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Chapter 8Chapter 8Correlational (passive) research strategyCorrelational (passive) research strategy

Nature of Correlational ResearchNature of Correlational Research Simple and Partial Correlational AnalysisSimple and Partial Correlational Analysis Multiple Regression Analysis (MRA)Multiple Regression Analysis (MRA) Some other Corr TechniquesSome other Corr Techniques Testing Mediational HypothesesTesting Mediational Hypotheses Factor AnalysisFactor Analysis SummarySummary

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Nature of Correlational ResearchNature of Correlational Research

Assumptions of Linearity and Additivity Assumptions of Linearity and Additivity – LinearityLinearity– AdditivityAdditivity

Assumes no interactionsAssumes no interactions

Factors affecting Correlational CoefficientFactors affecting Correlational Coefficient– Reliability of the measureReliability of the measure– Restriction of range (p 226 fig 8-2)Restriction of range (p 226 fig 8-2)– Outliers (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 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? exceed significance beyond p <.001. what value was necessary to achieve it?

– Subgroup Differences (227. fig 8.3))Subgroup Differences (227. fig 8.3))

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Nature of Correlations (con’t)Nature of Correlations (con’t)

Multifacted ConstructsMultifacted Constructs Cf Abramson et al. attributional style v. Ohio State Leadership modelCf Abramson et al. attributional style v. Ohio State Leadership model

– Keeping them separateKeeping them separate When theoretically distinct (constructs predict interaction)When theoretically distinct (constructs predict interaction)

– Depression and attributional style Depression and attributional style – Three conditions (internal, stable, global) predict depressionThree conditions (internal, stable, global) predict depression

When information would be lost (obscuring them in overall)When information would be lost (obscuring them in overall)– Antifat facets (4) have diff relationships to other constructsAntifat facets (4) have diff relationships to other constructs

Not simply for convenienceNot simply for convenience ? Describe a multfacted construct that plays a role in your ? Describe a multfacted construct that plays a role in your

theoretical frameworktheoretical framework

– Combining themCombining them When interested in latent variable variablesWhen interested in latent variable variables

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Multifaceted ConstructsMultifaceted ConstructsRecommentationsRecommentations

– 1. use reliable measures1. use reliable measures– 2. check the distribution 2. check the distribution

Compare sample to existing normsCompare sample to existing norms

– 2. plot scores for subgroups and combined groups2. plot scores for subgroups and combined groups– 4. compute subgroup means and corr4. compute subgroup means and corr

Make sure they don’t adversely affect combined corrMake sure they don’t adversely affect combined corr

– 5. Have a good reason to combine facets5. Have a good reason to combine facets

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Simple and Partical Corr AnalsysSimple and Partical Corr Analsys

Correlation coefficient (you know about this)Correlation coefficient (you know about this) Differences in correlation coefficientsDifferences in correlation coefficients

– Fisher’s Fisher’s zz transformation transformation Equality of r’sEquality of r’s

– Cohen & Cohen (1983)Cohen & Cohen (1983) Are > 2 r’s equal to one another?Are > 2 r’s equal to one another? Can relationships be different if r’s are same?Can relationships be different if r’s are same?

– Yes, test slopes (unstandardized) if SDs differYes, test slopes (unstandardized) if SDs differ– Check for moderators in the regression analysisCheck for moderators in the regression analysis

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Partial CorrelationPartial Correlation

Controlling for a third variableControlling for a third variable Feather (1985) p. 235 study withFeather (1985) p. 235 study with

– DepressionDepression– Self-esteemSelf-esteem– MasculinityMasculinity

What better explains depression? Masc or SE?What better explains depression? Masc or SE?– Self esteem (masc and self-esteem were confounded)Self esteem (masc and self-esteem were confounded)

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Multiple Regression (MRA)Multiple Regression (MRA)

Difference between MC & MRDifference between MC & MR– MC to establish relationships MC to establish relationships

Based on sample where Ps measured on all vars (IVs and DVs)Based on sample where Ps measured on all vars (IVs and DVs)

– MR used to predict DV from IVsMR used to predict DV from IVs When Ps are measured on only IVsWhen Ps are measured on only IVs

For exampleFor example– Predicting success in a grad programPredicting success in a grad program– Predicting likelihood of suicidePredicting likelihood of suicide

YYpredpred = = aa + + bb11XX11 + + bb22XX22 …+ …+ bbkkXXkk

? ? Which of your predictors in Lab 4 accounts for the largest and smallest Which of your predictors in Lab 4 accounts for the largest and smallest amounts of variance in your criterion?amounts of variance in your criterion?

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MRA FormsMRA Forms

Simultaneous (use)Simultaneous (use)– All predictors considered at once regardless of value of All predictors considered at once regardless of value of

each predictoreach predictor Hierarchical (use) Hierarchical (use) (table 8-5, p. 238)(table 8-5, p. 238)

– User decides order of considerationUser decides order of consideration Which predictors should be controlled forWhich predictors should be controlled for For theory testing or practical needsFor theory testing or practical needs

Stepwise (may be problematic)Stepwise (may be problematic)

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Information from MRAInformation from MRA

Multiple correlation coefficient Multiple correlation coefficient RR– RR2 2 degree of association degree of association

% variance accounted for by all predictors% variance accounted for by all predictors

– CoefficientCoefficient bb weight = raw (unstandardized) scores weight = raw (unstandardized) scores ββ (beta) (beta) weight = standardized scoreweight = standardized score

– Allows direct comparision of weightsAllows direct comparision of weights

– Change in Change in RR2 2 (In hierarchial MRA)(In hierarchial MRA) To show how much incremental variance each predictor addsTo show how much incremental variance each predictor adds Be careful…order of entry is importantBe careful…order of entry is important

? What is the difference between multiple correlation and multiple ? What is the difference between multiple correlation and multiple regression? regression?

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Multicollinearity Multicollinearity

two or more predictors are highly related (two or more predictors are highly related (rr>.8)>.8)

Effects of multicollinearity:Effects of multicollinearity:

1. inflates Standard Errors of regression1. inflates Standard Errors of regression

2. large errors lead to non sig predictors2. large errors lead to non sig predictors

CausesCauses

1. multiple measures of same construct1. multiple measures of same construct

- use latent variable approach- use latent variable approach

2. sampling error 2. sampling error

(accidentally oversampling highor low Ps on a variable)(accidentally oversampling highor low Ps on a variable)

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MulticollinearityMulticollinearity

Detecting MulticollinearityDetecting Multicollinearity– Look at correlation matrix for Look at correlation matrix for r’r’s > .8s > .8– Run series of MR to detect Run series of MR to detect RRs > .0s > .0– Check for VIF >10Check for VIF >10

Dealing with itDealing with it– Avoid redundant varsAvoid redundant vars– Use vars with least intercorrelationUse vars with least intercorrelation– Factor analyze to combine varsFactor analyze to combine vars

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MRA instead of ANOVAMRA instead of ANOVA

Moderated MR (similar to ANCOVA)Moderated MR (similar to ANCOVA)– To test interactionTo test interaction

Compute an interaction term (IV1 * IV2) in spssCompute an interaction term (IV1 * IV2) in spss Enter the interaction term AFTER main effects in MR (blocks)Enter the interaction term AFTER main effects in MR (blocks)

– Use instead of ANOVA Use instead of ANOVA When one or more IVs are continuousWhen one or more IVs are continuous When IVs are correlated (ANOVA assumes IVs are uncorrelated)When IVs are correlated (ANOVA assumes IVs are uncorrelated)

– Transforming continuous to dichotomous varsTransforming continuous to dichotomous vars Using median split,,,not usually a good idea!Using median split,,,not usually a good idea! Reduces power (loses precision)Reduces power (loses precision) Gives false “effect” when two median splits are usedGives false “effect” when two median splits are used

– Just say “no”…to median split Just say “no”…to median split

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Other Correlational TechniquesOther Correlational Techniques

Logistic regressionLogistic regression– Set of continuous IVs to predict categorical criterion Set of continuous IVs to predict categorical criterion

(DV)(DV)– Gives estimate of probability of group membershipGives estimate of probability of group membership

? Give an example of how you could use logistic regression in your ? Give an example of how you could use logistic regression in your project.project.

Multiway frequency analysisMultiway frequency analysis– Analyze pattern of relationships among set of nominal Analyze pattern of relationships among set of nominal

vars (vars (XX22)) Loglinear analysis extends chi sq to > 2 varsLoglinear analysis extends chi sq to > 2 vars Logit analysis (when vars are considered IVs and DV)Logit analysis (when vars are considered IVs and DV)

– ANOVA for categorical varsANOVA for categorical vars

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Testing Mediational HypothesesTesting Mediational Hypotheses

IV -> M -> DVIV -> M -> DV– See Condon & & Crano (1988)See Condon & & Crano (1988)

? Give an example of a mediating variable that could play a role in your ? Give an example of a mediating variable that could play a role in your projectproject

Similarity< Other like us?> =Attraction Similarity< Other like us?> =Attraction Simple mediation (3 Vars)Simple mediation (3 Vars) Complex models Complex models

– Path analysis (SEM) Path analysis (SEM) fig 8-7, p. 248fig 8-7, p. 248

– Latent vars analysis Latent vars analysis Covariance structure analysis (Covariance structure analysis (LISRELLISREL))

Prospective research (Prospective research (fig 8-8, p. 249fig 8-8, p. 249))– Cross lagged correlational analysisCross lagged correlational analysis

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Limits on Interpretation (path analysis)Limits on Interpretation (path analysis)

Completeness of modelCompleteness of model– Are all vars considered?Are all vars considered?– Any curvilinear or non additive relationships?Any curvilinear or non additive relationships?

Alternative ModelsAlternative Models– What other competing theories?What other competing theories?

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Factor AnalysisFactor Analysis

A statistical means for finding constructs within a A statistical means for finding constructs within a set of variablesset of variables– Identifies sets of items are most related to one another Identifies sets of items are most related to one another

Latent variables or constructs (e.g. attitudes toward computers)Latent variables or constructs (e.g. attitudes toward computers) Factors: Factors:

– 1. anxiety toward them 1. anxiety toward them – 2. perceived positive effects on society2. perceived positive effects on society– 3. perceived negative effects on society3. perceived negative effects on society– 4. personal usefulness of them4. personal usefulness of them

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Factor Analysis (EFA)Factor Analysis (EFA)

Uses (Exploratory)Uses (Exploratory)– Data reduction Data reduction – Scale developmentScale development

ConsiderationsConsiderations– Numbers of Ps needed (a lot): 200-300Numbers of Ps needed (a lot): 200-300– Quality of dataQuality of data– Methods of factor extraction and rotationMethods of factor extraction and rotation– Determining num of factorsDetermining num of factors– Interpreting the factorsInterpreting the factors– Retaining factor scoresRetaining factor scores

CFA (confirmatory FA)CFA (confirmatory FA)

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Correlational AnalsysesCorrelational Analsyses

Nature of Correlational ResearchNature of Correlational Research Simple and Partial Correlational AnalysisSimple and Partial Correlational Analysis Multiple Regression Analysis (MRA)Multiple Regression Analysis (MRA) Some other Corr TechniquesSome other Corr Techniques Testing Mediational HypothesesTesting Mediational Hypotheses Factor AnalysisFactor Analysis