The n-way ANOVA assumes that the design was orthogonal, or balanced (the number of cases in each cell was the same).

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The assumption of an n-way ANOVA is that the design is orthogonal, meaning that the number of cases in each cell is equal. This allows for accurate estimation of the effects of each independent variable on the dependent variable. If the design is not balanced, adjustments can be made using techniques such as weighted least squares.

The N-Way ANOVA Assumes That the Design Was Orthogonal, or Balanced