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# Data analysis markus brauer

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 Orthogonal contrasts Contrasts for a 2 x 2 ANOVA: Main Main Inter- Variable 1 Variable 2 effect effect action Group (V1) (V2) V1 V2 V1 X V2 ---------------------------------------------------------------------------------------------------- [1] 1st level 1st level –1 –1 +1 [2] 1st level 2nd level –1 +1 –1 [3] 2nd level 1st level +1 –1 –1 [4] 2nd level 2nd level +1 +1 +1 Contrasts for a 2 x 2 x 2 ANOVA: Main Main Main Inter- Inter- Inter- Inter- Var. 1 Var. 2 Var. 3 effect effect effect action action action action Gr. (V1) (V2) (V3) V1 V2 V3 V1 X V2 V1 X V3 V2 X V3 V1 X V2 X V3 ---------------------------------------------------------------------------------------------------------------------------------- [1] 1st lev. 1st lev. 1st lev. –1 –1 –1 +1 +1 +1 –1 [2] 1st lev. 1st lev. 2nd lev. –1 –1 +1 +1 –1 –1 +1 [3] 1st lev. 2nd lev. 1st lev. –1 +1 –1 –1 +1 –1 +1 [4] 1st lev. 2nd lev. 2nd lev. –1 +1 +1 –1 –1 +1 –1 [5] 2nd lev. 1st lev. 1st lev. +1 –1 –1 –1 –1 +1 +1 [6] 2nd lev. 1st lev. 2nd lev. +1 –1 +1 –1 +1 –1 –1 [7] 2nd lev. 2nd lev. 1st lev. +1 +1 –1 +1 –1 –1 –1 [8] 2nd lev. 2nd lev. 2nd lev. +1 +1 +1 +1 +1 +1 +1 Contrasts for a 2 x 3 ANOVA: Main V2 V2 Inter- Inter- Variable 1 Variable 2 effect Contrast 1 Contrast 2 action action Group (V1) (V2) V1 (C1) (C2) V1 X C1 V1 X C2 ------------------------------------------------------------------------------------------------------------------ [1] 1st lev. 1st lev. –1 –1 –1 +1 +1 [2] 1st lev. 2nd lev. –1 –1 +1 +1 –1 [3] 1st lev. 3rd lev. –1 +2 0 –2 0 [4] 2nd lev. 1st lev. +1 –1 –1 –1 –1 [5] 2nd lev. 2nd lev. +1 –1 +1 –1 –1 [6] 2nd lev. 3rd lev. +1 +2 0 +2 0 The main effect of Variable 2 is the following comparison (2 df): C: Y = b0 + b1V1 + b2(V1*C1) + b3(V1*C2) A: Y = b0 + b1V1 + b2C1 + b3C2 + b4(V1*C1) + b5(V1*C2) The interaction effect between Variables 1 et 2 is the following comparison (2 df): C: Y = b0 + b1V1 + b2C1 + b3C2 A: Y = b0 + b1V1 + b2C1 + b3C2 + b4(V1*C1) + b5(V1*C2) Polynomial contrasts (3 groups): Linear Quadratic Group trend trend --------------------------------------------------- [1] –1 –1 [2] 0 +2 [3] +1 –1 Polynomial contrasts (4 groups): Linear Quadratic Cubic Group trend trend trend -------------------------------------------------------------------- [1] –3 +1 –1 [2] –1 –1 +3 [3] +1 –1 –3 [4] +3 +1 +1 Polynomial contrasts (5 groups): Linear Quadratic Cubic Quartic ---------------------------------------------------------------------------------------- [1] –2 +2 –1 +1 [2] –1 –1 +2 –4 [3] 0 –2 0 6 [4] +1 –1 –2 –4 [5] +2 +2 +1 +1 Helmert contrasts (3 groups): Group [1] vs. [2]-[3] [2] vs. [3] --------------------------------------------------------- [1] –2 0 [2] +1 –1 [3] +1 +1 Helmert contrasts (4 groups): Group [1] vs. [2]-[4] [2] vs. [3]-[4] [3] vs. [4] -------------------------------------------------------------------------------- [1] –3 0 0 [2] +1 –2 0 [3] +1 +1 –1 [4] +1 +1 +1 Helmert contrasts (5 groups): Group [1] vs. [2]-[5] [2] vs. [3]-[5] [3] vs. [4]-[5] [4] vs. [5] ------------------------------------------------------------------------------------------------------- [1] –4 0 0 0 [2] +1 –3 0 0 [3] +1 +1 –2 0 [4] +1 +1 +1 –1 [5] +1 +1 +1 +1

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