Question

A researcher is using a chi-square test for independence to examine the relationship between TV preferences and gender for a sample of n = 100 children. Each child is asked to select his/her favorite from a fixed set of three TV shows and each child is classified as male or female. The chi-square statistic for this study would have df equal to _____.
a. 2
b. 3
c. 5
d. 99

Answer 1

Answer:

  Answer = a. 2

  Degree of freedom df = (r – 1)(c – 1) = (2 – 1)(3 – 1) = (1)(2) = 1 x 2 = 2

Step-by-step explanation:

The degree of freedom of a one-dimensional chi-square statistic is df = n– 1, where ‘n’ is the number of categories or levels of the independent variable. But in this case, we are to analyze a two-way contingency table. This Chi-square test of independence uses a contingency table format. It is also referred to as a contingency table test. A (row  X column) contingency table shows the observed frequencies for two categorical variables ( in the is case: TV shows and Gender) arranged in  ‘r’ rows and ‘c’ columns. The sum of the observed frequencies is ‘n’, the sample size, that is, the row and column totals adds up to form a grand total ‘n’ which is the sample size. Since the rows and columns have been classified into mutually exclusive categories where the three TV shows will serve as the column heads and the male and female classification will serve as the rows, the degree of freedom for the test will be to multiply the individual degree of freedom of both row (r-1)  and column (c-1) numbers in the (row  X column) contingency table format for the test. Thus the degrees of freedom df = (r – 1)(c – 1), where r = number of rows(Male/Female) and c = number of columns (TV shows) .

Now, the gender here is 2 and the TV shows are 3

 So,  r =   2 and C = 3

   Degree of freedom df = (r – 1)(c – 1) = (2 – 1)(3 – 1) = (1)(2) = 1 x 2 = 2