Chapter 8 Correlational passive research strategy

1. 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. 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. 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. 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. 5 Simple and Partial Corr Analsys Correlation coefficient (you know about this) Differences in correlation coefficients Fisher�s z transformation Equality of r�s Cohen & Cohen (1983) Can relationships be different if r�s are same? Yes, test slopes (unstandardized) if SDs differ Check for moderators in the regression analysis

6. 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. 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

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

9. 9 Information from MRA Multiple correlation coefficient R R2 degree of association % variance accounted for by all predictors Coefficient b weight = raw (unstandardized) scores � (beta) weight = standardized score Allows direct comparison of weights Change in R2 (In hierarchical 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. 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 over-sampling high or low Ps on a variable)

11. 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. 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. 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 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 one is a DV) ANOVA for categorical vars

14. 14 Testing Mediational Hypotheses p 246 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. 15 Limits on Interpretation (path analysis) Completeness of model Are all vars considered? Any curvilinear or non additive relationships? Alternative Models (p 252 fig 8-10) What other competing theories?

16. 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. 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. 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