Moderator and Mediator Analysis
|
|
|
- Jared Woods
- 7 years ago
- Views:
Transcription
1 Moderator and Mediator Analysis Seminar General Statistics Marijtje van Duijn October 8, Overview What is moderation and mediation? What is their relation to statistical concepts? Example(s) October 8, Moderator and mediator analysis
2 Mediation and Moderation X Y X October 8, Moderator and mediator analysis 3 Examples Y : test score X : sex, SES, etc. X : ability (IQ score) Y : test score X : brain volume, SES parents X : ability More? October 8, Moderator and mediator analysis 4
3 i Multiple regression Y + = β + βx i + βx i Goal: to explain variation in Y using Xs Assumptions Independent observations Normality (of residuals) and constant variance Linearity (of relationship Y and Xs) E i October 8, Moderator and mediator analysis 5 Regression X β Y E X β October 8, Moderator and mediator analysis 6 3
4 Explained variance in regression Y X X Circles represent variances X and X explain different parts of Y and are independent October 8, Moderator and mediator analysis 7 Multicollinearity competition between variables for explaining Y Y X X Degree depends on correlation between X s Variance inflation factor (VIF): worse (= less precise) parameter estimation October 8, Moderator and mediator analysis 8 4
5 Association between all (3) variables Several correlations to describe association Partial correlation: correlation between two variables with the third variable fixed (i.e. corrected for the third variable) (partial in SPSS) unique portion of variance Semi-partial correlation: correlation between two variables with one variable s association corrected for the third variable (part in SPSS output) extra variance explained Important in regression when variables are entered in a certain order Usually the partial correlation is smaller than the uncorrected ( zero-order ) correlation, and larger than the semi-partial correlation October 8, Moderator and mediator analysis 9 Multicollinearity/Mediation X Y X October 8, Moderator and mediator analysis 5
6 Mediation as a special case of multicollinearity and/or model selection Causal model defines direction of arrows X is the mediator (M) Also: intervening or process variable Or: indirect causal relationship Relations between all variables are assumed to be positive Question is whether direct effect between X and Y disappears when M is added to the regression equation October 8, Moderator and mediator analysis Mediation (Baron & Kenny, 986), X c c Y a M b October 8, Moderator and mediator analysis 6
7 Mediation as prescribed by Baron and Kenny (986) Estimate regression of Y on only X Estimated parameter c Estimate regression of M on X Estimated parameter a Estimate effect of M on Y, together with X Estimated parameters b and c Complete mediation: c = Partial mediation: c < c (can be tested) October 8, Moderator and mediator analysis 3 Testing of change in c Amount of mediation c-c Theoretically equal to ab (indirect path) Standard error of ab is approximately square root of b s a + a s b (Sobel test) see (do) Note: neither c nor c are needed! Some eye-balling also possible Or: nonparametric tests (based on bootstrapping) October 8, Moderator and mediator analysis 4 7
8 Example (Miles and Shevlin) Y: read, a measure of the number of books that people have read. X: enjoy, scale score to measure how much people enjoy reading books M: buy, a measure of how many books people have bought in the previous months Idea: how much people enjoy reading books -> the number of books bought -> the number of books read But: is the number of books a complete mediator.? (People could go to the library or borrow books from friends.) October 8, Moderator and mediator analysis 5 Descriptive Statistics Std. Mean Deviation N read 8,85 3,563 4 buy 5,73 8,65 4 enjoy 9,8 5,354 4 Pearson Correlation Correlations read buy enjoy read,,747,73 buy,747,,644 enjoy,73,644, Step a Unstandardized Standardized B Std. Error Beta t Sig. (Constant) 4,33,785 5,57, enjoy,487,74,73 6,65, a. Dependent Variable: read October 8, Moderator and mediator analysis 6 8
9 Step a Unstandardized Standardiz ed B Std. Error Beta t Sig. (Constant) 6,66, 3,74, enjoy,98,89,644 5,9, a. Dependent Variable: buy Step 3 Unstandardized a Standardized B Std. Error Beta t Sig. (Constant),973,765 3,887, Correlations Zeroorder Partial Part buy,5,54,47 3,786,,747,58,36 enjoy,86,83,49 3,45,,73,494,38 a. Dependent Variable: read October 8, Moderator and mediator analysis 7 Examples Baron/Kenny + Sobel a=.98 s a =.89 b=.487 s b =.74 ab=.478, s ab = (.487 * *.74 )=. z-test 4.8; p<. Eye-balling c=.487 (.74), then roughly.34 < c <.64 c =.86 (.83): partial mediation (because. < c <.45) October 8, Moderator and mediator analysis 8 9
10 choice is important Many other patterns of association are possible Arrows between X and X may be reversed not always clear which variable mediates No causal relation, just association Explicit assumption of positive associations and ordering of (semi-) partial correlations. Not guaranteed October 8, Moderator and mediator analysis 9 Moderation X Y X October 8, Moderator and mediator analysis
11 Moderation is interaction The effect of X depends on the value of X (or vice versa) different slopes for different folks can be a way to tackle non-linearity in regression Interpretation depends on type of variable Interaction usually (but not necessarily) product of X and X X and X may be correlated Importance of model formulation October 8, Moderator and mediator analysis Regression model i = β + βx i + βx i + β3x i X i Y + E Centering is (usually) advised Facilitates interpretation Reduces the inevitable multicollinearity incurred with interaction terms c c c c i = β + βx i + βx i + β3x i X i Y + E i i October 8, Moderator and mediator analysis
12 X dichotomous and X continuous X = or X = (e.g. man/woman; control/experimental group) Y = β + β X + β X + β 3 X X X = : Y = β + β X X = : Y = (β + β ) + (β + β 3 )X so: intercept and regressioneffect of X change interaction effect represents the change in effect of X or, the difference in the effect of X between the two groups interpretation of β General formula: Y = (β + β X ) + (β + β 3 X )X October 8, Moderator and mediator analysis 3 X and X dichotomous X = or X = (e.g. man/woman) X = or X = (e.g. control/experimental grp) Y = β + β X + β X + β 3 X X X =, X = : Y = β X =, X = : Y = β + β X =, X = : Y = β + β X =, X = : Y = β + β + β + β 3 so: defines four groups with their own mean Interaction defines extra effect of X = and X = October 8, Moderator and mediator analysis 4
13 X nominal and X continuous X takes on more than (c) values (e.g. age groups, control/exp/exp) Make dummies, for each contrast, wrt reference group (e.g. controls) Leads to c- dichotomous variables And also c- interaction terms Also possible: dummies (indicators) for each group leaving out the intercept October 8, Moderator and mediator analysis 5 c=3; group reference group group D D 3 Y = β + β d D + β d D + β X +β 3 D X +β 4 D X group: Y = β + β X group: Y = (β + β d ) + (β + β 3 )X group3: Y = (β + β d ) + (β + β 4 )X October 8, Moderator and mediator analysis 6 3
14 X and X continuous Y = β + β X +β X +β 3 X X Y = (β + β X ) + (β +β 3 X )X Y = (β +β X ) + (β +β 3 X )X X X c c = X X = X c c * β = β β X β X + β 3 X X * β = β β 3 X * β = β β 3 X X * * Y = β + β X * + β X + β X 3 c X c X X = X = X : Y : Y = β * = β * + β * + β * X X c c October 8, Moderator and mediator analysis 7 Example (Miles and Shevlin) Y: grade in statistics course X: number of books read (-4) X: number of classes attended (-) Descriptive Statistics Mean Std. Deviation N grade 63,55 6,755 4 books,,43 4 attend 4, 4,78 4 October 8, Moderator and mediator analysis 8 4
15 October 8, Moderator and mediator analysis 9 Unstandardized Standardiz ed Coefficient s a B Std. Error Beta t Sig. (Constant) 63,4,3 8,534, Correlations Zeroorder Partial Part Collinearity Statistics Toleran ce VIF booksc 4,37,753,346,33,7,49,354,3,83,45 attendc,83,587,39,87,35,48,338,95,83,45 (Constant) 6,469,3 6,494, booksc 4,8,677,35,433,,49,376,34,83,45 attendc,333,56,34,37,3,48,368,36,8,47 bookscxatte ndc a. Dependent Variable: grade,735,349,7,4,4,4,33,7,997,3 October 8, Moderator and mediator analysis 3 5
16 Other example (missed) interaction: non-linearity? 3 groups with each a distinct linear relation October 8, Moderator and mediator analysis 3 October 8, Moderator and mediator analysis 3 6
17 October 8, Moderator and mediator analysis 33 Summary b Adjusted Std. Error of R R Square R Square the Estimate.45 a a. Predictors: (Constant), x b. Dependent Variable: y Predicted Value Residual Std. Predicted Value Std. Residual a. Dependent Variable: y Residuals Statistics a Minimum Maximum Mean Std. Deviation N (Constant) x a. Dependent Variable: y Unstandardized Standardized a Correlations t Sig. Zero-order Partial Part Collinearity Statistics VIF B Std. Error Beta Tolerance Histogram Normal P-P Plot of Regression Standardized Residual Dependent Variable: y Dependent Variable: y, 6 Frequency 4 Expected Cum Prob,8,6,4, - Regression Standardized Residual Mean =-,78E-7 Std. Dev. =,983 N =3,,,,4,6,8 Observed Cum Prob, October 8, Moderator and mediator analysis 34 7
18 y Summary b Adjusted Std. Error of R R Square R Square the Estimate.98 a a. Predictors: (Constant), xkwadraat, x b. Dependent Variable: y Predicted Value Residual Std. Predicted Value Std. Residual a. Dependent Variable: y Residuals Statistics a Minimum Maximum Mean Std. Deviation N (Constant) x xkwadraat a. Dependent Variable: y Unstandardized Standardized a Correlations t Sig. Zero-order Partial Part Collinearity Statistics VIF B Std. Error Beta Tolerance Histogram Partial Regression Plot Dependent Variable: y Dependent Variable: y 6, Frequency 4, - Regression Standardized Residual Mean =-3,6E-6 Std. Dev. =,965 N =3 -, -5, -, -5,, x 5,, 5, October 8, Moderator and mediator analysis 35 Summary b Adjusted Std. Error of R R Square R Square the Estimate.4 a a. Predictors: (Constant), groep, x b. Dependent Variable: y Predicted Value Residual Std. Predicted Value Std. Residual a. Dependent Variable: y Residuals Statistics a Minimum Maximum Mean Std. Deviation N (Constant) x groep a. Dependent Variable: y Unstandardized Standardized a Correlations t Sig. Zero-order Partial Part Collinearity Statistics VIF B Std. Error Beta Tolerance Partial Regression Plot Histogram Dependent Variable: y Dependent Variable: y 6,5 Frequency 4 y, -,5 - Mean =5,69E-6 Std. Dev. =,965 N =3-5, Regression Standardized Residual -4, -,, x, 4, October 8, Moderator and mediator analysis 36 8
19 y y Summary b Adjusted Std. Error of R R Square R Square the Estimate.75 a a. Predictors: (Constant), groep3, groep, x b. Dependent Variable: y Predicted Value Residual Std. Predicted Value Std. Residual a. Dependent Variable: y Residuals Statistics a Minimum Maximum Mean Std. Deviation N (Constant) x groep groep3 a. Dependent Variable: y Unstandardized Standardized a Correlations t Sig. Zero-order Partial Part Collinearity Statistics VIF B Std. Error Beta Tolerance Partial Regression Plot Histogram Dependent Variable: y Dependent Variable: y 4, 8, Frequency 6 4, -, -4, - Regression Standardized Residual Mean =3,47E-6 Std. Dev. =,947 N =3-4, -,, x, 4, October 8, Moderator and mediator analysis 37 Summary b Adjusted Std. Error of R R Square R Square the Estimate.997 a a. Predictors: (Constant), intxgr3, intxgr, x, groep, groep3 b. Dependent Variable: y Predicted Value Residual Std. Predicted Value Std. Residual a. Dependent Variable: y Residuals Statistics a Minimum Maximum Mean Std. Deviation N (Constant) x groep groep3 intxgr intxgr3 a. Dependent Variable: y Unstandardized Standardized a Correlations t Sig. Zero-order Partial Part Collinearity Statistics VIF B Std. Error Beta Tolerance 4.97E Histogram Partial Regression Plot Dependent Variable: y Dependent Variable: y 4,, Frequency 8 6 4, -, - Mean =,8E-5 Std. Dev. =,9 N =3-4, Regression Standardized Residual -4, -,,, 4, x October 8, Moderator and mediator analysis 38 9
20 choice important Missing interaction may result in Violations of linearity assumption non-constant variance (heterogeneity) Incorrect model choice and interpretation October 8, Moderator and mediator analysis 39 Conclusion choice and selection crucial in detecting mediation and moderation Substantive / theoretical considerations should guide the model selection process! October 8, Moderator and mediator analysis 4
21 Other methods/models Mediation sometimes too simple More refined path analysis Regression analysis sometimes too simple More elaborate models for causal modeling Structural Equation s October 8, Moderator and mediator analysis 4
Simple linear regression
Simple linear regression Introduction Simple linear regression is a statistical method for obtaining a formula to predict values of one variable from another where there is a causal relationship between
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
Multiple Regression in SPSS This example shows you how to perform multiple regression. The basic command is regression : linear.
Multiple Regression in SPSS This example shows you how to perform multiple regression. The basic command is regression : linear. In the main dialog box, input the dependent variable and several predictors.
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
Chapter 13 Introduction to Linear Regression and Correlation Analysis
Chapter 3 Student Lecture Notes 3- Chapter 3 Introduction to Linear Regression and Correlation Analsis Fall 2006 Fundamentals of Business Statistics Chapter Goals To understand the methods for displaing
Doing Multiple Regression with SPSS. In this case, we are interested in the Analyze options so we choose that menu. If gives us a number of choices:
Doing Multiple Regression with SPSS Multiple Regression for Data Already in Data Editor Next we want to specify a multiple regression analysis for these data. The menu bar for SPSS offers several options:
Multiple Regression. Page 24
Multiple Regression Multiple regression is an extension of simple (bi-variate) regression. The goal of multiple regression is to enable a researcher to assess the relationship between a dependent (predicted)
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
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
Stepwise Regression. Chapter 311. Introduction. Variable Selection Procedures. Forward (Step-Up) Selection
Chapter 311 Introduction Often, theory and experience give only general direction as to which of a pool of candidate variables (including transformed variables) should be included in the regression model.
Additional sources Compilation of sources: http://lrs.ed.uiuc.edu/tseportal/datacollectionmethodologies/jin-tselink/tselink.htm
Mgt 540 Research Methods Data Analysis 1 Additional sources Compilation of sources: http://lrs.ed.uiuc.edu/tseportal/datacollectionmethodologies/jin-tselink/tselink.htm http://web.utk.edu/~dap/random/order/start.htm
Multicollinearity Richard Williams, University of Notre Dame, http://www3.nd.edu/~rwilliam/ Last revised January 13, 2015
Multicollinearity Richard Williams, University of Notre Dame, http://www3.nd.edu/~rwilliam/ Last revised January 13, 2015 Stata Example (See appendices for full example).. use http://www.nd.edu/~rwilliam/stats2/statafiles/multicoll.dta,
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...
Correlation and Regression Analysis: SPSS
Correlation and Regression Analysis: SPSS Bivariate Analysis: Cyberloafing Predicted from Personality and Age These days many employees, during work hours, spend time on the Internet doing personal things,
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
5. Linear Regression
5. Linear Regression Outline.................................................................... 2 Simple linear regression 3 Linear model............................................................. 4
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) -
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
Using Correlation and Regression: Mediation, Moderation, and More
Using Correlation and Regression: Mediation, Moderation, and More Part 2: Mediation analysis with regression Claremont Graduate University Professional Development Workshop August 22, 2015 Dale Berger,
1. The parameters to be estimated in the simple linear regression model Y=α+βx+ε ε~n(0,σ) are: a) α, β, σ b) α, β, ε c) a, b, s d) ε, 0, σ
STA 3024 Practice Problems Exam 2 NOTE: These are just Practice Problems. This is NOT meant to look just like the test, and it is NOT the only thing that you should study. Make sure you know all the material
Multiple Regression Using SPSS
Multiple Regression Using SPSS The following sections have been adapted from Field (2009) Chapter 7. These sections have been edited down considerably and I suggest (especially if you re confused) that
IAPRI Quantitative Analysis Capacity Building Series. Multiple regression analysis & interpreting results
IAPRI Quantitative Analysis Capacity Building Series Multiple regression analysis & interpreting results How important is R-squared? R-squared Published in Agricultural Economics 0.45 Best article of the
Correlation. What Is Correlation? Perfect Correlation. Perfect Correlation. Greg C Elvers
Correlation Greg C Elvers What Is Correlation? Correlation is a descriptive statistic that tells you if two variables are related to each other E.g. Is your related to how much you study? When two variables
False. Model 2 is not a special case of Model 1, because Model 2 includes X5, which is not part of Model 1. What she ought to do is estimate
Sociology 59 - Research Statistics I Final Exam Answer Key December 6, 00 Where appropriate, show your work - partial credit may be given. (On the other hand, don't waste a lot of time on excess verbiage.)
INTRODUCTION TO MULTIPLE CORRELATION
CHAPTER 13 INTRODUCTION TO MULTIPLE CORRELATION Chapter 12 introduced you to the concept of partialling and how partialling could assist you in better interpreting the relationship between two primary
Supplementary PROCESS Documentation
Supplementary PROCESS Documentation This document is an addendum to Appendix A of Introduction to Mediation, Moderation, and Conditional Process Analysis that describes options and output added to PROCESS
1.1. Simple Regression in Excel (Excel 2010).
.. Simple Regression in Excel (Excel 200). To get the Data Analysis tool, first click on File > Options > Add-Ins > Go > Select Data Analysis Toolpack & Toolpack VBA. Data Analysis is now available under
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
Projects Involving Statistics (& SPSS)
Projects Involving Statistics (& SPSS) Academic Skills Advice Starting a project which involves using statistics can feel confusing as there seems to be many different things you can do (charts, graphs,
Correlation key concepts:
CORRELATION Correlation key concepts: Types of correlation Methods of studying correlation a) Scatter diagram b) Karl pearson s coefficient of correlation c) Spearman s Rank correlation coefficient d)
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,
Regression Analysis (Spring, 2000)
Regression Analysis (Spring, 2000) By Wonjae Purposes: a. Explaining the relationship between Y and X variables with a model (Explain a variable Y in terms of Xs) b. Estimating and testing the intensity
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
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
Introduction. Research Problem. Larojan Chandrasegaran (1), Janaki Samuel Thevaruban (2)
Larojan Chandrasegaran (1), Janaki Samuel Thevaruban (2) Determining Factors on Applicability of the Computerized Accounting System in Financial Institutions in Sri Lanka (1) Department of Finance and
Using Excel for Statistical Analysis
Using Excel for Statistical Analysis You don t have to have a fancy pants statistics package to do many statistical functions. Excel can perform several statistical tests and analyses. First, make sure
EDUCATION AND VOCABULARY MULTIPLE REGRESSION IN ACTION
EDUCATION AND VOCABULARY MULTIPLE REGRESSION IN ACTION EDUCATION AND VOCABULARY 5-10 hours of input weekly is enough to pick up a new language (Schiff & Myers, 1988). Dutch children spend 5.5 hours/day
Econometrics Simple Linear Regression
Econometrics Simple Linear Regression Burcu Eke UC3M Linear equations with one variable Recall what a linear equation is: y = b 0 + b 1 x is a linear equation with one variable, or equivalently, a straight
2. Linear regression with multiple regressors
2. Linear regression with multiple regressors Aim of this section: Introduction of the multiple regression model OLS estimation in multiple regression Measures-of-fit in multiple regression Assumptions
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
Multiple 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
International Journal of Computer Trends and Technology (IJCTT) volume 4 Issue 8 August 2013
A Short-Term Traffic Prediction On A Distributed Network Using Multiple Regression Equation Ms.Sharmi.S 1 Research Scholar, MS University,Thirunelvelli Dr.M.Punithavalli Director, SREC,Coimbatore. Abstract:
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
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
Chapter 4 and 5 solutions
Chapter 4 and 5 solutions 4.4. Three different washing solutions are being compared to study their effectiveness in retarding bacteria growth in five gallon milk containers. The analysis is done in a laboratory,
Outline. Topic 4 - Analysis of Variance Approach to Regression. Partitioning Sums of Squares. Total Sum of Squares. Partitioning sums of squares
Topic 4 - Analysis of Variance Approach to Regression Outline Partitioning sums of squares Degrees of freedom Expected mean squares General linear test - Fall 2013 R 2 and the coefficient of correlation
An Introduction to Path Analysis. nach 3
An Introduction to Path Analysis Developed by Sewall Wright, path analysis is a method employed to determine whether or not a multivariate set of nonexperimental data fits well with a particular (a priori)
Analysing Questionnaires using Minitab (for SPSS queries contact -) Graham.Currell@uwe.ac.uk
Analysing Questionnaires using Minitab (for SPSS queries contact -) Graham.Currell@uwe.ac.uk Structure As a starting point it is useful to consider a basic questionnaire as containing three main sections:
X 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.
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
Unit 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
Elements of statistics (MATH0487-1)
Elements of statistics (MATH0487-1) Prof. Dr. Dr. K. Van Steen University of Liège, Belgium December 10, 2012 Introduction to Statistics Basic Probability Revisited Sampling Exploratory Data Analysis -
Correlational 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
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,
AGE AND EMOTIONAL INTELLIGENCE
White Paper Research on Emotional Intelligence AGE AND EMOTIONAL INTELLIGENCE Lorenzo Fariselli, Massimiliano Ghini, Joshua Freedman Publication Date: May 16, 2006 Last Updated: Jan 8, 2008 Abstract: There
Basic Statistics and Data Analysis for Health Researchers from Foreign Countries
Basic Statistics and Data Analysis for Health Researchers from Foreign Countries Volkert Siersma siersma@sund.ku.dk The Research Unit for General Practice in Copenhagen Dias 1 Content Quantifying association
Chapter 10. Key Ideas Correlation, Correlation Coefficient (r),
Chapter 0 Key Ideas Correlation, Correlation Coefficient (r), Section 0-: Overview We have already explored the basics of describing single variable data sets. However, when two quantitative variables
5. Multiple regression
5. Multiple regression QBUS6840 Predictive Analytics https://www.otexts.org/fpp/5 QBUS6840 Predictive Analytics 5. Multiple regression 2/39 Outline Introduction to multiple linear regression Some useful
MULTIPLE REGRESSION ANALYSIS OF MAIN ECONOMIC INDICATORS IN TOURISM. R, analysis of variance, Student test, multivariate analysis
Journal of tourism [No. 8] MULTIPLE REGRESSION ANALYSIS OF MAIN ECONOMIC INDICATORS IN TOURISM Assistant Ph.D. Erika KULCSÁR Babeş Bolyai University of Cluj Napoca, Romania Abstract This paper analysis
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
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
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
When to Use a Particular Statistical Test
When to Use a Particular Statistical Test Central Tendency Univariate Descriptive Mode the most commonly occurring value 6 people with ages 21, 22, 21, 23, 19, 21 - mode = 21 Median the center value the
SPSS-Applications (Data Analysis)
CORTEX fellows training course, University of Zurich, October 2006 Slide 1 SPSS-Applications (Data Analysis) Dr. Jürg Schwarz, juerg.schwarz@schwarzpartners.ch Program 19. October 2006: Morning Lessons
1. What is the critical value for this 95% confidence interval? CV = z.025 = invnorm(0.025) = 1.96
1 Final Review 2 Review 2.1 CI 1-propZint Scenario 1 A TV manufacturer claims in its warranty brochure that in the past not more than 10 percent of its TV sets needed any repair during the first two years
Statistical Control using Partial and Semi-partial (Part) Correlations
Statistical Control using Partial and Semi-partial (Part) A study of performance in graduate school produced the following correlations. 1st year graduate gpa -- criterion variable undergraduate gpa full
Introduction to Quantitative Methods
Introduction to Quantitative Methods October 15, 2009 Contents 1 Definition of Key Terms 2 2 Descriptive Statistics 3 2.1 Frequency Tables......................... 4 2.2 Measures of Central Tendencies.................
Adequacy of Biomath. Models. Empirical Modeling Tools. Bayesian Modeling. Model Uncertainty / Selection
Directions in Statistical Methodology for Multivariable Predictive Modeling Frank E Harrell Jr University of Virginia Seattle WA 19May98 Overview of Modeling Process Model selection Regression shape Diagnostics
Section 3 Part 1. Relationships between two numerical variables
Section 3 Part 1 Relationships between two numerical variables 1 Relationship between two variables The summary statistics covered in the previous lessons are appropriate for describing a single variable.
2. Simple Linear Regression
Research methods - II 3 2. Simple Linear Regression Simple linear regression is a technique in parametric statistics that is commonly used for analyzing mean response of a variable Y which changes according
THE RELATIONSHIP BETWEEN WORKING CAPITAL MANAGEMENT AND DIVIDEND PAYOUT RATIO OF FIRMS LISTED IN NAIROBI SECURITIES EXCHANGE
International Journal of Economics, Commerce and Management United Kingdom Vol. III, Issue 11, November 2015 http://ijecm.co.uk/ ISSN 2348 0386 THE RELATIONSHIP BETWEEN WORKING CAPITAL MANAGEMENT AND DIVIDEND
Section Format Day Begin End Building Rm# Instructor. 001 Lecture Tue 6:45 PM 8:40 PM Silver 401 Ballerini
NEW YORK UNIVERSITY ROBERT F. WAGNER GRADUATE SCHOOL OF PUBLIC SERVICE Course Syllabus Spring 2016 Statistical Methods for Public, Nonprofit, and Health Management Section Format Day Begin End Building
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
CLUSTER SAMPLE SIZE CALCULATOR USER MANUAL
1 4 9 5 CLUSTER SAMPLE SIZE CALCULATOR USER MANUAL Health Services Research Unit University of Aberdeen Polwarth Building Foresterhill ABERDEEN AB25 2ZD UK Tel: +44 (0)1224 663123 extn 53909 May 1999 1
APPLICATION OF LINEAR REGRESSION MODEL FOR POISSON DISTRIBUTION IN FORECASTING
APPLICATION OF LINEAR REGRESSION MODEL FOR POISSON DISTRIBUTION IN FORECASTING Sulaimon Mutiu O. Department of Statistics & Mathematics Moshood Abiola Polytechnic, Abeokuta, Ogun State, Nigeria. Abstract
THE USE OF REGRESSION ANALYSIS IN MARKETING RESEARCH
THE USE OF REGRESSION ANALYSIS IN MARKETING RESEARCH DUMITRESCU Luigi Lucian Blaga University of Sibiu, Romania STANCIU Oana Lucian Blaga University of Sibiu, Romania TICHINDELEAN Mihai Lucian Blaga University
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,
DAFTAR PUSTAKA. Arifin Ali, 2002, Membaca Saham, Edisi I, Yogyakarta : Andi. Bapepam, 2004, Ringkasan Data Perusahaan, Jakarta : Bapepam
03 DAFTAR PUSTAKA Arifin Ali, 00, Membaca Saham, Edisi I, Yogyakarta : Andi Bapepam, 004, Ringkasan Data Perusahaan, Jakarta : Bapepam Darmadji Tjiptono dan Fakhruddin M Hendy, 006, Pasar Modal di Indonesia,
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
THE IMPACT OF LOGISTICS PERFORMANCE ON ORGANIZATIONAL PERFORMANCE IN A SUPPLY CHAIN CONTEXT
Available online at http://cjlscience.org/ ISSN: 972-847 Vol. 17 No. 1 18-117 215 THE IMPACT OF LOGISTICS PERFORMANCE ON ORGANIZATIONAL PERFORMANCE IN A SUPPLY CHAIN CONTEXT Khadijeh Kheyrabadi 1* and
Business Statistics. Successful completion of Introductory and/or Intermediate Algebra courses is recommended before taking Business Statistics.
Business Course Text Bowerman, Bruce L., Richard T. O'Connell, J. B. Orris, and Dawn C. Porter. Essentials of Business, 2nd edition, McGraw-Hill/Irwin, 2008, ISBN: 978-0-07-331988-9. Required Computing
1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number
1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number A. 3(x - x) B. x 3 x C. 3x - x D. x - 3x 2) Write the following as an algebraic expression
Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences
Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences Third Edition Jacob Cohen (deceased) New York University Patricia Cohen New York State Psychiatric Institute and Columbia University
COMPARISONS OF CUSTOMER LOYALTY: PUBLIC & PRIVATE INSURANCE COMPANIES.
277 CHAPTER VI COMPARISONS OF CUSTOMER LOYALTY: PUBLIC & PRIVATE INSURANCE COMPANIES. This chapter contains a full discussion of customer loyalty comparisons between private and public insurance companies
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
Chicago Booth BUSINESS STATISTICS 41000 Final Exam Fall 2011
Chicago Booth BUSINESS STATISTICS 41000 Final Exam Fall 2011 Name: Section: I pledge my honor that I have not violated the Honor Code Signature: This exam has 34 pages. You have 3 hours to complete this
Comparing a Multiple Regression Model Across Groups
Comparing a Multiple Regression Across Groups We might want to know whether a particular set of predictors leads to a multiple regression model that works equally effectively for two (or more) different
An Analysis of the Undergraduate Tuition Increases at the University of Minnesota Duluth
Proceedings of the National Conference On Undergraduate Research (NCUR) 2012 Weber State University March 29-31, 2012 An Analysis of the Undergraduate Tuition Increases at the University of Minnesota Duluth
Calculating the Probability of Returning a Loan with Binary Probability Models
Calculating the Probability of Returning a Loan with Binary Probability Models Associate Professor PhD Julian VASILEV (e-mail: vasilev@ue-varna.bg) Varna University of Economics, Bulgaria ABSTRACT The
6 Variables: PD MF MA K IAH SBS
options pageno=min nodate formdlim='-'; title 'Canonical Correlation, Journal of Interpersonal Violence, 10: 354-366.'; data SunitaPatel; infile 'C:\Users\Vati\Documents\StatData\Sunita.dat'; input Group
CORRELATION ANALYSIS
CORRELATION ANALYSIS Learning Objectives Understand how correlation can be used to demonstrate a relationship between two factors. Know how to perform a correlation analysis and calculate the coefficient
Correlation Coefficient The correlation coefficient is a summary statistic that describes the linear relationship between two numerical variables 2
Lesson 4 Part 1 Relationships between two numerical variables 1 Correlation Coefficient The correlation coefficient is a summary statistic that describes the linear relationship between two numerical variables
Data Mining and Data Warehousing. Henryk Maciejewski. Data Mining Predictive modelling: regression
Data Mining and Data Warehousing Henryk Maciejewski Data Mining Predictive modelling: regression Algorithms for Predictive Modelling Contents Regression Classification Auxiliary topics: Estimation of prediction
Statistics. Measurement. Scales of Measurement 7/18/2012
Statistics Measurement Measurement is defined as a set of rules for assigning numbers to represent objects, traits, attributes, or behaviors A variableis something that varies (eye color), a constant does
The Impact of Affective Human Resources Management Practices on the Financial Performance of the Saudi Banks
327 The Impact of Affective Human Resources Management Practices on the Financial Performance of the Saudi Banks Abdullah Attia AL-Zahrani King Saud University azahrani@ksu.edu.sa Ahmad Aref Almazari*
International 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
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,
Factor Analysis. Principal components factor analysis. Use of extracted factors in multivariate dependency models
Factor Analysis Principal components factor analysis Use of extracted factors in multivariate dependency models 2 KEY CONCEPTS ***** Factor Analysis Interdependency technique Assumptions of factor analysis
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
SPSS Guide How-to, Tips, Tricks & Statistical Techniques
SPSS Guide How-to, Tips, Tricks & Statistical Techniques Support for the course Research Methodology for IB Also useful for your BSc or MSc thesis March 2014 Dr. Marijke Leliveld Jacob Wiebenga, MSc CONTENT