Question

1. a physical therapist plans to conduct an experiment using a randomized block design with patients from her clinic to determine the effectiveness of two different exercises on reducing joint pain and increasing mobility. she is considering two variables to create the blocks: age of the patients (under 50 years old and 50 or more years old) and time of appointment (morning and afternoon).

a. which variable should be chosen to create the blocks? why?
b. what is one advantage of using a randomized block design compared to a completely randomized design.

Explanation:

a. The variable "age of the patients" should be chosen to create the blocks. Age is likely to be a confounding variable that can affect joint pain and mobility. Patients of different ages may respond differently to the exercises. Time of appointment is less likely to be related to the effectiveness of the exercises in reducing joint pain and increasing mobility.
b. One advantage of using a randomized block design compared to a completely randomized design is that it can reduce the variability within each block. By grouping patients with similar characteristics (in this case, age), the treatment effects can be more accurately measured. This can lead to more precise estimates of the treatment effects and increase the power of the statistical tests.

Answer:

a. The variable "age of the patients" should be chosen. Age is a confounding variable affecting joint pain and mobility.
b. Randomized block design reduces within - block variability for more accurate treatment effect measurement.