  Tiny systematic uncertainty caused by cosmological hypotheses is hard to be
detected, not only because the present observational errors are relatively
large but also because hypothesis-induced uncertainty is indistinguishable from
other sources of systematic errors. We introduce an efficient and sensitive
method for detecting tiny systematic errors, which contain the
cosmological-hypothesis-induced uncertainty and other secondary systematic
errors, hidden behind residuals of chi-square analysis. In this paper, we apply
our analysis to JLA compilation of SN Ia observations and latest cosmic
chronometer data-set. We find slight but noticeable evolutional feature in
residuals of chi-square analysis under present systematic uncertainty control,
when combining JLA samples with standard cosmological model. Meanwhile, cosmic
chronometer observation has no noticeable similar feature with various
cosmological models, which may be covered up by relatively large observational
uncertainties. Our method can be useful when various independent observational
samples with high observational precision are available, since the cosmological
hypothesis-induced error appears unbiasedly in all related data-sets.
