Aa Aa E. 6. Calculating the phi-coefficient Suppose a researcher is interested i

Question

Aa Aa E. 6. Calculating the phi-coefficient Suppose a researcher is interested in examining the relationship between a person's age and whether he or she listens to rap music. She collects a sample of n 0 people and asks them whether they listen to rap music. The following table summarizes the results. Does Not Listen to Listens to Rap Music Rap Music 18 Years Old 18+ Years Old The researcher wants to calculate the correlation between a person's age and whether he or she listens to rap music. To do so, the researcher first creates a table of the data by converting each variable to a numerical value. She assigns 0 to 18 years old" and 1 to "18+ years old." She then assigns 0 to "does not listen to rap music" and 1 to "listens to rap music." Complete the bottom two rows of the researcher's data Listens to Rap Music Age 0 18 years old 0 no 1- 18+ years old 1 yes

Explanation / Answer

The last two rows of the data are

1 1

1 1

Phi coefficient is the appropriate correlation here because binary variables are being used. It is especially useful in case of binary variables.

The phi-coefficient is given by (AD-BC) /SQRT( (A+B)(C+D)(A+C)(B+D))

where A = 3,b=2,c=2,d=3

phi-coefficient = (3*3- 2*2)/ sqrt(5*5*5*5) = 5 / 25 = 0.2

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