Question

A chi-square test for independence is being used to evaluate the relationship between two variables. If the test has df = 3, what can you conclude about the two variables?

One variable consists of 2 categories and the other consists of 3 categories |

One variable consists of 2 categories and the other consists of 4 categories |

Both variables consists of 2 categories |

Both variables consists of 3 categories |

Answer #1

Answer: **One variable consists of 2 categories and the
other consists of 4 categories**

Reason: For Chi square test for independence , Degrees of freedom = (r-1)*(c-1)

where r - number of rows and

c - number of columns

we know that df = 3

df = (r-1)*(c-1) = 3

if we consider r= 2 and c= 2, the df = 1 which is not correct

if we consider r=3, c=3 then df = 2*2 =4 which is also not correct

if we consider r = 2, c= 3, then df = 1*2 = 2 which is also not correct

but if we consider r = 2, c= 4 , then df = 1*3 = 3 which is the given df

Henec we have One variable consists of 2 categories and the other consists of 4 categories

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