Chapter 8 Correlational (passive) research strategy

1. Chapter 8Correlational (passive) research strategy • Nature of Correlational Research • Simple and Partial Correlational Analysis • Multiple Regression Analysis (MRA) • Some other Corr Techniques • Testing Mediational Hypotheses • Factor Analysis • Summary

2. Nature of Correlational Research • Assumptions of Linearity and Additivity • Linearity • Additivity • Assumes no interactions • Factors affecting Correlational Coefficient • Reliability of the measure • Restriction of range (p 226 fig 8-2) • Outliers (p 226, fig 8-2) ? Using your data set, insert an outlier that will cause the bivariate correlation to exceed significance beyond p <.001. what value was necessary to achieve it? • Subgroup Differences (227. fig 8.3))

3. Nature of Correlations (con’t) • Multifacted Constructs • Cf Abramson et al. attributional style v. Ohio State Leadership model • Keeping them separate • When theoretically distinct (constructs predict interaction) • Depression and attributional style • Three conditions (internal, stable, global) predict depression • When information would be lost (obscuring them in overall) • Antifat facets (4) have diff relationships to other constructs • Not simply for convenience • ? Describe a multfacted construct that plays a role in your theoretical framework • Combining them • When interested in latent variable variables

4. Multifaceted ConstructsRecommentations • 1. use reliable measures • 2. check the distribution • Compare sample to existing norms • 2. plot scores for subgroups and combined groups • 4. compute subgroup means and corr • Make sure they don’t adversely affect combined corr • 5. Have a good reason to combine facets

5. Simple and Partical Corr Analsys • Correlation coefficient (you know about this) • Differences in correlation coefficients • Fisher’s z transformation • Equality of r’s • Cohen & Cohen (1983) • Are > 2 r’s equal to one another? • Can relationships be different if r’s are same? • Yes, test slopes (unstandardized) if SDs differ • Check for moderators in the regression analysis

6. Partial Correlation • Controlling for a third variable • Feather (1985) p. 235 study with • Depression • Self-esteem • Masculinity • What better explains depression? Masc or SE? • Self esteem (masc and self-esteem were confounded)

7. Multiple Regression (MRA) • Difference between MC & MR • MC to establish relationships • Based on sample where Ps measured on all vars (IVs and DVs) • MR used to predict DV from IVs • When Ps are measured on only IVs • For example • Predicting success in a grad program • Predicting likelihood of suicide • Ypred = a + b1X1 + b2X2 …+ bkXk ? Which of your predictors in Lab 4 accounts for the largest and smallest amounts of variance in your criterion?

8. MRA Forms • Simultaneous (use) • All predictors considered at once regardless of value of each predictor • Hierarchical (use) (table 8-5, p. 238) • User decides order of consideration • Which predictors should be controlled for • For theory testing or practical needs • Stepwise (may be problematic)

9. Information from MRA • Multiple correlation coefficient R • R2 degree of association • % variance accounted for by all predictors • Coefficient • b weight = raw (unstandardized) scores • β (beta) weight = standardized score • Allows direct comparision of weights • Change in R2 (In hierarchial MRA) • To show how much incremental variance each predictor adds • Be careful…order of entry is important ? What is the difference between multiple correlation and multiple regression?

10. Multicollinearity two or more predictors are highly related (r>.8) Effects of multicollinearity: 1. inflates Standard Errors of regression 2. large errors lead to non sig predictors Causes 1. multiple measures of same construct - use latent variable approach 2. sampling error (accidentally oversampling highor low Ps on a variable)

11. Multicollinearity • Detecting Multicollinearity • Look at correlation matrix for r’s > .8 • Run series of MR to detect Rs > .0 • Check for VIF >10 • Dealing with it • Avoid redundant vars • Use vars with least intercorrelation • Factor analyze to combine vars

12. MRA instead of ANOVA • Moderated MR (similar to ANCOVA) • To test interaction • Compute an interaction term (IV1 * IV2) in spss • Enter the interaction term AFTER main effects in MR (blocks) • Use instead of ANOVA • When one or more IVs are continuous • When IVs are correlated (ANOVA assumes IVs are uncorrelated) • Transforming continuous to dichotomous vars • Using median split,,,not usually a good idea! • Reduces power (loses precision) • Gives false “effect” when two median splits are used • Just say “no”…to median split

13. Other Correlational Techniques • Logistic regression • Set of continuous IVs to predict categorical criterion (DV) • Gives estimate of probability of group membership ? Give an example of how you could use logistic regression in your project. • Multiway frequency analysis • Analyze pattern of relationships among set of nominal vars (X2) • Loglinear analysis extends chi sq to > 2 vars • Logit analysis (when vars are considered IVs and DV) • ANOVA for categorical vars

14. Testing Mediational Hypotheses • IV -> M -> DV • See Condon & & Crano (1988) ? Give an example of a mediating variable that could play a role in your project • Similarity< Other like us?> =Attraction • Simple mediation (3 Vars) • Complex models • Path analysis (SEM) fig 8-7, p. 248 • Latent vars analysis • Covariance structure analysis (LISREL) • Prospective research (fig 8-8, p. 249) • Cross lagged correlational analysis

15. Limits on Interpretation (path analysis) • Completeness of model • Are all vars considered? • Any curvilinear or non additive relationships? • Alternative Models • What other competing theories?

16. Factor Analysis • A statistical means for finding constructs within a set of variables • Identifies sets of items are most related to one another • Latent variables or constructs (e.g. attitudes toward computers) • Factors: • 1. anxiety toward them • 2. perceived positive effects on society • 3. perceived negative effects on society • 4. personal usefulness of them

17. Factor Analysis (EFA) • Uses (Exploratory) • Data reduction • Scale development • Considerations • Numbers of Ps needed (a lot): 200-300 • Quality of data • Methods of factor extraction and rotation • Determining num of factors • Interpreting the factors • Retaining factor scores • CFA (confirmatory FA)

18. Correlational Analsyses • Nature of Correlational Research • Simple and Partial Correlational Analysis • Multiple Regression Analysis (MRA) • Some other Corr Techniques • Testing Mediational Hypotheses • Factor Analysis