Individual and simultaneous confidence intervals using the data adaptively are constructed for the effects in orthogonal saturated designs under the assumption of effect sparsity. The minimum coverage probabilities of the intervals are equal to the nominal level $1 - \alpha$.
"Control of error rates in adaptive analysis of orthogonal saturated designs." Ann. Statist. 29 (4) 1058 - 1065, August 2001. https://doi.org/10.1214/aos/1013699992