In a full factorial experimental design, factors A, B, C, and D are tested at 2 levels. How many experimentsare conducted (without considering replications)?

1. Break Down the Problem

To solve the problem, we need to determine how many combinations of factors will be tested in a full factorial design. The factors are A, B, C, and D, and each of these factors has 2 levels.

2. Relevant Concepts

In a full factorial design, the total number of experiments is calculated using the formula:

$N = L^k$

where:

• $N$ is the total number of experiments,
• $L$ is the number of levels for each factor,
• $k$ is the number of factors.

3. Analysis and Detail

In this case:

• $L = 2$ (since each factor is at 2 levels),
• $k = 4$ (since there are 4 factors: A, B, C, and D).

Using the formula:

$N = 2^4$

Calculating $2^4$:

$2^4 = 16$

4. Verify and Summarize

After calculating, we find that $N = 16$. Thus, there will be a total of 16 unique combinations of factor levels across the four factors.

Final Answer

The total number of experiments conducted is $16$.