  The AGILE space mission (whose instrument is sensitive in the energy ranges
18-60 keV, and 30 MeV - 50 GeV) has been operating since 2007. Assessing the
statistical significance of time variability of gamma-ray sources above 100 MeV
is a primary task of the AGILE data analysis. In particular, it is important to
check the instrument sensitivity in terms of Poisson modeling of the data
background, and to determine the post-trial confidence of detections. The goals
of this work are: (i) evaluating the distributions of the likelihood ratio test
for "empty" fields, and for regions of the Galactic plane; (ii) calculating the
probability of false detection over multiple time intervals. In this paper we
describe in detail the techniques used to search for short-term variability in
the AGILE gamma-ray source database. We describe the binned maximum likelihood
method used for the analysis of AGILE data, and the numerical simulations that
support the characterization of the statistical analysis. We apply our method
to both Galactic and extra-galactic transients, and provide a few examples.
After having checked the reliability of the statistical description tested with
the real AGILE data, we obtain the distribution of p-values for blind and
specific source searches. We apply our results to the determination of the
post-trial statistical significance of detections of transient gamma-ray
sources in terms of pre-trial values. The results of our analysis allow a
precise determination of the post-trial significance of {\gamma}-ray sources
detected by AGILE.
