Question

What is the degrees of freedom associated with each independent variable (factor) in a two-way ANOVA?

a) (a-1) and (b-1)
b) (a+b-1)
c) (a-1) * (b-1)
d) (a*b)

Answer 1

In a two-way ANOVA, the degrees of freedom for each independent variable are (a-1) and (b-1), where 'a' and 'b' are the number of levels for the first and second factors, respectively.

Step-by-step explanation:

The degrees of freedom associated with each independent variable (factor) in a two-way ANOVA would be (a-1) and (b-1). Here, 'a' represents the number of levels for the first factor, and 'b' represents the number of levels for the second factor. This calculation comes from the idea that degrees of freedom is the number of values in the final calculation of a statistic that are free to vary. In a two-way ANOVA, the degrees of freedom for each factor helps to describe the variability attributed to each factor independently.