The idea is simple: since the test statistic is discrete, it can only take a finite set of values and there exists a minimum attainable P-value strictly greater than 0. As Tarone showed, one can exploit that to obtain an improved Bonferroni correction factor which exhibits a great increase in statistical power in many cases of interest.
However, all of those approaches cannot work directly with the exact minimum attainable P-value function Ψ (x ).
Next, we review the concept of the minimum attainable P-value for discrete test statistics, which we will extensively exploit in our contribution.
The method as proposed by Tarone had to be solved by a brute-force approach requiring computation of the minimum attainable P-values for every single test.
The concept of the minimum attainable P-value Ψ (x τ, l ) has profound implications for multiple hypothesis testing problems involving discrete test statistics.
One can then compute the minimum attainable P-value as Ψ (x τ, l, n 1, n 2 ) = min { p τ, l (a τ, l, x τ, l, n 1, n 2 ) | a τ, l ∈ [ a min, a max ] }.
Both methods exploit the concept of minimum attainable P-value reviewed in Section 2.2.3 along with a novel pruning technique to obtain a corrected significance threshold δ * for the significant interval search problem.
Next, we present our contribution: two alternative algorithms to solve the significant interval search problem by making use of the exact minimum attainable P-value; one based on Tarone's method and another on WY permutation testing.
Tarone was the first to discuss in (Tarone, 1990) the existence of a minimum attainable P-value when discrete test statistics, such as Fisher's exact test, are used.
We also focus on the maximum attainable value of transmittance and the energetic requirements to achieve it.
The score is also stored as a percentage of the maximum attainable value within the database.
