Consider the following partial ANOVA table: $$\begin{array} { | l | l l l l | }
\hline \text { Source of Variation } & \boldsymbol { S S } & \boldsymbol { d f } & \boldsymbol { M S } & \boldsymbol { F } \
\hline \text { Treatments } & 75 & * & 25 & 6.67 \
\text { Error } & 60 & * & 3.75 & \
\hline \text { Total } & 135 & 19 & & \
\hline
\end{array}$$ The numerator and denominator degrees of freedom (identified by asterisks)are,respectively,
A) 4 and 15.
B) 3 and 16.
C) 15 and 4.
D) 16 and 3.

Question

Consider the following partial ANOVA table: $$\begin{array} { | l | l l l l | } 
\hline \text { Source of Variation } & \boldsymbol { S S } & \boldsymbol { d f } & \boldsymbol { M S } & \boldsymbol { F } \
\hline \text { Treatments } & 75 & * & 25 & 6.67 \
\text { Error } & 60 & * & 3.75 & \
\hline \text { Total } & 135 & 19 & & \
\hline
\end{array}$$ The numerator and denominator degrees of freedom (identified by asterisks)are,respectively,
A) 4 and 15.
B) 3 and 16.
C) 15 and 4.
D) 16 and 3.

Quizplus · Accepted Answer

The degrees of freedom for treatments is equal to the number of groups minus 1, which we cannot determine from the given information. However, since the total degrees of freedom is 19 and the error degrees of freedom is not listed, we can use the fact that:

Total Degrees of Freedom = Treatments Degrees of Freedom + Error Degrees of Freedom

Substituting in the values we have:

19 = * + *

Since the error mean square is equal to:

Error Mean Square = Error Sum of Squares / Error Degrees of Freedom

We can solve for the error degrees of freedom using the error sum of squares value given:

60 = Error Sum of Squares
3.75 = Error Mean Square = 60 / Error Degrees of Freedom
Error Degrees of Freedom = 60 / 3.75 = 16

Substituting back in to the equation for total degrees of freedom:

19 = * + 16
* = 3

Therefore, the numerator and denominator degrees of freedom are 3 and 16, respectively.

Consider the Following Partial ANOVA Table The Numerator and Denominator Degrees of Freedom (Identified by Asterisks)are,respectively