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A researcher wants to know if 2nd graders and 8th graders differ in their preferences for TV shows. The researcher has ten 2nd graders and ten 8th graders at Smith Elementary watch "Kenny the Clown" and "Action Rangers." Ten 2nd graders and ten 8th graders at Wilson Elementary watch the same two shows. Each child rates how much they liked each show on a scale from 1 to 10.

At both schools, "Kenny the Clown" is shown on a small television set in the cafeteria, and "Action Rangers" is projected on the large screen in the school auditorium.

The mean ratings for 2nd graders:
- Kenny the Clown: 8.4
- Action Rangers: 4.8

The mean ratings for 8th graders:
- Kenny the Clown: 6.7
- Action Rangers: 3.1

Which of the following best describes this research design?

A. 2x2 independent groups factorial design
B. 2x2 mixed factorial design
C. 2x2 repeated measures factorial design
D. 2x2x2 independent groups factorial design

Answer :

The research design best described in the question is a) 2x2 independent groups factorial design, as there are two factors (age group and TV show) and separate, independent groups for each combination of the levels of the two factors.

A researcher wanting to know if 2nd graders and 8th graders differ in their preferences for TV shows might employ various research designs to analyze the preferences of the two distinct age groups. Given that each group of students watched the same two TV shows and rated them, and keeping in mind the way the TV shows were presented (on different sized screens and different locales), we must discern which design was used based on the information provided. Considering the age groups (2nd and 8th graders) and the TV shows as two factors, each with two levels, we can conclude that the research design is indeed factorial.

However, looking at the specifics, since there are two levels of one factor (grade levels: 2nd graders, 8th graders) and two levels of the second factor (TV shows: Kenny the Clown, Action Rangers) and the same individuals did not rate both TV shows but were instead separate groups from two schools, the design is an independent groups factorial design. But, since there is no mention of a third factor in the study presented, option d) which suggests a 2x2x2 independent groups factorial design is not suitable. Thus, the best description of the research design provided by the options is a) 2x2 independent groups factorial design, where the two factors are grade level and TV show, but each factor has separate groups of individuals providing the ratings.

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