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:

Is there a conjecture?

What is the response variable?

What is the explanatory variable?

What levels of the factor(s) were used in the expereiment?

What are the treatments for this experiment?

What are the experimental units?

What is the control?

Hoe much replication was used?

How was randomization used?

Answer 1

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Conjecture:

A conjecture is an educated guess. In Statistics, conjecture may be linked to the hypothesis statement, wherein the researcher believes one condition to be fitted to a particular situation, based on their understanding and experience, which they wish to establish by conducting a formal test.

In this case, it is to be tested whether rubber A is more durable when compared to rubber B. Hence, the conjecture would be, “rubber A is more effective than rubber B”.

Response variable:

Response variable is the variable of interest in a study, which is to be measured. Often, the response variable is considered to depend on various factors affecting it.

In this case, the researchers first measure the heel wear in rubber A and rubber B (wA and wB respectively). Then, they take the difference (wA – wB) for each experimental unit and use these differences for their comparison purposes. Here, the difference (wA – wB) is the response variable, as it is the variable of interest to the researcher.

Explanatory variable:

Explanatory variable is the variable which is believed to affect the response variable, and explains the variability in it.

In this case, the researchers mainly aim to find whether the type of rubber affects the amount of heel wear. Hence, the explanatory variable is the type of rubber.

Level of factor:

The different types of categories of a particular explanatory variable are called its levels.

Here, the explanatory variable, type of rubber, has 2 categories, that is, 2 levels, which are- rubber A and rubber B.