Q 1.89. - Elementary Statistics

Question

In a designed experiment, there are two factors. One factor has m levels and the other factor has n levels. Determine the number of treatments. 

Hint: Refer to Exercise 1.87 or Exercise 1.88.

Step-by-Step Solution

Answer

The total number of levels is mn.

Step 1. Given information.

The given statement is:

In a designed experiment, there are two factors. One factor has m levels and the other factor has n levels.

Step 2. Determine the number of treatments.

The number of levels for factor one is "m", while the second factor has "n" levels.

The number of treatments will equal the product of the two factors is:

$$\begin{gathered} =\mathrm{Number} \mathrm{of} \mathrm{levels} \mathrm{of} \mathrm{factor} 1 \times \mathrm{Number} \mathrm{of} \mathrm{levels} \mathrm{of} \mathrm{factor} 2nd \\ =m\times n \\ =mn \end{gathered}$$