Question

Comparing weight-loss treatments Twenty overweight females have agreed to participate in a study of the effectiveness of four weight-loss treatments: A, B, C, and D. The researcher first calculates how overweight each subject is by comparing the subject’s actual weight with her “ideal” weight. The subjects and their excess weights in pounds are as follows:

The response variable is the weight lost after 8 weeks of treatment. Previous studies have shown that the effects of a diet may vary based on a subject’s initial weight.

(a) Explain why a randomized block design would be better than a completely randomized design in this setting.

(b) Should researchers form blocks of size 4 based on subjects’ last names in alphabetical order or by how overweight the subjects are? Explain.

(c) Use technology or Table D to carry out the random assignment required by your design. Explain your method clearly.

Short answer

Part (a) Existence of blocks provides randomization in each block.

Part (b) Construct a block design based on overweight diet treatments.

Part (c) Construct four blocks based on excess weight that is, in the interval 0-20, 21-30, 31-40, 41-50.

Step-by-step solution

Part (a) Step 1. Explanation

Twenty overweight females participated in an experiment related to the effectiveness of four weight-loss treatments, that is, A, B, C, and D. These four weight-loss treatments are the block respective to which the effects of treatments are observed. As a result, there does not exist randomness in assigning treatment without any block. So, a completely randomized design is not applicable. In fact, the research design is randomized to each block which is why the research design is called randomized block design.

Part (b) Step 1. The basis of the construction of the block 

The blocks should be formed in order of the subject’s overweight and classify them into four overweight diet treatments.

Part (c) Step 1. Divide the dataset into four blocks or intervals. 

Consider 20 females data given, construct four blocks consisting of excess weight in the interval 0-20, 21-30, 31-40, 41-50. The randomized block design can be applied and random assignment of the treatment can be made among the block.