Question

1. the athletic trainer for the high school soccer team is planning a study to investigate the comfortability of a new shin guard compared to the standard shin guard. there are 20 students on the soccer team willing to participate in the study. after wearing the shin guards for 3 full practice sessions, the players will rate the comfortability on a scale from 1 to 10.

a. identify the experimental units, treatments, and the response variable.
b. the athletic trainer plans to have each player use both shin guards at the same time, with one on the left shin and one on the right shin. what is the name for this experimental design? explain.
c. describe a process for randomly assigning the new shin guard and the standard shin guard to each player in the study.
d. what is one advantage of this experimental design over a completely randomized design?

Explanation:

Part a

• Experimental units: The entities on which the experiment is performed. Here, it's the 20 students on the soccer team.
• Treatments: The different conditions or factors being tested. In this case, the new shin guard and the standard shin guard.
• Response variable: The variable that is measured as an outcome. Here, it's the comfortability rating on a scale from 1 - 10.

Part b

• When each experimental unit (player) receives both treatments (new and standard shin - guard) with one on the left and one on the right (or vice - versa), it is a matched pairs design. In a matched pairs design, each unit is used as its own control. By having each player test both shin - guards, we can control for individual differences among players (such as different pain tolerances, playing styles etc.) that could affect the comfortability rating.

Part c

• One way to randomly assign the shin - guards:
• For each player, flip a coin. If it's heads, assign the new shin - guard to the left shin and the standard to the right. If it's tails, assign the standard shin - guard to the left shin and the new to the right.
• Another method could be using a random number generator. For each player, generate a random number. If the number is even, new on the left and standard on the right; if odd, standard on the left and new on the right.

Part d

• In a completely randomized design, we would randomly divide the 20 players into two groups (one group with new shin - guards and one with standard). But in a matched pairs design (as in this case):
• It reduces variability. Since we are comparing within the same player (using them as their own control), the variability due to differences between players (e.g., one player may be more sensitive to discomfort in general) is minimized. In a completely randomized design, this between - player variability can confound the results.

Answer:

• a. Experimental units: 20 soccer - team students; Treatments: new shin guard, standard shin guard; Response variable: comfortability rating (1 - 10).
• b. Matched pairs design. Each player acts as their own control, reducing variability from individual differences.
• c. Flip a coin for each player: heads - new on left/standard on right; tails - standard on left/new on right (or use a random number generator: even - new on left/standard on right; odd - standard on left/new on right).
• d. Reduces variability as it uses each player as their own control (minimizes between - player variability that could affect results in a completely randomized design).