Question

a b total c x 0.25 g d y 0.68 h e z 0.07 j total 1.0 1.0 1.0 which value for y in the table would be least likely to indicate an association between the variables? 0.06 0.24 0.69 1.0

Explanation:

Step1: Recall the concept of independence

In a two - way table, if the variables are independent, the joint probabilities follow the rule \(P(A\cap B)=P(A)\times P(B)\). When the rows and columns are in proportion, there is no association. For a row - total and column - total perspective, if the distribution of one variable is the same across the levels of the other variable, there is no association. A value of \(Y\) close to the proportion of the column total for \(A\) (since the column total for \(A\) is \(1.0\)) would suggest independence.

Step2: Analyze the column totals

The column total for \(B\) is \(1.0\). If there is no association, the values in the rows should be in proportion to the column totals. The value of \(Y\) that is closest to the proportion of the column total for \(A\) (i.e., a value that makes the distribution of the variable in rows similar across columns) is the one that least indicates an association. The closer \(Y\) is to \(0.24\) (since \(0.25 + 0.68+0.07 = 1.0\) and we want to maintain a similar distribution pattern as if the variables were independent), the less likely there is an association.

Answer:

B. 0.24