1 Significance Tests for Binomial Experiments : 2 Ordering the Sample Space by Bayes Factors and 3 Using Adaptive Significance Levels for Decisions . 4

The main objective of this paper is to find a close link between the adaptive level of 12 significance, presented here, and the sample size. We, statisticians, know of the inconsistency, or 13 paradox, in the current classical tests of significance that are based on p-value statistics that is 14 compared to the canonical significance levels (10%, 5% and 1%): "Raise the sample to reject the null 15 hypothesis" is the recommendation of some ill-advised scientists! This paper will show that it is 16 possible to eliminate this problem of significance tests. The Bayesian Lindley's paradox – "increase 17 the sample to accept the hypothesis" – also disappears. Obviously, we present here only the 18 beginning of a possible prominent research. The intention is to extend its use to more complex 19 applications such as survival analysis, reliability tests and other areas. The main tools used here are 20 the Bayes Factor and the extended Neyman-Pearson Lemma. 21