On the reliability of microvariability tests in quasars
  Microvariations probe the physics and internal structure of quasars.
Unpredictability and small flux variations make this phenomenon elusive and
difficult to detect. Variance based probes such as the C and F tests, or a
combination of both, are popular methods to compare the light-curves of the
quasar and a comparison star. Recently, detection claims in some studies depend
on the agreement of the results of the C and F tests, or of two instances of
the F-test, in rejecting the non-variation null hypothesis. However, the C-test
is a non-reliable statistical procedure, the F-test is not robust, and the
combination of tests with concurrent results is anything but a straightforward
methodology. A priori Power Analysis calculations and post hoc analysis of
Monte-Carlo simulations show excellent agreement for the Analysis of Variance
test to detect microvariations, as well as the limitations of the F-test.
Additionally, combined tests yield correlated probabilities that make the
assessment of statistical significance unworkable. However, it is possible to
include data from several field stars to enhance the power in a single F-test,
increasing the reliability of the statistical analysis. This would be the
preferred methodology when several comparison stars are available. An example
using two stars and the enhanced F-test is presented. These results show the
importance of using adequate methodologies, and avoid inappropriate procedures
that can jeopardize microvariability detections. Power analysis and Monte-Carlo
simulations are useful tools for research planning, as they can reveal the
robustness and reliability of different research approaches.
