Passive Observational Correlational Research

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Passive Observational (Correlational) Research

• January 29

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Objectives

• Distinguish correlational from experimental.
• Describe why linearity, additivity, reliability,
  restriction of range, outliers, subgroup
  differences, and multicollinearity are issues,
  how to test for them, and what to do about them.
• Describe a suppressor and other partial
  correlation effects.
• Describe information available from MRA and
  relation to ANOVA.
• Describe the advantages and disadvantages of
  path, latent, discriminant, loglinear, and factor
  analysis and when and how to use each.

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Correlational Research

• Misnomer
• Passive observation (no manipulation of
  variables)
• Can use ANOVA (or can use correlational on
  experimental data)
• All forms of general linear model
• _________________________ are misapplied terms

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Linearity

• Correlation and Regression describe a line (with
  correlation the difference in standard deviations
  are corrected)
• However, can transform data or use power terms to
  describe curves
• E.g., test the significance of a squared term
• Another test of curvilinearity is to categorize
  the data, apply ANOVA, get an eta and compare it
  to r
• Finally, one could look at residuals

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Additivity

• Regression does not assume independence of
  predictors
• Does assume additive, but can test products
• E.g., moderation
• Can test incremental validity
• Does variable add significantly to explained
  variance?
• What is amazing is

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Reliability

• Reliability of measures attenuates r
• Can correct to estimate true effect, but depends
  on purpose (used in meta-analysis and SEM)
• If assessing criterion-related validity of scores
  of predictor, cannot correct for predictor
  unreliability (e.g., validity of
  marker/predictor)
• If seek estimate of true relationship, okay to
  correct both, provided each has reasonable level
  of reliability

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Restriction of range

• Consider correlation between GRE of Yale graduate
  students and success in graduate school

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Outliers and Subgroup Differences

• Outliers are extreme values
• They can occur in either experimental or
  correlation research.
• Analyze with and without
• Subgroup differences
• If same level of analysis
• Test product term
• Test for significant differences of simple mean
  intercepts
• If different level of analysis use multilevel
  modeling (e.g. HLM)

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better
performance
worse
low
high
Self-efficacy
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Partial and Multiple Correlation

• Effects of each variable partialled from others

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Partial Correlations
Y
X
Z
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Suppressor Effects
Y
Z
X
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Multicollinearity

• R of .90 or r of .80 between exogenous variables
• Creates unstable beta weights
• Suggests multi-measures of single construct
• i.e., Good thing

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Moderation v. mediation

• Moderation When, who, or which
• Nature of relationship between two variables
  depends on level of third (moderator) variable
• Mediation Why
• A third variable represents the mechanism through
  which a relationship between two other variables
  flow

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Representations (modalities)

• Path
• statistical
• Graphs

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Path Presentation
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Path (statistical) Presentation
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Graphs (Moderation)Crossover Interaction
high
Level 1
DV
Level 2
low
low
high
IV
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Why MHR
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Graphs (Moderation)No Effect Interaction
high
Level 1
DV
Level 2
low
low
high
IV
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Graphs (Moderation)Skewed Interaction
high
Level 1
Level 2
DV
low
low
high
IV
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Problems with tests of moderation

• Significance of c issue
• difficult (low power) if main effects
• Some argue spurious if random variables
• Use interaction term rather than simple main
  effects
• What is moderating what?

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Graphs (Mediation)(not done this way)
high
DV
low
low
high
IV
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Path (statistical) Presentation
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Problems with tests of mediation

• Significance of c issue
• .31 .30, ns
• .45.30
• Report effect sizes!
• Sobel test (http//quantrm2.psy.ohio-state.edu/kri
  s/sobel/sobel.htm)
• Unreliability of mediator and partial mediation

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Mediation
Y
Z
X
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Problems with tests of mediation

• Significance of c issue
• .31 .30, ns
• .45.30
• Report effect sizes!
• Sobel test (http//quantrm2.psy.ohio-state.edu/kri
  s/sobel/sobel.htm)
• Unreliability of mediator and partial mediation
  (SEM can correct)
• Directions of causality (Can SEM correct?)

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Directions of Causality Issues
Manipulate IV
Use time precedent
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Squared Deviations
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Using moderation to test mediation

• Because of causality issue, may be prudent to
  design moderation studies to test mediation
  hypotheses.
• E.g., attentional resources literature and the
  dual task paradigm
• Have cognitively distracting, non-cognitively
  distracting duel task as factor
• Findings of moderation, clue to mediator!

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Graphs (Mediation)(why clue)
high
DV
low
low
high
IV
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Factor analysis

• Meaning
• Rotation (orthogonal v. oblique)
• Number of factors
• Meanings
• Eigenvalue of 1
• Scree test
• Creating composite based on factor score or unit
  weighting

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SEM (e.g. LISREL)

• Confirmatory factor analysis
• Path analysis
• Handles partials (direct and indirect effects)
• Latent Structural Equations
• Handles measurement model (see CFA)
• Causality and tests of the model
• Only if strong theory, but that is what you are
  testing.
• Model completeness (3rd variables, interactions)
• Model fit and alternative models

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Other Issues

• Dichotomous or categorical endogenous variables
• Use discriminant or chi-square/loglinear
• Particularly as assumptions of normality are
  violated
• Stepwise
• Use sparingly,
• Capitalizes on chance
• Should have hypotheses to test