Answer
Part A:
Creation of four blocks of two volunteers:
PART A: Skin cleanliness based on age:
Volunteer Gender Age, year
5 Male 22
1 Male 23
4 Female 24
2 Female 25
3 Female 51
7 Male 52
The criteria for creating the blocks is age. The gender is not a material consideration.
Part B:
Creation of four blocks of two volunteers:
PART B: Skin cleanliness based on Age and Gender:
Volunteer Gender Age, year
5 Male 22
4 Female 24
1 Male 23
2 Female 25
3 Female 51
6 Male 53
7 Male 52
8 Female 56
The criteria for creating the four blocks are age and gender. Each gender is included in each group.
Part C:
Randomly assigning treatment to groups without regard to their group dynamics may not be the most efficient. The new treatment formula should be assigned to one of the young groups and one of the old groups, using stratification. This will help to explain if age or gender causes skin cleanliness or not.
Step-by-step explanation:
a) Data and Calculations:
Volunteer Gender Age, year
1 Male 23
2 Female 25
3 Female 51
4 Female 24
5 Male 22
6 Male 53
7 Male 52
8 Female 56
PART A: Skin cleanliness based on Age:
Volunteer Gender Age, year
5 Male 22
1 Male 23
4 Female 24
2 Female 25
3 Female 51
7 Male 52
6 Male 53
8 Female 56
PART B: Skin cleanliness based on Age and Gender:
Volunteer Gender Age, year
5 Male 22
4 Female 24
1 Male 23
2 Female 25
3 Female 51
6 Male 53
7 Male 52
8 Female 56
Answer:
Part A:
The scientists running the experiment think skin cleanliness changes as people age, not based on their gender. To create eight blocks of two volunteers, I would group the volunteers by age. Each block would have one volunteer from each age group. For example, block 1 could have volunteer 1 (24 years old) and volunteer 5 (22 years old). Block 2 could have volunteer 2 (35 years old) and volunteer 6 (42 years old), and so on.
Part B:
The company brings in an outside analysis firm that believes skin cleanliness changes based on age and gender. The firm also uses block design with eight blocks of two volunteers for each block. To group the volunteers, I would first divide them by gender. Then, within each gender group, I would divide them by age. For example, block 1 could have volunteer 1 (female, 24 years old) and volunteer 10 (female, 20 years old). Block 2 could have volunteer 2 (male, 35 years old) and volunteer 5 (male, 22 years old), and so on.
Part C:
The outside analysis firm from part B assigns treatments by giving four blocks the new formula and four blocks the current formula. This is not an appropriate way to assign treatments. The purpose of blocking is to create groups of volunteers who are similar to each other in terms of the factors that are thought to affect the outcome of the experiment. In this case, the firm has created blocks of volunteers who are similar in terms of age and gender. However, the firm is only interested in the effect of the new formula on skin cleanliness. The firm should assign treatments randomly to the blocks. This will ensure that the results of the experiment are not biased by the way in which the treatments are assigned.
A suitable process for selecting the blocks that receive the new formula would be to use a random number generator. The firm could assign each block a number from 1 to 8. Then, the firm could use a random number generator to select four numbers from 1 to 8. The blocks that correspond to the selected numbers would receive the new formula. The other four blocks would receive the current formula.
Explanation:
