There are four levels in an experiment. Emma wants to employ complete counterbalancing. The minimum number of participants she would require are

To determine the minimum number of participants required for complete counterbalancing in an experiment with four levels, we need to follow these steps:

1. Break Down the Problem

Complete counterbalancing means that each participant experiences every possible order of the levels. With four levels, we need to calculate the number of permutations of these levels.

2. Relevant Concepts

The number of ways to arrange $n$ items (levels in this case) is given by $n!$ (n factorial). For $n = 4$: $n! = 4! = 4 \times 3 \times 2 \times 1$

3. Analysis and Detail

Calculating $4!$: $4! = 4 \times 3 \times 2 \times 1 = 24$ This means there are 24 unique orders in which the four levels can be presented.

4. Verify and Summarize

Since each participant experiences one complete order of the four levels, the minimum number of participants required for complete counterbalancing of four levels is 24.

Final Answer

The minimum number of participants required is $24$.