Question

Runiowa is a fashion shoe company that tries to manufacture much more durable heels in 2020. The management team of Runiowa suggests two rubber materials A and B and the research team of Runiowa is asked to design an experiment to gauge whether the rubber A is more durable than the rubber B. 300 people in the US aged between 18 and 65 were randomly chosen. The rubber A is allocated at random to the right shoe or the left shoe of each individual. Then, the rubber B has been assigned to the other. For example, if Mr. Nathaniel is one of 300 people randomly chosen, then the right heel of Mr. Nathaniel is randomly assigned to be made with the rubber A and then his left heel is to be made with the rubber B. The research team measures the amounts of heel wear both the rubber A (wA) and the rubber B (wB) in each individual and records the difference wA − wB of 300 individuals. Even though the individuals are heterogeneous with different heights and weights, those individual heterogeneities will not obscure the comparison of treatment groups by focusing on the paired differences of each individual. Also as long as the heel materials are randomly assigned for each individual, there has been no restrictions on shoe styles. Note that the age of subjects is ranging from 18 to 65. In this way, researchers compare treatments within blocks controlling heterogeneity of individuals. The research team also repeats this experiment design with 300 people in the US aged between 18 and 65 chosen at random.

Question:

What are the experimental units?

What is the control?

Hoe much replication was used?

How was randomization used?

Answer 1

Solution:

Experimental unit : In an experiment an experimental unit is the entity which can be assigned to different treatments.

In the given experiment, the experimental units are the shoes of the randomly selected 300 people in the US aged between 18 and 65 to which rubber A and rubber B are assigned.

Control : Since, the selected individuals are heterogeneous with different heights and weights, therefore these things need to be controlled. Hence, research has controlled the heterogeneity by taking the paired difference of each group.

Replication : Replication is the method in which we assign treatments repeatedly.

In the given experiment, replication was used by assigning the both of the two treatments (rubber A and rubber B) randomly to the each of the randomly selected 300 people's shoes. Hence, total 300 replications were used for both type of rubbers.

Randomization: Randomization is the process in which treatments are assigned to the experimental units randomly.

In the given experiment, the randomization is used by selecting 300 individuals from USA aged between 18 and 65 and then rubber A is assigned randomly to the right or left shoe of each individuals and then rubber B is assigned to other shoe of each individuals.

For example, if Mr. Nathaniel is one of 300 people randomly chosen, then the right heel of Mr. Nathaniel is randomly assigned to be made with the rubber A and then his left heel is to be made with the rubber B.

The same process is repeated for each of the 300 individuals.

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