Microvariability (intranight variability) is a low amplitude flux change at short time-scales (i.e. hours). It has been detected in unobscured type 1 active galactic nuclei (AGN) and blazars. However in type 2 AGN, 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 Diego. The presented results show that out of four observed target, we are 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, and they are present in one of the nights of observations, 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 medium. There is a possible interesting connection between the merging state of the targets and detection of microvariability.