Wednesday AM  Presentation of yesterday’s results  Associations  Correlation  Linear regression  Applications: reliability.

Slides:



Advertisements
Similar presentations
Chapter 16: Correlation.
Advertisements

Correlation, Reliability and Regression Chapter 7.
CORRELATION. Overview of Correlation u What is a Correlation? u Correlation Coefficients u Coefficient of Determination u Test for Significance u Correlation.
Correlation Chapter 6. Assumptions for Pearson r X and Y should be interval or ratio. X and Y should be normally distributed. Each X should be independent.
Correlation and Linear Regression.
Bivariate and Partial Correlations. X (HT) Y (WT) The Graphical View– A Scatter Diagram X’ Y’
Correlation CJ 526 Statistical Analysis in Criminal Justice.
Correlation Chapter 9.
Correlation. Introduction Two meanings of correlation –Research design –Statistical Relationship –Scatterplots.
CORRELATION. Overview of Correlation u What is a Correlation? u Correlation Coefficients u Coefficient of Determination u Test for Significance u Correlation.
CJ 526 Statistical Analysis in Criminal Justice
Bivariate Regression CJ 526 Statistical Analysis in Criminal Justice.
Chapter Eighteen MEASURES OF ASSOCIATION
Analyzing quantitative data – section III Week 10 Lecture 1.
Perfect Negative Correlation Perfect Positive Correlation Non-Existent Correlation Imperfect Negative Correlation Imperfect Positive Correlation.
Correlational Designs
Correlation 1. Correlation - degree to which variables are associated or covary. (Changes in the value of one tends to be associated with changes in the.
Summary of Quantitative Analysis Neuman and Robson Ch. 11
Correlation Question 1 This question asks you to use the Pearson correlation coefficient to measure the association between [educ4] and [empstat]. However,
Review Regression and Pearson’s R SPSS Demo
Correlation Coefficient Correlation coefficient refers to the type of relationship between variables that allows one to make predications from one variable.
Correlational Research Strategy. Recall 5 basic Research Strategies Experimental Nonexperimental Quasi-experimental Correlational Descriptive.
Chapter 21 Correlation. Correlation A measure of the strength of a linear relationship Although there are at least 6 methods for measuring correlation,
Inferential statistics Hypothesis testing. Questions statistics can help us answer Is the mean score (or variance) for a given population different from.
Leedy and Ormrod Ch. 11 Gray Ch. 14
PRED 354 TEACH. PROBILITY & STATIS. FOR PRIMARY MATH Lesson 14 Correlation & Regression.
Chapter 12 Correlation and Regression Part III: Additional Hypothesis Tests Renee R. Ha, Ph.D. James C. Ha, Ph.D Integrative Statistics for the Social.
Variability Range, variance, standard deviation Coefficient of variation (S/M): 2 data sets Value of standard scores? Descriptive Statistics III REVIEW.
Bivariate Correlation Lesson 10. Measuring Relationships n Correlation l degree relationship b/n 2 variables l linear predictive relationship n Covariance.
ASSOCIATION BETWEEN INTERVAL-RATIO VARIABLES
Learning Objective Chapter 14 Correlation and Regression Analysis CHAPTER fourteen Correlation and Regression Analysis Copyright © 2000 by John Wiley &
Copyright © 2010 Pearson Education, Inc Chapter Seventeen Correlation and Regression.
L 1 Chapter 12 Correlational Designs EDUC 640 Dr. William M. Bauer.
Bivariate Correlation Lesson 11. Measuring Relationships n Correlation l degree relationship b/n 2 variables l linear predictive relationship n Covariance.
Experimental Research Methods in Language Learning Chapter 11 Correlational Analysis.
Copyright © 2010 Pearson Education, Inc Chapter Seventeen Correlation and Regression.
Multiple Linear Regression. Purpose To analyze the relationship between a single dependent variable and several independent variables.
Examining Relationships in Quantitative Research
Correlation & Regression Chapter 15. Correlation It is a statistical technique that is used to measure and describe a relationship between two variables.
Copyright © 2010 Pearson Education, Inc Chapter Seventeen Correlation and Regression.
Chapter 16 Data Analysis: Testing for Associations.
Examining Relationships in Quantitative Research
Copyright © 2010 Pearson Education, Inc Chapter Seventeen Correlation and Regression.
Linear Correlation. PSYC 6130, PROF. J. ELDER 2 Perfect Correlation 2 variables x and y are perfectly correlated if they are related by an affine transform.
The basic task of most research = Bivariate Analysis
Statistical Analysis. Z-scores A z-score = how many standard deviations a score is from the mean (-/+) Z-scores thus allow us to transform the mean to.
© Buddy Freeman, 2015 Let X and Y be two normally distributed random variables satisfying the equality of variance assumption both ways. For clarity let.
Module 8: Correlations. Overview: Analyzing Correlational Data “Eyeballing” scatterplots Coming up with a number What does it tell you? Things to watch.
1.What is Pearson’s coefficient of correlation? 2.What proportion of the variation in SAT scores is explained by variation in class sizes? 3.What is the.
Analysis of Variance ANOVA. Example Suppose that we have five educational levels in our population denoted by 1, 2, 3, 4, 5 We measure the hours per week.
LESSON 6: REGRESSION 2/21/12 EDUC 502: Introduction to Statistics.
Multiple Regression. PSYC 6130, PROF. J. ELDER 2 Multiple Regression Multiple regression extends linear regression to allow for 2 or more independent.
PART 2 SPSS (the Statistical Package for the Social Sciences)
Research Methodology Lecture No :26 (Hypothesis Testing – Relationship)
Week of March 23 Partial correlations Semipartial correlations
Bivariate Correlation Lesson 15. Measuring Relationships n Correlation l degree relationship b/n 2 variables l linear predictive relationship n Covariance.
Correlations: Linear Relationships Data What kind of measures are used? interval, ratio nominal Correlation Analysis: Pearson’s r (ordinal scales use Spearman’s.
STATISTICAL TESTS USING SPSS Dimitrios Tselios/ Example tests “Discovering statistics using SPSS”, Andy Field.
Chapter 11 Linear Regression and Correlation. Explanatory and Response Variables are Numeric Relationship between the mean of the response variable and.
McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc.,All Rights Reserved. Part Four ANALYSIS AND PRESENTATION OF DATA.
Chapter 2 Bivariate Data Scatterplots.   A scatterplot, which gives a visual display of the relationship between two variables.   In analysing the.
Dr. Siti Nor Binti Yaacob
Chapter 10 CORRELATION.
Regression Analysis.
Dr. Siti Nor Binti Yaacob
SPSS OUTPUT & INTERPRETATION
BIVARIATE REGRESSION AND CORRELATION
SPSS OUTPUT & INTERPRETATION
Bivariate Linear Regression July 14, 2008
Correlation and Prediction
Presentation transcript:

Wednesday AM  Presentation of yesterday’s results  Associations  Correlation  Linear regression  Applications: reliability

Associations  We’re often interested in the association between two variables, especially two interval scales.  Associations are measured by their: direction (positive, negative, u-shaped, etc.) direction (positive, negative, u-shaped, etc.) magnitude (how well can you predict one variable by knowing the score on the other?) magnitude (how well can you predict one variable by knowing the score on the other?)

Correlation  The (Pearson) correlation (r) between two variables is the most common measure of association Varies from -1 to 1 Varies from -1 to 1 Sign represents direction Sign represents direction r 2 is the proportion of variance in common between the two variables (how much one can account for in the other) r 2 is the proportion of variance in common between the two variables (how much one can account for in the other) Relationship is assumed to be linear Relationship is assumed to be linear

Correlation in SPSS  Analyze…Correlate…Bivariate  Enter variables to be correlated with one other. Q1Q2Q3 Q1Q2Q3 Q1Pearson Correlation Sig. (2-tailed) Sig. (2-tailed) N N Q2Pearson Correlation Sig. (2-tailed) Sig. (2-tailed) N N Q3Pearson Correlation Sig. (2-tailed) Sig. (2-tailed) N N  There was a significant positive correlation between Q2 and Q3 (r = 0.62, p <.05).

Linear regression  Correlation is a measure of association based on a linear fit.  Linear regression provides the equation for the line itself (e.g. Y = b 1 X + b 0 )  That is, in addition to providing a correlation, it tells how much change in the independent variable is produced by a given change in the dependent variable... ... in both natural units and standardized units.

Linear regression in SPSS  Analyze…Regression…Linear  Enter dependent and independent variables  Three parts to output: Model summary: how well did the line fit? Model summary: how well did the line fit? ANOVA table: did the line fit better than a null model? ANOVA table: did the line fit better than a null model? Regression equation: what is the line? How much change in the dependent variable do you get from a 1 unit (or 1 standard deviation) change in the independent variable Regression equation: what is the line? How much change in the dependent variable do you get from a 1 unit (or 1 standard deviation) change in the independent variable

Linear regression output  Predicting Q2 from Q3: Model Summary RR SquareAdjusted R Square  R is the correlation  R 2, the squared correlation, is proportion of variance in Q2 accounted for by variance in Q3  Adjusted R 2 is a less optimistic estimate

Linear regression output ANOVA Sum of SqdfMean SquareFSig. Regression Residual Total  Shows that the regression equation accounts for a significant amount of the variance in the dependent variable compared to a null model.  (A null model is a model that says that the mean of Q2 is the predicted Q2 for all subjects).

Linear regression ouput Coefficients UnstandardizedStandardized UnstandardizedStandardized BStd. ErrorBetatSig BStd. ErrorBetatSig (Constant) Q  Unstandardized coefficients (B) give the actual equation: Q2 = * Q These are raw units. An increase of 1 point in Q3 increases Q2 by points on average. People who have Q3 = 0 have Q2 = on average, etc. These are raw units. An increase of 1 point in Q3 increases Q2 by points on average. People who have Q3 = 0 have Q2 = on average, etc. Because SE of B is estimated, we can perform t-tests to see if a B is significantly different than 0 (has a significant effect). Because SE of B is estimated, we can perform t-tests to see if a B is significantly different than 0 (has a significant effect).  Standardized coefficients (  ) give the amount of change in Q2 caused by a change in Q3, measured in standard deviation units. They are useful in multiple regression (later)...

Measuring reliability of a scale  Test-retest reliability is usually measured as the correlation between tests (ranks of subjects stay the same at each testing)  Cronbach’s  is another common internal reliability measure based on the average inter-item correlation of items in a scale.

Cronbach’s  in SPSS  Analyze…Scale...Reliability analysis  Enter item variables that make up the scale  Go to Statistics dialog box and ask for scale and scale if item deleted descriptives.

Cronbach’s  in SPSS Item-total Statistics ScaleScaleCorrected MeanVarianceItem-Alpha if Itemif ItemTotalif Item DeletedDeletedCorrelationDeleted Q Q Q Q Q Reliability Coefficients N of Cases= N of Items= 5 Alpha=.6229Standardized item alpha=.6367

Wednesday AM assignment  Using the clerksp data set: Examine the correlations between items 1-17 (self- ratings of different clerkship skills). What do you notice about the correlation matrix? Examine the correlations between items 1-17 (self- ratings of different clerkship skills). What do you notice about the correlation matrix? Select any one of those 17 items. Run a linear regression to determine if the pre-clerkship rating on that item predicts the post-clerkship rating. Select any one of those 17 items. Run a linear regression to determine if the pre-clerkship rating on that item predicts the post-clerkship rating. Assume that we want to combine post-clerkship items 1-17 into a single scale of self-related clerk skill. What would the reliability of this scale be? Assume that we want to combine post-clerkship items 1-17 into a single scale of self-related clerk skill. What would the reliability of this scale be?