In a fictional study, a cognitive psychologist studied memory for names after a group activity. The researcher randomly assigned 120 participants to one of three conditions: (1) group members introduced themselves once, (2) group members were introduced by the experimenter and by themselves, and (3) group members were introduced by the experimenter and themselves, and they wore name tags throughout the group activity. 

a. How could the researcher redesign this study so it would be analyzed with a two-way between- groups ANOVA? Be specific. 

b. How could the researcher redesign this study so it would be analyzed with a two-way mixed-design ANOVA? Be specific.