Let's help with that!
a. Here's the data in a suitable form for computing the phi-coefficient:
| Intelligence (X) | Willingness to Participate (Y) | Frequency |
| --- | --- | --- |
| 0 (Lower) | 0 (Not Willing) | 3 |
| 0 (Lower) | 1 (Willing) | 7 |
| 1 (Higher) | 0 (Not Willing) | 8 |
| 1 (Higher) | 1 (Willing) | 2 |
b. To compute the phi-coefficient (φ), we'll use the following formula:
φ = √[(χ² / N)]
where χ² is the chi-squared statistic, and N is the total sample size.
First, let's calculate χ²:
χ² = Σ[(observed frequency - expected frequency)^2 / expected frequency]
Using the frequencies from the table, we get:
χ² = [(3-4.5)^2/4.5 + (7-5.5)^2/5.5 + (8-5.5)^2/5.5 + (2-4.5)^2/4.5] = 4.5
Now, let's calculate φ:
φ = √[(4.5 / 20)] = √(0.225) = 0.474
So, the phi-coefficient (φ) is approximately 0.474.
The phi-coefficient measures the strength of association between two binary variables. In this case, it indicates a moderate positive association between higher intelligence and willingness to participate.
