Question

In a two-factor analysis of variance, the F-ratios for factor A, factor B, and the AxB interaction _____. Group of answer choices may have different df values but they all have the same denominator all have the same df values and they all have the same denominator may have different df values and may have different denominators all have the same df values but they may have different denominators

Answer 1

Answer:

may have different df values but they all have the same denominator

Step-by-step explanation:

In a two-factor analysis of variance, the F-ratios for factor A, factor B, and the AxB interaction _____. may have different df values but they all have the same denominator

In two--factor analysis of variance, the estimates of the variance can be obtained by partitioning the total sum of squares into three components corresponding to the three possible sources of variation , viz; Between Rows, Between Columns, and Within Samples or error.

As the number of rows and columns may differ the degrees of freedom differ with them.

In other words

Total df= Rows df + Columns df + Error df

Since the variance is identically the same for each row of the c values and variance is the same for each observation in the jth column of r values the sum of squares becomes an identity.

Therefore it may have different df values but they all have the same denominator.