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Correlation 6. (Research and Knowledge (Replicable (Results must be …

- - - - a Measure of how 2 Variables
        Change in Relation to Each other
        
        Covariance: how Similarly 2 Variables Vary
        
        Reciprocal Dependence, Relation
    - - a Measure of how 2 Variables Vary Compared to Each other
        
        Strenght of a Relation btw 2 Variables
        
        Cons
        
        Difficult to Isolate Causes (No Control/Manipulation)
        
        Causality Problems
        
        Cause Direction? (X->Y / Y->X)
        
        Third Variables
        
        Often Retrospective: first find Correlation
        and Then ask: Why? La scienza a posteriori ....
        
        Spurious
        Correlation
        
        2 Variables Seem to have a Relation
        but they Actually do Not
        
        Mostly: completely Casual
        
        In Practice also due to Causality Problems
        
        Pros
        
        Quantifying and Measuring Relations
        
        Naturalistic (in the Real World)
        
        Replicable
  - - - No Control nor Manipulation of Variables
        
        No Cause-Effect relations
        
        we Observe things in the Real World
        and then try to Describe their Relation
    - - only Natural Variation
        
        No Distintction btw:
        
        Systematic (True) Variation
        
        Unsystematic (Random E.) Variation
    - - Causality Problems
        
        a Correlation btw X and Y
        can be Explained by Diff. Causal Models
        
        Causal Models
        
        Influence Each Other
        
        X <- -> Y
        
        Confounding Variable
        
        Third Variable (Z)
        Influence Both X and Y
        
        Z-> X
        Z-> Y
        
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        Mediator Variable
        
        Third Variable lies
        Wholly or Partly in Between
        
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        X -> Y
        
        Y -> X
        
        Moderator Variable
        
        Influences the Effect that X has on Y
        
        Ex. Violent Videogames (X) influence Aggression (Y),
        but Emotional Regulation (Z) moderates this Influence
        
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        Sum up
        
        Correlation does Not necessarily imply Causation,
        but Causation Always implies Correlation
  - - - to Study how 2 Variables
        Vary in Relation to Each other
        
        Create Hypotheses
        
        make possible to Predict Results of a Variable (Regression)
- - - - we look Only at the Sign +/-
        
        Either Positive or Negative
        
        we talk Only about the Direction of
        the Relation, Not the Degree
        
        but we Use the Degree to
        Calculate Correlation #
      - Formula
        
        or:
  - - - r = Covariance (of X and Y) /
        ( (SD of X) (SD of Y) )
        
        r = Covariance /
        ( SD(x) SD(y) )
    - - Conventionally:
        
        0.00 - 0.30 Small or No C.
        
        0.30 - 0.50 Low
        
        0.50 - 0.70 Moderate
        
        0.70 - 0.90 High
        
        0.90 - 1.00 Very High
    - - Coefficient of Determination
        
        Value from 0 to 1
        
        Definition
        
        Formal
        
        used to Explain how Much Variability of one Variable can be Caused by its Relationship to another Variable
        
        how Much of the Variance of the Two Variables is Actually a Shared Variance
        
        the Degree of Variance in Y (Dependent Var.) that can be Explained by the Variation in X
        
        Proportion of the Variance in the Dependent Variable that is Predictable from the Independent variable
        
        Kid
        
        how Much Change in Y can I Predict with X
        
        how Much Change of Y can I Expect to Predict with Values of X
        
        Ex. Stress (X) and Performance (Y) have a r = 0.40
        
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        it's Still a Measure of Correlation,
        we canNot infer Causation
        
        Personal
        
        how Much does X Explain the Variation of Y
        
        how Much of the Variation of Y can we Predict with X
        
        how Much of Y can we Determine with X
- - - - what we Can Say /
        we canNot Say
        
        Distinguish btw correlations:
        
        True and Informative
        
        Incorrect and Misleading