CERN-THESIS-2012-153 26/07/2012 - CERN Document Server

Chapter 8
Limit Evaluation
8.1 Introduction
As observed in Table 6.3 and Table 6.4, for the 2ID+TL and the 3ID channel, respectively, good agreement
between data and expected background is observed. No evidence for the t → Zq decay mode is found and
95% confidence level upper limits on the number of signal events are derived using the modified frequentist
(CLs) likelihood method [106]. The following description is taken from Reference [106].
8.2 The CLs method
For searches as the one discussed in this document, where small signal rates are expected, the loss of sen-
sitivity becomes a major issue in the interpretation of results. The CLs method aims to avoid excluding
or discovering signals which the search is in fact not sensitive to. This could be, avoiding exclusion in
cases where there should be a discovery (‘false exclusion’). The search results are formulated in terms of a
hypothesis test. A background-only and a signal+background hypotheses are considered. Thus the result
quantifies the degree to which the hypotheses are favored or excluded by the experimental observation.
In general, for the analysis of search results, a test-statistic, or function of the observable number of
candidate events, should be defined. This serves to characterize the data with background and hypothetical
signal. The ranges of values of the test-statistic in which observations will lead to an exclusion or discovery
conclusion should also be defined. This is done by establishing a confidence level (a measure of the signifi-
cance) for the exclusion or discovery to be quoted.
This test-statistic, Q, is constructed so it increases monotonically for increasingly signal-like experiments.
The confidence in the signal+background hypothesis is given by the probability that the test-statistic is less
92