Question

in a designed experiment, there are two factors with each having four levels. how many treatments are there? choose the correct answer below a. there are four treatments. b. there are eight treatments. c. there are sixteen treatments. d. there is one treatment.

Explanation:

Step1: Recall the principle of counting treatments in a factorial experiment

In a factorial experiment with \(n\) factors, where the first factor has \(a\) levels, the second factor has \(b\) levels, etc., the total number of treatments is the product of the number of levels of each factor. Here, we have 2 factors, each with 4 levels.

Step2: Calculate the number of treatments

The formula for the number of treatments \(T\) when there are two factors with \(a\) and \(b\) levels respectively is \(T=a\times b\). Substituting \(a = 4\) and \(b=4\) (since both factors have 4 levels), we get \(T = 4\times4=16\).

Answer:

C. There are sixteen treatments.