Dr Phillips Is a Cognitive-Developmental Psychologist Who Studies How Children

Dr. Phillips is a cognitive-developmental psychologist who studies how children learn mathematical principles. His current interest is in studying how children learn multiplication. He recruits 54 second-graders who have not yet learned how to multiply numbers to participate in his study. He is curious as to whether different teaching styles lead to better mastery of the subject. One condition (A) involves having students read a chapter on multiplication from their textbook. One condition (B) involves having students watch a video of cartoon characters explaining multiplication. One condition (C) involves having students being taught multiplication by a teacher. One condition (D) involves having students being taught multiplication by a fourth-grader. In all conditions, participants spend 30 minutes learning the fundamentals of multiplication and are then given the same 15-question multiplication test. The number of questions answered correctly is recorded. The data are below.

Explain why Dr. Phillips cannot conduct a within-groups design.