Class 7 Everything is Related

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Martin Weaver
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1 Class 7 Everything is Related Correlational Designs l 1 Topics Types of Correlational Designs Understanding Correlation Reporting Correlational Statistics Quantitative Designs l 2 Types of Correlational Designs Explanatory Design Prediction Design l 3 1

2 Understanding Correlation the form of association (relationship) direction of the association degree of association l 4 A relationship between two variables Range from 1.00 to is perfect linear - is negative is positive direction l 5 Example of a Scatterplot Hours of Internet use per week Depression scores from Depression scores Y=D.V. - M 10 M Hours of Internet Use X=I.V. l 6-2

3 Patterns of Association Between Two Variables A. Positive Linear (r=.75) B. Negative Linear (r=-.68) l 7 Patterns of Association Between Two Variables C. No Correlation (r=.00) D. Curvilinear l 8 Patterns of Association Between Two Variables E. Curvilinear F. Curvilinear l 9 3

4 Pearson Product Moment correlation coefficient r = degree to which X and Y vary together degree to which X and Y vary separately l 10 Uses of r observer or judge reliability correlation of repeated observations test-retest reliability correlation of repeated test administrations internal consistency correlation of split-halves construct validity correlation among measures amount of variance accounted for r 2 confirm or disconfirm hypotheses Requires random sample and normal distribution l 11 Calculating Association Between Variables Display correlation coefficients in a matrix (r with p *) Calculate the coefficient of determination r 2 Test r 2 for statistical significance (effect size) l 12 4

5 Using Correlations For Prediction Use the correlation to predict future scores Plotting the scores provides information about the direction of the relationship Plotting correlation scores does not provide specific information about predicting scores from one value to another Use a regression line ( best fit for all ) for prediction Y (predicted) = b(x) a predicted Y, slope, score, constant (Y with X = 0) l 13 Simple Regression Line Depression Scores Regression Line 30 Slope Intercept Hours of Internet Use Per Week l 14 Rainbow, 1965 Musical Aptitude Source R R 2 SE F df Jr. High * 97 53% of variance in aptitude explained by the 14 variables Scores on the average range /-.46 from prediction The relationship was significant 98 participants l 15 5

6 Variable Β F Pitch discrimination Tonal memory Rhythm Musical memory Academic intelligence School achievement Gender Chronological age Musical achievement Musical training Home environment Interest in music Relatives in music Socioeconomic background * * * * 0.57 l 16 Other Correlation Coefficients Spearman rho (r s ) - correlation coefficient for nonlinear ordinal data Point-biserial - used to correlate continuous interval data with a dichotomous variable Phi-coefficient - used to determine the degree of association when both variable measures are dichotomous l 17 Advanced Statistical Procedures Partial Correlations - use to determine extent to which mediating variable influences both IV and DV Multiple Regression - multiple IVs may combine to correlate with a DV Path analysis Latent variable causal modeling (structural equation modeling) l 18 6

7 Common Variance Shared for Bivariate Correlation Independent Variable Practice Time r=.50 Dependent Variable Practice Time r 2 =.25 Shared Variance l 19 Common Variance Shared for Partial Correlation Independent Variable Practice Time Practice Time r=.50 Dependent Variable Motivation r 2 =.12 Shared Variance, effects of X2 removed l 20 Regression versus Path Analysis Regression Practice Time Motivation - Prior Achievement Practice Time Peer Friend Influence Path Analysis.13 Peer Achievement Motivation Peer Friend Influence l 21 7

8 Criteria For Evaluating Correlational Research 1. Is the size of the sample adequate for hypothesis testing? (sufficient power?) 2. Does the researcher adequately display the results in matrixes or graphs? 3. Is there an interpretation about the direction and magnitude of the association between the two variables? l Is there an assessment of the magnitude of the relationship based on the coefficient of determination, p-values, effect size, or the size of the coefficient? 5. Is the researcher concerned about the form of the relationship so that an appropriate statistic is chosen for analysis? l Has the researcher identified the predictor and criterion variables? 7. If a visual model of the relationships is advanced, does the researcher indicate the expected relationships among the variables, or, the predicted direction based on observed data? 8. Are the statistical procedures clearly defined? l 24 8

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On the purpose of testing: Why Evaluation & Assessment is Important Feedback to students Feedback to teachers Information to parents Information for selection and certification Information for accountability Incentives to increase