The core point here is that the psychologists declared about something that had happened earlier. So the act of declaration requires a simple past such as declared and the earlier event failing requires a past perfect such as had filed.

A. psychologists, declaring that since most of the studies had failed to control for such variables as social class and family size,----- lacks a working verb for the subject psychologists. So a fragment


B psychologists, declaring that most of the studies failed in not controlling for such variables like social class and family size, and ….same problem as in A; in addition the use of like to denote example is incorrect.

C psychologists declared that since most of the studies, having failed to control for such variables as social class and family size, ---- The subordinate clause introduced by since lacks a verb and hence a fragment

D. psychologists declared that since most of the studies fail in controlling for such variables like social class and family size, ------- shift of tense using a present tense verb fail is wrong; as also, use of like is wrong.

E psychologists declared that since most of the studies had failed to control for variables such as social class and family size, ------- correct choice with proper sequence of tense and use of such as to mark examples.
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