 01 Z j + γ 11 Z j X ij ] contains all the fixed coefficients, it is the fixed part of the model [u 1j X ij + u 0j + e ij ] contains all the random error terms, it is the random part of the model Plus: The cross-level interaction Z j X ij results from modeling the regression slope β 1j of individual level variable X ij with the group level variable Z j the error term u 1j is connected to X ij. Thus the residuals are larger for large values of X ij, implying heteroscedasticity 25 The Multilevel Regression Model: Interpretation Y ij = [γ 00 + γ 10 X ij + γ 01 Z j + γ 11 Z j X ij ] + [u 1j X ij + u 0j + e ij ] Fixed part is an ordinary regression model Complicated error term: [u 1j X ij + u 0j + e ij ] Several error variances σ e ² variance of the lowest level errors e ij σ 00 variance of the highest level errors u 0j σ 11 variance of the highest level errors u 1j σ 01 covariance of u 0j and u 1j Note: σ 00, σ 11, and σ 01 also interpreted as (co)variances of lowest level coefficients β j 26 The Multilevel Regression Model: Estimation At the lowest (individual) level we have Y ij = β 0j + β 1j X ij + e ij and at the second (group) level β 0j = γ 00 + γ 01 Z j + u 0j β 1j = γ 10 + γ 11 Z j + u 1j Maximum Likelihood (ML) estimation Gamma coefficients, standard errors, p-values Variance components σ e ² and σ 00, σ 01, σ 11 (significance of (co)variances in Σ) Model deviance 27 9

10 Data Structure Multilevel Regression Model MLwiN & most other software All data in one single file Levels identified by identification numbers school number, class number, pupil number HLM Separate file for each level Reads SPSS, SAS, EXCEL & other files Note: SPSS 11.0 mixed model module is seriously flawed, do not use 28 Preparing Data for MLwiN Group and individual identification numbers Regression constant computed in SPSS const = 1 (not visible here) Write data out as fixed ascii -file 29 Porting Data to MLwiN Write data out as fixed ascii -file Using Save As Save gives all variables Or Paste into syntax window and replace all with list of variables WRITE OUTFILE = 'd:\joop\intervention\example.dat' TABLE / id group expcon pretest posttest const. EXECUTE

11 Start MLwiN & Input Data Under File open fixed ascii file Specify columns = # of variables Specify location & file 31 MLwiN: Next Nothing seems to happen Click on Data Manipulation to assign names Assigning names to columns is important c1=person, c2=group, c3=expcon, c4=pretest, c5=posttest, c6=const 32 MLwiN: Next Select column to assign name Type name in textbox, next hit Enter or click on unmarked button 33 11

12 MLwiN: Next Go to Model, open Equations window Which produces this: The Equations window is where we specify the model 34 The Equations Window: Heart of MLwiN Specify the outcome variable Specify the variables that identify levels Add predictors Including the regression constant Specify which 1 st level predictors have random (=varying) regression coefficients across level 2 units Including the regression constant Almost always random at all levels 35 Specify Outcome & Levels click on y 36 12

13 Specify Constant as 1 st Predictor click on x constant always varies at all levels indicate variation here 37 Things to do in the Equations Window show names show random part add predictors show estimates not symbols 38 Things to do in the MLwiN Window start / stop estimating complicated: RTFM like SPSS compute & recode specify estimation method Logical order in analysis of grouped (multilevel) data Only constant Add 1st level predictors, then add 2nd level predictors, etc Specify varying coefficients 39 13

14 Start Computations As by magic, estimates appear Constant plus the two variance components The intraclass correlation is (σ11/(σ11+ σe2)) Here (25.79/( ) = % of variance at group level 40 Multilevel Analysis Add predictor variables Assess significance Like usual multiple regression BUT 1st level predictors may have regression coefficients varying across groups Interesting hypothesis: is intervention effect constant across groups? If not: which group variables explain differences in intervention effect? 41 Back to Longitudinal Data Six persons measured on up to four occasions Levels are occasion level, and person level We can mix time variant (occasion level) and time invariant (person level) predictors Note that missing occasions are no problem 42 14

15 Typical Longitudinal Data File 43 Typical Longitudinal Data File, Prepared for Multilevel Analysis Multilevel longitudinal data file as raw data and as SPSS file SPSS file useful for preliminaries: inspect distributions, outliers, exploratory analyses 44 Intervention Data File Person Identification, Exp/Con group, 1 pretest, immediate posttest, follow-up posttest 45 15

16 Creating the Multilevel Longitudinal Data File SPSS-file intervention.sav In SPSS: make sure each variable has enough columns No system missing values but explicit missing data code Write raw data to interventionflat.dat Data are read back in SPSS in free format (variables separated by spaces) in new data layout Saved in SPSS file interventionflat.sav 46 Creating the Multilevel Longitudinal Data File Data are read back in SPSS in free format (variables separated by spaces) in new data layout Saved in SPSS file interventionflat.sav 47 Creating the Multilevel Longitudinal Data File Remove in this file all cases ( = occasions) that have a missing value on test ( = missed occasion) Write remainder to raw data file, transport to MLwiN Male levels: 1 st = occasion, 2 nd = person (ident) Dummies for pretest & 2 posttests Effect of expcon modeled as interaction with post1 or post2 dummy 48 16

17 Creating the Multilevel Longitudinal Data File Note: effect of expcon modeled as interaction with post1 or post2 dummy means less power Just as in manova But testscore may be missing at any occasion Alternative (pretest as covariate) only fesible if both pretest and posttest1 virtually no missings Which does happen 49 Usual Longitudinal Multilevel Analysis Baseline model always includes occasions as linear predictor or series of dummies Check for autonomous shift over time Add covariate expcon as interaction with post1 and / or post2 dummy We may add covariate expcon as interaction with pretest to check initial equality of groups 50 Remember If your data have a grouping structure and / or If you have a panel design with substantial dropout You need multilevel analysis! 51 17

18 Because SPSS ancova & manova completely handle random: dropout by casewise deletion do you really Cases with missings anywhere believe that? are deleted Minor disadvantage: waste of power Major disadvantage: assumes dropout is completely at random 52 Just to Hammer it in The advantage of multilevel models in pretest - posttest designs Is the softer assumption of missing at random (MAR) Instead completely at random (MCAR) MAR is plausible if dropout can be predicted from available variables Including the pretest! 53 Let s get moving! OK 54 18

### Introduction to Longitudinal Data Analysis

Introduction to Longitudinal Data Analysis Longitudinal Data Analysis Workshop Section 1 University of Georgia: Institute for Interdisciplinary Research in Education and Human Development Section 1: Introduction

### Illustration (and the use of HLM)

Illustration (and the use of HLM) Chapter 4 1 Measurement Incorporated HLM Workshop The Illustration Data Now we cover the example. In doing so we does the use of the software HLM. In addition, we will

### The Basic Two-Level Regression Model

2 The Basic Two-Level Regression Model The multilevel regression model has become known in the research literature under a variety of names, such as random coefficient model (de Leeuw & Kreft, 1986; Longford,

### A Basic Introduction to Missing Data

John Fox Sociology 740 Winter 2014 Outline Why Missing Data Arise Why Missing Data Arise Global or unit non-response. In a survey, certain respondents may be unreachable or may refuse to participate. Item

### Introduction to Data Analysis in Hierarchical Linear Models

Introduction to Data Analysis in Hierarchical Linear Models April 20, 2007 Noah Shamosh & Frank Farach Social Sciences StatLab Yale University Scope & Prerequisites Strong applied emphasis Focus on HLM

### Introducing the Multilevel Model for Change

Department of Psychology and Human Development Vanderbilt University GCM, 2010 1 Multilevel Modeling - A Brief Introduction 2 3 4 5 Introduction In this lecture, we introduce the multilevel model for change.

### HLM software has been one of the leading statistical packages for hierarchical

Introductory Guide to HLM With HLM 7 Software 3 G. David Garson HLM software has been one of the leading statistical packages for hierarchical linear modeling due to the pioneering work of Stephen Raudenbush

### HYPOTHESIS 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

### Missing Data. A Typology Of Missing Data. Missing At Random Or Not Missing At Random

[Leeuw, Edith D. de, and Joop Hox. (2008). Missing Data. Encyclopedia of Survey Research Methods. Retrieved from http://sage-ereference.com/survey/article_n298.html] Missing Data An important indicator

### Descriptive Statistics

Descriptive Statistics Primer Descriptive statistics Central tendency Variation Relative position Relationships Calculating descriptive statistics Descriptive Statistics Purpose to describe or summarize

### This chapter will demonstrate how to perform multiple linear regression with IBM SPSS

CHAPTER 7B Multiple Regression: Statistical Methods Using IBM SPSS This chapter will demonstrate how to perform multiple linear regression with IBM SPSS first using the standard method and then using the

### A REVIEW OF CURRENT SOFTWARE FOR HANDLING MISSING DATA

123 Kwantitatieve Methoden (1999), 62, 123-138. A REVIEW OF CURRENT SOFTWARE FOR HANDLING MISSING DATA Joop J. Hox 1 ABSTRACT. When we deal with a large data set with missing data, we have to undertake

### SCHOOL OF HEALTH AND HUMAN SCIENCES DON T FORGET TO RECODE YOUR MISSING VALUES

SCHOOL OF HEALTH AND HUMAN SCIENCES Using SPSS Topics addressed today: 1. Differences between groups 2. Graphing Use the s4data.sav file for the first part of this session. DON T FORGET TO RECODE YOUR

### Assignments Analysis of Longitudinal data: a multilevel approach

Assignments Analysis of Longitudinal data: a multilevel approach Frans E.S. Tan Department of Methodology and Statistics University of Maastricht The Netherlands Maastricht, Jan 2007 Correspondence: Frans

### Εισαγωγή στην πολυεπίπεδη μοντελοποίηση δεδομένων με το HLM. Βασίλης Παυλόπουλος Τμήμα Ψυχολογίας, Πανεπιστήμιο Αθηνών

Εισαγωγή στην πολυεπίπεδη μοντελοποίηση δεδομένων με το HLM Βασίλης Παυλόπουλος Τμήμα Ψυχολογίας, Πανεπιστήμιο Αθηνών Το υλικό αυτό προέρχεται από workshop που οργανώθηκε σε θερινό σχολείο της Ευρωπαϊκής

### Longitudinal Data Analyses Using Linear Mixed Models in SPSS: Concepts, Procedures and Illustrations

Research Article TheScientificWorldJOURNAL (2011) 11, 42 76 TSW Child Health & Human Development ISSN 1537-744X; DOI 10.1100/tsw.2011.2 Longitudinal Data Analyses Using Linear Mixed Models in SPSS: Concepts,

### Introduction 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

### SPSS Guide: Regression Analysis

SPSS Guide: Regression Analysis I put this together to give you a step-by-step guide for replicating what we did in the computer lab. It should help you run the tests we covered. The best way to get familiar

### DEPARTMENT OF PSYCHOLOGY UNIVERSITY OF LANCASTER MSC IN PSYCHOLOGICAL RESEARCH METHODS ANALYSING AND INTERPRETING DATA 2 PART 1 WEEK 9

DEPARTMENT OF PSYCHOLOGY UNIVERSITY OF LANCASTER MSC IN PSYCHOLOGICAL RESEARCH METHODS ANALYSING AND INTERPRETING DATA 2 PART 1 WEEK 9 Analysis of covariance and multiple regression So far in this course,

### Longitudinal Meta-analysis

Quality & Quantity 38: 381 389, 2004. 2004 Kluwer Academic Publishers. Printed in the Netherlands. 381 Longitudinal Meta-analysis CORA J. M. MAAS, JOOP J. HOX and GERTY J. L. M. LENSVELT-MULDERS Department

### SPSS Explore procedure

SPSS Explore procedure One useful function in SPSS is the Explore procedure, which will produce histograms, boxplots, stem-and-leaf plots and extensive descriptive statistics. To run the Explore procedure,

### The 3-Level HLM Model

James H. Steiger Department of Psychology and Human Development Vanderbilt University Regression Modeling, 2009 1 2 Basic Characteristics of the 3-level Model Level-1 Model Level-2 Model Level-3 Model

### Multilevel Modeling Tutorial. Using SAS, Stata, HLM, R, SPSS, and Mplus

Using SAS, Stata, HLM, R, SPSS, and Mplus Updated: March 2015 Table of Contents Introduction... 3 Model Considerations... 3 Intraclass Correlation Coefficient... 4 Example Dataset... 4 Intercept-only Model

### Introduction to Multilevel Modeling Using HLM 6. By ATS Statistical Consulting Group

Introduction to Multilevel Modeling Using HLM 6 By ATS Statistical Consulting Group Multilevel data structure Students nested within schools Children nested within families Respondents nested within interviewers

### I L L I N O I S UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN

Beckman HLM Reading Group: Questions, Answers and Examples Carolyn J. Anderson Department of Educational Psychology I L L I N O I S UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Linear Algebra Slide 1 of

### Research 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

### 1 Theory: The General Linear Model

QMIN GLM Theory - 1.1 1 Theory: The General Linear Model 1.1 Introduction Before digital computers, statistics textbooks spoke of three procedures regression, the analysis of variance (ANOVA), and the

### NCSS Statistical Software Principal Components Regression. In ordinary least squares, the regression coefficients are estimated using the formula ( )

Chapter 340 Principal Components Regression Introduction is a technique for analyzing multiple regression data that suffer from multicollinearity. When multicollinearity occurs, least squares estimates

### 10. Analysis of Longitudinal Studies Repeat-measures analysis

Research Methods II 99 10. Analysis of Longitudinal Studies Repeat-measures analysis This chapter builds on the concepts and methods described in Chapters 7 and 8 of Mother and Child Health: Research methods.

### Binary Logistic Regression

Binary Logistic Regression Main Effects Model Logistic regression will accept quantitative, binary or categorical predictors and will code the latter two in various ways. Here s a simple model including

### Module 5: Multiple Regression Analysis

Using Statistical Data Using to Make Statistical Decisions: Data Multiple to Make Regression Decisions Analysis Page 1 Module 5: Multiple Regression Analysis Tom Ilvento, University of Delaware, College

### Module 5: Introduction to Multilevel Modelling SPSS Practicals Chris Charlton 1 Centre for Multilevel Modelling

Module 5: Introduction to Multilevel Modelling SPSS Practicals Chris Charlton 1 Centre for Multilevel Modelling Pre-requisites Modules 1-4 Contents P5.1 Comparing Groups using Multilevel Modelling... 4

### Pearson's Correlation Tests

Chapter 800 Pearson's Correlation Tests Introduction The correlation coefficient, ρ (rho), is a popular statistic for describing the strength of the relationship between two variables. The correlation

### 1/27/2013. PSY 512: Advanced Statistics for Psychological and Behavioral Research 2

PSY 512: Advanced Statistics for Psychological and Behavioral Research 2 Introduce moderated multiple regression Continuous predictor continuous predictor Continuous predictor categorical predictor Understand

### Chapter 7: Simple linear regression Learning Objectives

Chapter 7: Simple linear regression Learning Objectives Reading: Section 7.1 of OpenIntro Statistics Video: Correlation vs. causation, YouTube (2:19) Video: Intro to Linear Regression, YouTube (5:18) -

### Missing Data: Part 1 What to Do? Carol B. Thompson Johns Hopkins Biostatistics Center SON Brown Bag 3/20/13

Missing Data: Part 1 What to Do? Carol B. Thompson Johns Hopkins Biostatistics Center SON Brown Bag 3/20/13 Overview Missingness and impact on statistical analysis Missing data assumptions/mechanisms Conventional

### Simple Linear Regression, Scatterplots, and Bivariate Correlation

1 Simple Linear Regression, Scatterplots, and Bivariate Correlation This section covers procedures for testing the association between two continuous variables using the SPSS Regression and Correlate analyses.

### Experimental Design and Hypothesis Testing. Rick Balkin, Ph.D.

Experimental Design and Hypothesis Testing Rick Balkin, Ph.D. 1 Let s s review hypothesis testing and experimental design 3 types of hypothesis testing in experimental research: z-test t-test F-test Balkin,

### Chapter 15. Mixed Models. 15.1 Overview. A flexible approach to correlated data.

Chapter 15 Mixed Models A flexible approach to correlated data. 15.1 Overview Correlated data arise frequently in statistical analyses. This may be due to grouping of subjects, e.g., students within classrooms,

### Data Analysis Tools. Tools for Summarizing Data

Data Analysis Tools This section of the notes is meant to introduce you to many of the tools that are provided by Excel under the Tools/Data Analysis menu item. If your computer does not have that tool

### Problem of Missing Data

VASA Mission of VA Statisticians Association (VASA) Promote & disseminate statistical methodological research relevant to VA studies; Facilitate communication & collaboration among VA-affiliated statisticians;

### Introduction to Hierarchical Linear Modeling with R

Introduction to Hierarchical Linear Modeling with R 5 10 15 20 25 5 10 15 20 25 13 14 15 16 40 30 20 10 0 40 30 20 10 9 10 11 12-10 SCIENCE 0-10 5 6 7 8 40 30 20 10 0-10 40 1 2 3 4 30 20 10 0-10 5 10 15

### Chapter Seven. Multiple regression An introduction to multiple regression Performing a multiple regression on SPSS

Chapter Seven Multiple regression An introduction to multiple regression Performing a multiple regression on SPSS Section : An introduction to multiple regression WHAT IS MULTIPLE REGRESSION? Multiple

### II. DISTRIBUTIONS distribution normal distribution. standard scores

Appendix D Basic Measurement And Statistics The following information was developed by Steven Rothke, PhD, Department of Psychology, Rehabilitation Institute of Chicago (RIC) and expanded by Mary F. Schmidt,

### Example: 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

### MULTIPLE REGRESSION WITH CATEGORICAL DATA

DEPARTMENT OF POLITICAL SCIENCE AND INTERNATIONAL RELATIONS Posc/Uapp 86 MULTIPLE REGRESSION WITH CATEGORICAL DATA I. AGENDA: A. Multiple regression with categorical variables. Coding schemes. Interpreting

### Directions for using SPSS

Directions for using SPSS Table of Contents Connecting and Working with Files 1. Accessing SPSS... 2 2. Transferring Files to N:\drive or your computer... 3 3. Importing Data from Another File Format...

### Data analysis process

Data analysis process Data collection and preparation Collect data Prepare codebook Set up structure of data Enter data Screen data for errors Exploration of data Descriptive Statistics Graphs Analysis

### Part 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

### INTRODUCTORY STATISTICS

INTRODUCTORY STATISTICS FIFTH EDITION Thomas H. Wonnacott University of Western Ontario Ronald J. Wonnacott University of Western Ontario WILEY JOHN WILEY & SONS New York Chichester Brisbane Toronto Singapore

### One-Way ANOVA using SPSS 11.0. SPSS ANOVA procedures found in the Compare Means analyses. Specifically, we demonstrate

1 One-Way ANOVA using SPSS 11.0 This section covers steps for testing the difference between three or more group means using the SPSS ANOVA procedures found in the Compare Means analyses. Specifically,

### UNDERSTANDING ANALYSIS OF COVARIANCE (ANCOVA)

UNDERSTANDING ANALYSIS OF COVARIANCE () In general, research is conducted for the purpose of explaining the effects of the independent variable on the dependent variable, and the purpose of research design

### Premaster Statistics Tutorial 4 Full solutions

Premaster Statistics Tutorial 4 Full solutions Regression analysis Q1 (based on Doane & Seward, 4/E, 12.7) a. Interpret the slope of the fitted regression = 125,000 + 150. b. What is the prediction for

### Bill Burton Albert Einstein College of Medicine william.burton@einstein.yu.edu April 28, 2014 EERS: Managing the Tension Between Rigor and Resources 1

Bill Burton Albert Einstein College of Medicine william.burton@einstein.yu.edu April 28, 2014 EERS: Managing the Tension Between Rigor and Resources 1 Calculate counts, means, and standard deviations Produce

### Module 3: Correlation and Covariance

Using Statistical Data to Make Decisions Module 3: Correlation and Covariance Tom Ilvento Dr. Mugdim Pašiƒ University of Delaware Sarajevo Graduate School of Business O ften our interest in data analysis

### 1.5 Oneway Analysis of Variance

Statistics: Rosie Cornish. 200. 1.5 Oneway Analysis of Variance 1 Introduction Oneway analysis of variance (ANOVA) is used to compare several means. This method is often used in scientific or medical experiments

### Section 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

### Auxiliary Variables in Mixture Modeling: 3-Step Approaches Using Mplus

Auxiliary Variables in Mixture Modeling: 3-Step Approaches Using Mplus Tihomir Asparouhov and Bengt Muthén Mplus Web Notes: No. 15 Version 8, August 5, 2014 1 Abstract This paper discusses alternatives

### A Mixed Model Approach for Intent-to-Treat Analysis in Longitudinal Clinical Trials with Missing Values

Methods Report A Mixed Model Approach for Intent-to-Treat Analysis in Longitudinal Clinical Trials with Missing Values Hrishikesh Chakraborty and Hong Gu March 9 RTI Press About the Author Hrishikesh Chakraborty,

### Qualitative vs Quantitative research & Multilevel methods

Qualitative vs Quantitative research & Multilevel methods How to include context in your research April 2005 Marjolein Deunk Content What is qualitative analysis and how does it differ from quantitative

### MULTIPLE REGRESSION AND ISSUES IN REGRESSION ANALYSIS

MULTIPLE REGRESSION AND ISSUES IN REGRESSION ANALYSIS MSR = Mean Regression Sum of Squares MSE = Mean Squared Error RSS = Regression Sum of Squares SSE = Sum of Squared Errors/Residuals α = Level of Significance

### Introduction to proc glm

Lab 7: Proc GLM and one-way ANOVA STT 422: Summer, 2004 Vince Melfi SAS has several procedures for analysis of variance models, including proc anova, proc glm, proc varcomp, and proc mixed. We mainly will

### Module 4 - Multiple Logistic Regression

Module 4 - Multiple Logistic Regression Objectives Understand the principles and theory underlying logistic regression Understand proportions, probabilities, odds, odds ratios, logits and exponents Be

### Overview of Violations of the Basic Assumptions in the Classical Normal Linear Regression Model

Overview of Violations of the Basic Assumptions in the Classical Normal Linear Regression Model 1 September 004 A. Introduction and assumptions The classical normal linear regression model can be written

### Answer: C. The strength of a correlation does not change if units change by a linear transformation such as: Fahrenheit = 32 + (5/9) * Centigrade

Statistics Quiz Correlation and Regression -- ANSWERS 1. Temperature and air pollution are known to be correlated. We collect data from two laboratories, in Boston and Montreal. Boston makes their measurements

### Simple 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

### research/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

### Overview Classes. 12-3 Logistic regression (5) 19-3 Building and applying logistic regression (6) 26-3 Generalizations of logistic regression (7)

Overview Classes 12-3 Logistic regression (5) 19-3 Building and applying logistic regression (6) 26-3 Generalizations of logistic regression (7) 2-4 Loglinear models (8) 5-4 15-17 hrs; 5B02 Building and

### E(y i ) = x T i β. yield of the refined product as a percentage of crude specific gravity vapour pressure ASTM 10% point ASTM end point in degrees F

Random and Mixed Effects Models (Ch. 10) Random effects models are very useful when the observations are sampled in a highly structured way. The basic idea is that the error associated with any linear,

### Moderation. Moderation

Stats - Moderation Moderation A moderator is a variable that specifies conditions under which a given predictor is related to an outcome. The moderator explains when a DV and IV are related. Moderation

### Introduction to mixed model and missing data issues in longitudinal studies

Introduction to mixed model and missing data issues in longitudinal studies Hélène Jacqmin-Gadda INSERM, U897, Bordeaux, France Inserm workshop, St Raphael Outline of the talk I Introduction Mixed models

### SAS Syntax and Output for Data Manipulation:

Psyc 944 Example 5 page 1 Practice with Fixed and Random Effects of Time in Modeling Within-Person Change The models for this example come from Hoffman (in preparation) chapter 5. We will be examining

### Power and sample size in multilevel modeling

Snijders, Tom A.B. Power and Sample Size in Multilevel Linear Models. In: B.S. Everitt and D.C. Howell (eds.), Encyclopedia of Statistics in Behavioral Science. Volume 3, 1570 1573. Chicester (etc.): Wiley,

### Mixed 2 x 3 ANOVA. Notes

Mixed 2 x 3 ANOVA This section explains how to perform an ANOVA when one of the variables takes the form of repeated measures and the other variable is between-subjects that is, independent groups of participants

### Financial Risk Management Exam Sample Questions/Answers

Financial Risk Management Exam Sample Questions/Answers Prepared by Daniel HERLEMONT 1 2 3 4 5 6 Chapter 3 Fundamentals of Statistics FRM-99, Question 4 Random walk assumes that returns from one time period

### Chapter 23. Inferences for Regression

Chapter 23. Inferences for Regression Topics covered in this chapter: Simple Linear Regression Simple Linear Regression Example 23.1: Crying and IQ The Problem: Infants who cry easily may be more easily

### KSTAT MINI-MANUAL. Decision Sciences 434 Kellogg Graduate School of Management

KSTAT MINI-MANUAL Decision Sciences 434 Kellogg Graduate School of Management Kstat is a set of macros added to Excel and it will enable you to do the statistics required for this course very easily. To

### Multivariate Analysis of Variance (MANOVA)

Multivariate Analysis of Variance (MANOVA) Aaron French, Marcelo Macedo, John Poulsen, Tyler Waterson and Angela Yu Keywords: MANCOVA, special cases, assumptions, further reading, computations Introduction

### Handling attrition and non-response in longitudinal data

Longitudinal and Life Course Studies 2009 Volume 1 Issue 1 Pp 63-72 Handling attrition and non-response in longitudinal data Harvey Goldstein University of Bristol Correspondence. Professor H. Goldstein

### An introduction to hierarchical linear modeling

Tutorials in Quantitative Methods for Psychology 2012, Vol. 8(1), p. 52-69. An introduction to hierarchical linear modeling Heather Woltman, Andrea Feldstain, J. Christine MacKay, Meredith Rocchi University

### Electronic Thesis and Dissertations UCLA

Electronic Thesis and Dissertations UCLA Peer Reviewed Title: A Multilevel Longitudinal Analysis of Teaching Effectiveness Across Five Years Author: Wang, Kairong Acceptance Date: 2013 Series: UCLA Electronic

### Univariate Regression

Univariate Regression Correlation and Regression The regression line summarizes the linear relationship between 2 variables Correlation coefficient, r, measures strength of relationship: the closer r is

### Introduction to Regression and Data Analysis

Statlab Workshop Introduction to Regression and Data Analysis with Dan Campbell and Sherlock Campbell October 28, 2008 I. The basics A. Types of variables Your variables may take several forms, and it

### Multiple Choice: 2 points each

MID TERM MSF 503 Modeling 1 Name: Answers go here! NEATNESS COUNTS!!! Multiple Choice: 2 points each 1. In Excel, the VLOOKUP function does what? Searches the first row of a range of cells, and then returns

### Ordinal Regression. Chapter

Ordinal Regression Chapter 4 Many variables of interest are ordinal. That is, you can rank the values, but the real distance between categories is unknown. Diseases are graded on scales from least severe

### Imputing Missing Data using SAS

ABSTRACT Paper 3295-2015 Imputing Missing Data using SAS Christopher Yim, California Polytechnic State University, San Luis Obispo Missing data is an unfortunate reality of statistics. However, there are

### Consider a study in which. How many subjects? The importance of sample size calculations. An insignificant effect: two possibilities.

Consider a study in which How many subjects? The importance of sample size calculations Office of Research Protections Brown Bag Series KB Boomer, Ph.D. Director, boomer@stat.psu.edu A researcher conducts

### Formula for linear models. Prediction, extrapolation, significance test against zero slope.

Formula for linear models. Prediction, extrapolation, significance test against zero slope. Last time, we looked the linear regression formula. It s the line that fits the data best. The Pearson correlation

### ASSIGNMENT 4 PREDICTIVE MODELING AND GAINS CHARTS

DATABASE MARKETING Fall 2015, max 24 credits Dead line 15.10. ASSIGNMENT 4 PREDICTIVE MODELING AND GAINS CHARTS PART A Gains chart with excel Prepare a gains chart from the data in \\work\courses\e\27\e20100\ass4b.xls.

### 5. Linear Regression

5. Linear Regression Outline.................................................................... 2 Simple linear regression 3 Linear model............................................................. 4

Lecture 16: Generalized Additive Models Regression III: Advanced Methods Bill Jacoby Michigan State University http://polisci.msu.edu/jacoby/icpsr/regress3 Goals of the Lecture Introduce Additive Models

### Multivariate Logistic Regression

1 Multivariate Logistic Regression As in univariate logistic regression, let π(x) represent the probability of an event that depends on p covariates or independent variables. Then, using an inv.logit formulation

### Analyzing Structural Equation Models With Missing Data

Analyzing Structural Equation Models With Missing Data Craig Enders* Arizona State University cenders@asu.edu based on Enders, C. K. (006). Analyzing structural equation models with missing data. In G.

### Didacticiel - Études de cas

1 Topic Regression analysis with LazStats (OpenStat). LazStat 1 is a statistical software which is developed by Bill Miller, the father of OpenStat, a wellknow tool by statisticians since many years. These

ALLISON 1 TABLE OF CONTENTS 1. INTRODUCTION... 3 2. ASSUMPTIONS... 6 MISSING COMPLETELY AT RANDOM (MCAR)... 6 MISSING AT RANDOM (MAR)... 7 IGNORABLE... 8 NONIGNORABLE... 8 3. CONVENTIONAL METHODS... 10

### T-test & factor analysis

Parametric tests T-test & factor analysis Better than non parametric tests Stringent assumptions More strings attached Assumes population distribution of sample is normal Major problem Alternatives Continue

### Data Cleaning and Missing Data Analysis

Data Cleaning and Missing Data Analysis Dan Merson vagabond@psu.edu India McHale imm120@psu.edu April 13, 2010 Overview Introduction to SACS What do we mean by Data Cleaning and why do we do it? The SACS