Pooled Error Variance for Factorial Effects

When a $2^k$ factorial design is replicated $m$ times, the replicated observations provide a pooled estimate $s^2$ of the experimental error variance.

This leads to

$$ \operatorname{Var}(\text{effect}) = \frac{4 s^2}{m 2^k}. $$

That variance is the basis for standard errors and significance tests for factorial effects.

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Related

• STA305
• Replication in Factorial Designs
• Confidence Interval for a Factorial Effect
• 2^k Factorial Linear Model