This is from a zCOSMOS paper (Silverman et al., arXiv:0810.3653), looking at the interrelationship between star formation and AGN activity. The two panels are showing the difference between selecting your sample by luminosity (left) and mass (right). Just focus on the black points, which show the AGN fraction as a function of restframe (U-V) color.
Because there is a relationship between color and mass-to-light ratio, whereby star forming galaxies are both bluer and brighter for a given mass, if you select by luminosity you will include a bunch of lower mass blue galaxies. In other words, the average mass you're probing will be color-dependent. In this case, because AGN activity is mass-dependent (see their Figure 4 if you wanna), that translates to an artificial color-dependence of the AGN fraction.
So, you can see that the AGN fraction is roughly constant for all blue galaxies, provided you select by mass. But if you looked in a luminosity-selected sample, you might think that AGN lie preferentially in green galaxies -- ie less actively star forming ones -- and so that maybe AGN only switched on after SF slowed down. But you'd be wrong. (Maybe.)
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