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Week Four Statistics (Correlation (Considerations for interpreting…

- - - - Characteristics of relationship
        
        Direction (positive or negative)
        
        Positive: change in the same direction
        
        Negative: go in opposite directions (inverse relationship)
        
        Form
        
        Strength or consistency
        
        Perfect correlation: data points perfectly fit the specific form being measured
  - - - Sum of products of deviations (SP)
        
        Definitional formula
        
        SP = ∑ (X - Mx) (Y - My)
        
        Mx: mean for X scores My: mean for Y scores
        
        Computational formula
        
        SP = ∑XY - ((∑X∑Y) / n)
      - Measures the degree and direction of the linear relationship between two variables
      - Alternatives:
        
        Spearman correlation: measures relationship between two variables when both are measured on an ordinal scale
        
        SS = ( n (n² - 1)) / 12
        
        Point-biserial correlation: a correlation between two variables where one of the variables is dichotomous
        
        Phi-coefficient: correlation between two variables, both of which are dichotomous
  - - - Correlation, not causation
    - - Coefficient of determination
        
        r²: measures the proportion of variability in one variable that can be determined from the relationship with the other variable
- - - - Estimated standard error: sM
        
        computed from sample variance or sample standard deviation and provides an estimate of the standard distance between a sample mean M and the population mean µ
        
        sM = √(s² / n)
        
        used as an estimate of the real standard error σM when the value of σ is unknown
  - - - t distribution
        
        complete set of t values computed for every possible random sample for specific sample size (n) or a specific degrees of freedom (df)
  - - - Values in the sample must consist of independent observations
      - Population sample must be normal
    - - estimated d = (M - µ) / s
    - - r² = t² / (t² + df)
    - - µ = M+/- tsM
      - Larger level of confidence = larger t value and wider interval
      - Larger sample size = smaller interval