Chapter 8 Correlational passive research strategy

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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

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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 lt.001. what value was
  necessary to achieve it?
• Subgroup Differences (227. fig 8.3))

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Nature of Correlations (cont)

• 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

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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 dont adversely affect combined
  corr
• 5. Have a good reason to combine facets

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Simple and Partial Corr Analsys

• Correlation coefficient (you know about this)
• Differences in correlation coefficients
• Fishers z transformation
• Equality of rs
• Cohen Cohen (1983)
• Can relationships be different if rs are same?
• Yes, test slopes (unstandardized) if SDs differ
• Check for moderators in the regression analysis

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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)

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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

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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)

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Information from MRA

• Multiple correlation coefficient R
• R2 degree of association
• variance accounted for by all predictors
• Coefficient
• b weight raw (unstandardized) scores
• ß (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 carefulorder of entry is important
• ? What is the difference between multiple
  correlation and multiple regression?

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Multicollinearity

• two or more predictors are highly related (rgt.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)

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Multicollinearity

• Detecting Multicollinearity
• Look at correlation matrix for rs gt .8
• Run series of MR to detect Rs gt .0
• Check for VIF gt10
• Dealing with it
• Avoid redundant vars
• Use vars with least intercorrelation
• Factor analyze to combine vars

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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 noto median split

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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 gt 2 vars
• Logit analysis (when vars are considered IVs and
  one is a DV)
• ANOVA for categorical vars

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Testing Mediational Hypotheses p 246

• IV -gt M -gt DV
• See Condon Crano (1988)
• ? Give an example of a mediating variable that
  could play a role in your project
• Similaritylt Other like us?gt 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

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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?

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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

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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)

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Correlational Analsyses

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