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In a previous paper, we studied two statistical methods used to analyse the variability of active galactic nuclei (AGNs): the C and F statistics. Applying them to observed differential light-curves of 39 AGNs, we found that, even though the C criterion cannot be considered as an actual statistical test, it could still be a useful parameter to detect variability, whereas F is a good detector of non-variability. In order to test these results under controlled input conditions, so that the different error sources could be individually evaluated, we generated a series of synthetic differential light curves simulating astronomical images with different atmospheric conditions, such as cloud cover, seeing or sky brightness, as well as several types of intrinsic variability of the AGN, all with a specific instrumental configuration. Having obtained light curves for each case, we applied both statistics to them in order to test their reliability. We found that a weight factor should always be used with these indices. The F test has a tendency to classify noisy non-variable curves as variable (i.e. false positives), although it is reliable and robust to correctly classify non-variable curves. On the contrary, although the C index tends to give false negatives, we found that whenever the C index indicates a source to be variable, it effectively is. Finally, light curves with low amplitude variabilities are more likely to be affected by changes in atmospheric conditions.