Calculating the Yules Coefficient of Association for N = 35
Understanding the Yule’s Coefficient of Association is crucial for anyone involved in statistical analysis. This coefficient is a measure of association between two binary variables, providing a value between -1 and 1. A positive value indicates a positive association, a negative value indicates a negative association, and a value of zero indicates no association. In this article, we will delve into how to calculate the Yule’s Coefficient of Association for N = 35, with the frequency of A being 18, the frequency of AB being 8, and the frequency of αβ being 5.
Understanding the Yule’s Coefficient of Association
The Yule’s Coefficient of Association, also known as Yule’s Q, is a statistical measure used to quantify the degree of association between two binary variables. It is based on the odds ratio, which is the ratio of the odds of an event occurring in one group to the odds of it occurring in another group. The formula for Yule’s Q is:
Q = (AD - BC) / (AD + BC)
Where A, B, C, and D are the frequencies of the four possible outcomes in a 2×2 contingency table.
Calculating the Yule’s Coefficient of Association
Given the frequencies of A, AB, and αβ, we can calculate the Yule’s Coefficient of Association as follows:
- First, calculate the frequencies of B, C, and D. Since we know that N = 35, A = 18, AB = 8, and αβ = 5, we can calculate B = N – A = 35 – 18 = 17, C = A – AB = 18 – 8 = 10, and D = N – A – B – C = 35 – 18 – 17 – 10 = 0.
- Next, substitute these values into the formula for Yule’s Q. This gives us Q = (AD – BC) / (AD + BC) = (18*0 – 10*17) / (18*0 + 10*17) = -170 / 170 = -1.
Therefore, the Yule’s Coefficient of Association for the given frequencies is -1, indicating a strong negative association between the two variables.
Interpreting the Yule’s Coefficient of Association
The Yule’s Coefficient of Association can range from -1 to 1. A value of -1 indicates a perfect negative association, meaning that as one variable increases, the other decreases. A value of 1 indicates a perfect positive association, meaning that both variables increase or decrease together. A value of 0 indicates no association between the variables.
In this case, a Yule’s Coefficient of Association of -1 indicates a strong negative association between the two variables. This means that as the frequency of one variable increases, the frequency of the other variable decreases.
Understanding the Yule’s Coefficient of Association and how to calculate it is crucial for anyone involved in statistical analysis. It provides a valuable measure of the degree of association between two binary variables, helping to inform decision-making and analysis.
