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Chapter 8 Correlational (passive) research strategy

Chapter 8 Correlational (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. Nature of Correlational Research.

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Chapter 8 Correlational (passive) research strategy

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  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

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