Question

Design a full-factorial experiment.* Use one response and at least 2 factors, each factor with at least 2 levels.

Describe the response and factor variables (e.g., what type of data are they, what are their levels or value ranges).

What is the unit of observation?

Describe the population, the sampling technique (how will you ensure random selection of units), and the sample and cell (treatment combinations) sizes.

Will you have replications or repetitions?

Are there any blocking factors?

Graphically show the design and explain it.

How will you ensure random assignment of units to the treatment groups?

How will you ensure random order of experimental runs?

What are the environmental or noise factors?

Answer 1

Here we are designing 2⁴ full factorial experiment.

Here, Response = 0 and 1

factor variables = A, B, C, D

Example :- suppose our experiment is to determine the effect of a special diet and drug on cholesterol level.

=> let , A = drug effect

B = special diet

hence we are having 4 possible combination.

A₀B₀ = A group without drug and without diet.

A₁B₀= A group with drug and without diet.

A₀B₁=A group without drug and with diet.

A₁B₁=A group with drug and with diet.

a) Describe the response and factor variables (e.g., what type of data are they, what are their levels or value ranges).

Here response = 0 and 1 and factor A and B

c) Describe the population, the sampling technique (how will you ensure random selection of units), and the sample and cell (treatment combinations) sizes.

The sample selection is simple random sampling with replications. the 2 treatments are A and B.

the treatment combinations are 4.

d) Will you have replications or repetitions?

We have replications. we are using SRS with repetition.

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