The correct option is E psychologists declared that since most of the studies had failed to control for variables such as social class and family size,
Here, options A and B are incorrect because the subject 'psychologists' needs a main verb and 'declaring' cannot be a main verb (as 'declaring' functions as a noun here). Thus, we come to the conclusion that the use of the verb 'declared' would be correct. Option C is also incorrect because 'having failed' is a participle form and cannot be the main verb in the clause. D cannot be correct because it does not follow the sequence of events - the sentence means to state that because the studies failed to control the variables, they [the studies] could not be taken seriously. The use of 'fail' disrupts this sequence of events - 'fail' reflects the present aspect of time, whereas the sentence is in Past Perfect tense. Therefore, the correct answer is E.