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WK2: MULTIPLE AND PLANNED COMPARISONS (Terms (Purpose of Planned…

- - - - -1, 1
      - 1, -1
    - - Linear (no bend)
        
        -1, 0, 1
      - Quadratic (1 bend)
        
        1, -2, 1
    - - Quadratic (1, -1, -1, 1)
      - Cubic (-1, 3, -3, 1)
      - Linear (-3, -1, 1, 3)
- - - - Welch's F-test
      - Brown-Forsythe F-test
- - - - All weightings should sum = 0
      - Each case have a sum of (1 weighting x 1 mean) + (1W x 1M)
      - Instead of subtracting in t-test, contrast adds the means together
    - - More useful bc comparing more means
      - Each case have (1W x 1M) + (1W x 1M) + (1W x 1M)
      - :!:Can create an upward / downward linear trend with weightings
    - - :!:Refers to pattern of means not increasing / decreasing in monotonic fashion
      - e.g. Quadratic Function / Contrast
      - Quadratic have one bend, Cubic have two bends etc, etc.
    - - Compare one mean against the other
      - Weighting for each (+1 and -1)
    - - Combine 2 or more means to contrast 1 mean (e.g. low-dose + medium-dose vs. high-dose)
      - Combined means have same weightings (0.5, 0.5)
      - Contrasted mean have a different weighting (positive / negative depending on expected direction -1)
      - :star: ANOVA = signf = Multi-Comparison = not signf?? (Because you didn't test for non-pairwise)
    - - Difference in what weightings are used for the means
      - e.g. NPW (0.5, 0.5, -1) / Linear Contrast (-1, 0, +1)
      - k = 3, k - 1 = 2 planned comparisons (NPW, Contrast)