No. 84 (00205)

Family name : Bityukov
Given name : Sergei I.
Affiliation : Institute for high energy physics
Abbreviation : IHEP
E-mail address : Serguei.Bitioukov@cern.ch
Title : Distinguishability of Hypotheses
Authors : S.I. Bityukov(IHEP), N.V. Krasnikov (INR RAS)
Abstract : 
In the report the approach to estimation of quality of planned
experiments is considered. This approach is based on the analysis
of uncertainty, which will take place under the future hypotheses
testing about the existence of a new phenomenon in Nature.
We consider a simple statistical hypothesis
H_0:  new physics is present in Nature (i.e. lambda = n_s + n_b)
against a simple alternative hypothesis
H_1: new physics is absent $\lambda = n_b$,
where n_s is expected number of signal events and n_b is expected
number of background events. The value of uncertainty is defined by
the values of the probability to reject the hypothesis H_0 when it
is true (Type I error alpha) and the probability to accept the
hypothesis H_0 when the hypothesis H_1 is true (Type II error beta).

The probability of choice of a correct decision in hypotheses testing is
1 - (alpha+beta)/(2-(alpha+beta)). This value is the estimator of a
distinguishability of hypotheses and, correspondingly, a quality of
planned experiments. This estimator allows to take into account
systematics and statistical uncertainties in determination of signal
and background rates.