Formal Model (1 of 2)

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In an analysis of variance design, each score in the "a" populations can be defined in terms of the following formal model:

y_ij = μ_g + α_j + ε_ij where:

• y_ij is the score of the ith subject in the jth population,
  
• μ_g is the mean of all the population means,
  
• α_j equals μ_j - μ_g where μ_j is the mean of the jth population,
  
• α_j represents the effect of being in the jth population, where Σα_j = 0,
  
• ε_ij is the sum of all other effects on the ith person in the jth population and is referred to as error.

The error within each population is assumed to be normally distributed and have a mean of zero. The error variances within the "a" populations are assumed to be equal.