Education 795 Class Notes P-Values, Partial Correlation, Multi-Collinearity Note set 4.

Slides:



Advertisements
Similar presentations
Bivariate &/vs. Multivariate
Advertisements

Items to consider - 3 Multicollinearity
6-1 Introduction To Empirical Models 6-1 Introduction To Empirical Models.
Education 795 Class Notes Quasi-Experimental Design Path Analysis Note set 9.
1 Multiple Regression A single numerical response variable, Y. Multiple numerical explanatory variables, X 1, X 2,…, X k.
LINEAR REGRESSION: Evaluating Regression Models Overview Assumptions for Linear Regression Evaluating a Regression Model.
LINEAR REGRESSION: Evaluating Regression Models. Overview Assumptions for Linear Regression Evaluating a Regression Model.
Korelasi Ganda Dan Penambahan Peubah Pertemuan 13 Matakuliah: I0174 – Analisis Regresi Tahun: Ganjil 2007/2008.
Stat 512 – Lecture 18 Multiple Regression (Ch. 11)
Multiple Regression Models Advantages of multiple regression Important preliminary analyses Parts of a multiple regression model & interpretation Differences.
Multiple Regression Models: Some Details & Surprises Review of raw & standardized models Differences between r, b & β Bivariate & Multivariate patterns.
Multivariate Data Analysis Chapter 4 – Multiple Regression.
January 6, morning session 1 Statistics Micro Mini Multiple Regression January 5-9, 2008 Beth Ayers.
© 2003 Prentice-Hall, Inc.Chap 14-1 Basic Business Statistics (9 th Edition) Chapter 14 Introduction to Multiple Regression.
Lecture 6: Multiple Regression
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc. Chap 15-1 Chapter 15 Multiple Regression Model Building Basic Business Statistics 11 th Edition.
Correlational Designs
Chapter 7 Correlational Research Gay, Mills, and Airasian
Correlation and Regression Analysis
Chapter 14 Inferential Data Analysis
Multiple Regression Dr. Andy Field.
Relationships Among Variables
Correlation & Regression
Chapter 8 Forecasting with Multiple Regression
Statistics for the Social Sciences Psychology 340 Fall 2013 Tuesday, November 19 Chi-Squared Test of Independence.
Marketing Research Aaker, Kumar, Day and Leone Tenth Edition
Correlation and Regression
Elements of Multiple Regression Analysis: Two Independent Variables Yong Sept
© 2004 Prentice-Hall, Inc.Chap 15-1 Basic Business Statistics (9 th Edition) Chapter 15 Multiple Regression Model Building.
Lecture 14 Multiple Regression Model
© 2002 Prentice-Hall, Inc.Chap 14-1 Introduction to Multiple Regression Model.
Chapter 12 Examining Relationships in Quantitative Research Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin.
L 1 Chapter 12 Correlational Designs EDUC 640 Dr. William M. Bauer.
Extension to Multiple Regression. Simple regression With simple regression, we have a single predictor and outcome, and in general things are straightforward.
Multiple regression - Inference for multiple regression - A case study IPS chapters 11.1 and 11.2 © 2006 W.H. Freeman and Company.
Chapter 9 Analyzing Data Multiple Variables. Basic Directions Review page 180 for basic directions on which way to proceed with your analysis Provides.
Multiple Linear Regression. Purpose To analyze the relationship between a single dependent variable and several independent variables.
Power Point Slides by Ronald J. Shope in collaboration with John W. Creswell Chapter 12 Correlational Designs.
Chapter 4 Linear Regression 1. Introduction Managerial decisions are often based on the relationship between two or more variables. For example, after.
Lesson Multiple Regression Models. Objectives Obtain the correlation matrix Use technology to find a multiple regression equation Interpret the.
Regression Chapter 16. Regression >Builds on Correlation >The difference is a question of prediction versus relation Regression predicts, correlation.
11 Chapter 12 Quantitative Data Analysis: Hypothesis Testing © 2009 John Wiley & Sons Ltd.
SW388R6 Data Analysis and Computers I Slide 1 Multiple Regression Key Points about Multiple Regression Sample Homework Problem Solving the Problem with.
CORRELATION: Correlation analysis Correlation analysis is used to measure the strength of association (linear relationship) between two quantitative variables.
Chapter 16 Data Analysis: Testing for Associations.
MARKETING RESEARCH CHAPTER 18 :Correlation and Regression.
Regression Analysis © 2007 Prentice Hall17-1. © 2007 Prentice Hall17-2 Chapter Outline 1) Correlations 2) Bivariate Regression 3) Statistics Associated.
Education 795 Class Notes Introduction and Overview Note set 1.
© 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 1 Chapter 12 Testing for Relationships Tests of linear relationships –Correlation 2 continuous.
 Relationship between education level, income, and length of time out of school  Our new regression equation: is the predicted value of the dependent.
Correlation & Regression Analysis
I271B QUANTITATIVE METHODS Regression and Diagnostics.
Education 795 Class Notes Factor Analysis Note set 6.
Copyright © 2010 Pearson Education, Inc Chapter Seventeen Correlation and Regression.
Lesson 14 - R Chapter 14 Review. Objectives Summarize the chapter Define the vocabulary used Complete all objectives Successfully answer any of the review.
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 15-1 Chapter 15 Multiple Regression Model Building Basic Business Statistics 10 th Edition.
Multiple Regression David A. Kenny January 12, 2014.
26134 Business Statistics Week 4 Tutorial Simple Linear Regression Key concepts in this tutorial are listed below 1. Detecting.
Chapter 8 Relationships Among Variables. Outline What correlational research investigates Understanding the nature of correlation What the coefficient.
Multiple Independent Variables POLS 300 Butz. Multivariate Analysis Problem with bivariate analysis in nonexperimental designs: –Spuriousness and Causality.
Topics, Summer 2008 Day 1. Introduction Day 2. Samples and populations Day 3. Evaluating relationships Scatterplots and correlation Day 4. Regression and.
Market Intelligence Class 11. Regression - Basics Terminology – In simple regression with a single variable, we get a zero-order effect (full effect)
26134 Business Statistics Week 4 Tutorial Simple Linear Regression Key concepts in this tutorial are listed below 1. Detecting.
Chapter 12 REGRESSION DIAGNOSTICS AND CANONICAL CORRELATION.
Yandell – Econ 216 Chap 15-1 Chapter 15 Multiple Regression Model Building.
The Problem of Large Correlations Among the Independent Variables
Regression Diagnostics
Multiple Regression – Part II
Product moment correlation
Regression Part II.
Presentation transcript:

Education 795 Class Notes P-Values, Partial Correlation, Multi-Collinearity Note set 4

Today’s Agenda Announcements (ours and yours) Q/A? Leveraging what we already know Partial Correlation and Multi-Collinearity

P-Values “p-value refers to the probability of the evidence having arisen as a result of sampling error given that the null hypothesis is true” (Pedhazur & Pedhazure, 1991) What is inherently wrong the p-values? Why do we use them?

P-Values “Even though I am very critical of statistical inference… I shall probably continue to pay homage to “tests of significance” in the papers I submit to psychological journals. My rationale for this admitted hypocrisy is straightforward: until the rules of the science game are changed, one must abide by at least some of the old rules, or drop out of the game” (Mahoney, 1976, p. xiii)

What to do? “Perhaps p values are like mosquitos. They have an evolutionary niche somewhere and no amount of scratching, swatting, or spraying will dislodge them” (Campbell, 1982, p 698)

Statistical Significance vs. Practical Significance We should refrain from what Tukey calls “statistical sanctification.” Concern with practical significance is addressed through effect sizes or relational magnitudes (betas in regression). “A difference is a difference only if it makes a difference” (Huff, 1954, p. 58)

Introduction to Effect Size Effect sizes imply strength of meaningfulness or importance General Rule set forth by Cohen (1988) for small, medium, large ES We will address how effect sizes are computed later in the course

Transition Back to Multiple Regression 1.Multiple predictors typically yield better technical solutions (e.g., higher R 2 ) 2.Multiple predictors provide opportunities to test more realistic models (e.g., why is nothing as simple as it should be?) 3.Multiple regression models allow for an examination of more complex research hypotheses than is possible with simple regression / correlation approaches

Regression Raw score depiction: where each b: is the unique and independent contribution of that predictor to the model for quantitative IVs, the expected direction and amount of change in the DV for each unit change in the IV, holding all other IVs constant For dichotomous IVs, the direction and amount of group mean difference on DV, holding all other IVs constant

Revisit  ’s Example: Dependent Variable: Promote Racial Understanding Independent Variable: Sex, Race  sex = r sex,promote if sex and race are not correlated. These are population based estimates and they are “effect sizes” because we can compare relative strength of predictors in the model In the Venn diagram on the following slide, note X1 and X2 are not correlated but X2 and X3 are

Venn Diagram Depiction Correlation Regression Coefficients

Warning Pedhazur believes that the topics of partial correlations and semi-partial correlations can be confusing and lead to misinterpretations of regression coefficients. Why talk about them? Awareness and enough knowledge to evaluate research where partials are used

Partial Correlations A variation on the idea of residualization (removal of the predictable part of y from y) First-order partial correlations: correlation of variable 1 and 2 partialling variable 3 from 1 and 2

Plug and Chug rQuizExamSpeedMotiv Quiz1.00 Exam Speed Motiv What is the correlation between quiz and exam score, controlling for test taking speed? 2. What is the correlation between exam score and motivation, controlling for test taking speed?

Semi-Partial Correlations r 1(2.3 ) =correlation of variables 1 and 2 after having partialed variable 3 only from variable 2. (semi-partial) VS r 12.3 =correlation of variables 1 and 2 after having partialed variable 3 from both variable 1 and variable 2 (partial)

Before Jumping Into Regression Examine the data using common-sense (e.g., are the data appropriate for producing interpretable correlation coefficients?) as well as standard diagnostic procedures Review the r among the predictors for collinearity problems

Multicollinearity Multicollinearity refers to correlations among the independent variables only Multicollinearity is measured by the tolerance statistic, defined as 1 – R 2 predicting each predictor using all other predictors (values close to 1 are better, values close to 0 are bad) Excessive collinearity (even singularity – perfect correlation between two or more IVs) suggests that predictors have extensive overlaps, and we may need to be selective in picking predictors or combining them (through factor analytic techniques)

Dangers Multicollinearity has adverse effects on regression analysis High multicollinearity leads to a reduction in the magnitude of the b’s High multicollinearity leads to inflated se’s, reducing the t-ratios for the coefficients

Solutions Be selective in choosing variables that are related Combine like variables into an index using scales or ‘factor analysis’ which we will talk about soon

Suppressors When a partial correlation is larger than the original r, it is considered to be the result of a suppressor effect Suppressor variables effectively mask (suppress) the relationship between other variables This effect occurs when there is an unbalanced mix of +/- correlations between the DV and the IVs

Project Activity Dataset: Chose a dataset and run a multiple regression Dependent variable: SATC=SATM+SATV Independent variables: sex, family income, mother’s education and father’s education Use syntax to get the tolerance statistic Rerun the regression summing mothers and fathers education into one variable. Compare the tolerance statistic for mothers and fathers education with the summed index.

For Next Week Read Pedhazur Ch 10 p Read Pedhazur Ch 14 p Read Pedhazur Ch 19 p Read Pedhazur Ch 21 p , p