  Microvariability (intra-night variability) is a low amplitude flux change at
short time scales (i.e. hours). It has been detected in unobscured type 1 AGNs
and blazars. However in type 2 AGNs, the detection is hampered by the low
contrast between the presumably variable nucleus and the host galaxy. In this
paper, we present a search for microvariability in a sample of four type 2
quasars as an astrostatistical problem. We are exploring the use of a newly
introduced enhanced F-test, proposed by de Diego 2014. The presented results
show that out of our four observed targets, we were able to apply this
statistical method to three of them. Evidence of microvariations is clear in
the case of quasar J0802+2552 in all used filters (g',r' and i') during both
observing nights, the microvariations are present in one of the nights of
observations of J1258+5239 in one filter (i'), while for the J1316+4452, there
is evidence for microvariability within our detection levels during one night
and two filters (r' and i'). We demonstrate the feasibility of the enhanced
F-test to detect microvariability in obscured type 2 quasars. At the end of
this paper, we discuss possible causes of microvariability. One of the options
is the misclassification of the targets. A likely scenario for explanation of
the phenomenon involves optically thin gaps in a clumpy obscuring medium, in
accordance with the present view of the circumnuclear region. There is a
possible interesting connection between the merging state of the targets and
detection of microvariability.
