Confidence Interval for a Factorial Effect
In a replicated $2^k$ factorial design, a factorial effect can be tested and estimated using a $t$-based confidence interval.
If the design has $m$ replications and pooled error variance $s^2$, then
$$ \text{SE}(\text{effect}) = \sqrt{\frac{4 s^2}{m 2^k}}, $$and a $100(1-\alpha)\%$ confidence interval is
$$ \text{effect} \pm t_{1-\alpha/2,\;2^k(m-1)} \sqrt{\frac{4 s^2}{m 2^k}}. $$If the interval excludes $0$, that effect is significant at level $\alpha$.