IDNLearn.com connects you with a global community of knowledgeable individuals. Whether it's a simple query or a complex problem, our experts have the answers you need.
Sagot :
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.
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.
Thank you for participating in our discussion. We value every contribution. Keep sharing knowledge and helping others find the answers they need. Let's create a dynamic and informative learning environment together. Discover insightful answers at IDNLearn.com. We appreciate your visit and look forward to assisting you again.
