the 3D and projected radius are different, and the slope of the quiescent fractions is also different between the 3D and projected case. The solid lines represent the fits, while the dashed lines with the error bars show the data and statistical errors estimated from the deviation in 128 realizations. The quiescent fraction due to the projection and photo-$z$ effect clearly agree very well. The photo-$z$ effect appears to not significantly affect the quiescent fraction of the estimation. That is, if the background subtraction can properly recover the group members, it is expected that the resulting quiescent fraction retrieves the original 2D case.

Consistency Checks
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In our previous study, [@lin14], we accounted for the contamination and incompleteness effects introduced in the PFOF group identification by estimating the rate of recovering true group memberships as well as the contamination rate from the field galaxies using galaxies that were cross-matched with spectroscopically identified group members. That is, the contamination removal method in our previous work is distinct from the current method. To understand the consistency between the two approaches, we compute the SSFR and the quiescent fraction as a function of stellar mass without the dimming factor correction via background subtraction 