Question

In a designed experiment, there are two factors, say, Factor Aand Factor B. Factor Ahas four levels, say, $a_1,a_2,a_{3}and{a}_4$; Factor B has two levels, say,$b_1\mathrm{and}{b}_2$.

(a) Construct a schematic for the treatments similar to Table 1.8 on page 27.

(b) Use part ( a ) to determine the number of treatments.

(c) Could you have determined the answer for part ( b ) without constructing the schematic in part ( a )? Explain your answer.

Short answer

Part (a)

Part (b) 8.

Part (c) 8.

Step-by-step solution

Part (a) Step 1. Given information.

The given statement is:

In a designed experiment, there are two factors, say, FactorAand FactorB. FactorAhas four levels, say, $a_1,a_2,a_{3}and{a}_4$; Factor B has two levels, say,$b_1\mathrm{and}{b}_2$.

Part (a) Step 2. Construct a schematic for the treatments.

Construct a schematic for the treatments as shown below:

Part (b) Step 1. Determine the number of treatments.

There are eight combinations based on the schematic for the treatments obtained in part (a).

As a result, there are a total of eight treatments.

Part (c) Step 1. Determine the number of treatments without constructing the schematic.

The number of levels for factor Ais four, while factor Bhas two levels.

The number of treatments will equal the product of factor Aand factor B:

$$\begin{gathered} =\mathrm{Number}\mathrm{of}\mathrm{levels}\mathrm{of}\mathrm{factor}A\times \mathrm{Number}\mathrm{of}\mathrm{levels}\mathrm{of}\mathrm{factor}B \\ =4\times 2 \\ =8 \end{gathered}$$

As a result, The total number of levels is 8.