Exact measurement of the second-order correlation function g (2) (t) of a light source is essential when investigating the photon statistics and the light generation process of the source. For a stationary single-mode light source, Mandel Q factor is directly related to g (2) (0). For a large mean photon number in the mode, the deviation of g (2) (0) from unity is so small that even a tiny error in measuring g (2) (0) would result in an inaccurate Mandel Q. In this work, we have found that detector dead time can induce a serious error in g (2) (0) and thus in Mandel Q in those cases even in a two-detector configuration. Our finding contradicts the conventional understanding that detector dead time would not affect g (2) (t) in two-detector configurations. Utilizing the cavity-QED microlaser, a well-established sub-Poissonian light source, we measured g (2) (0) with two different types of photodetectors with different dead time. We also introduced prolonged dead time by intentionally deleting the photodetection events following a preceding one within a specified time interval. We found that the observed Q of the cavity-QED microlaser was underestimated by 19% with respect to the dead-time-free Q when its mean photon number was about 600. We derived an analytic formula which well explains the behavior of the g (2) (0) as a function of the dead time.