Which of the following would be a plausible way to write the full model for a 2x

Question

Which of the following would be a plausible way to write the full model for a 2x3x4 ANOVA?

A. Score = Effect Factor 1 + Effect Factor 2 + Effect Factor 3 + Interaction between Factors 1&2 + Interaction between Factors 1&3 + Interaction Interaction between Factors 2&3 + Interaction between Factors 1&2&3 + Error

B. Score = Grand mean + Effect Factor 1 + Effect Factor 2 + Effect Factor 3 + Interaction between Factors 1&2 + Interaction between Factors 1&3 + Interaction Interaction between Factors 2&3 + Error

C. Score = Grand mean + Effect Factor 1 + Effect Factor 2 + Effect Factor 3 + Interaction between Factors 1&2 + Interaction between Factors 1&3 + Interaction Interaction between Factors 2&3 + Interaction between Factors 1&2&3

D. Score = Grand mean + Effect Factor 1 + Effect Factor 2 + Effect Factor 3 + Interaction between Factors 1&2 + Interaction between Factors 1&3 + Interaction Interaction between Factors 2&3 + Interaction between Factors 1&2&3 + Error

E. Score = Grand mean * Effect Factor 1 * Effect Factor 2 * Effect Factor 3 * Interaction between Factors 1&2 * Interaction between Factors 1&3 * Interaction Interaction between Factors 2&3 * Interaction between Factors 1&2&3 + Error

Explanation / Answer

Lets say that the 3 variables are Sex , Age and conditions

so the effects can be calculated as

#> Treatment   
#> Sex
#> Age
#> Conditions
#> Sex*Age   
#> Sex*Conditions   
#> Age*Conditions   
#> Sex*Age*Conditions   

so the correct answer would be

A. Score = Effect Factor 1 + Effect Factor 2 + Effect Factor 3 + Interaction between Factors 1&2 + Interaction between Factors 1&3 + Interaction Interaction between Factors 2&3 + Interaction between Factors 1&2&3 + Error

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