Here is an Excel ANOVA table for an experiment that analyzed two factors that may affect patients' blood pressure (some information is missing). $$\begin{array} { | l | c | c | c | c | c | }
\hline \text { Source of Variation } & S S & d f & M S & F & \text { P-value } \
\hline \text { Medication type } & 16.5313 & 1 & 16.5313 & 9.173 & 0.006 \
\hline \text { Patient age group } & 25.0938 & & 8.3646 & 4.642 & 0.011 \
\hline \text { Interaction } & 1.8438 & 3 & 0.6146 & 0.341 & 0.796 \
\hline \text { Error } & 43.2504 & 24 & 1.8021 & & \
\hline & & & & & \
\hline \text { Total } & 86.7192 & & & & \
\hline
\end{array}$$ The overall sample size is:
A)7.
B)25.
C)32.
D)impossible to determine as given.

Question

Here is an Excel ANOVA table for an experiment that analyzed two factors that may affect patients' blood pressure (some information is missing). $$\begin{array} { | l | c | c | c | c | c | } 
\hline \text { Source of Variation } & S S & d f & M S & F & \text { P-value } \
\hline \text { Medication type } & 16.5313 & 1 & 16.5313 & 9.173 & 0.006 \
\hline \text { Patient age group } & 25.0938 & & 8.3646 & 4.642 & 0.011 \
\hline \text { Interaction } & 1.8438 & 3 & 0.6146 & 0.341 & 0.796 \
\hline \text { Error } & 43.2504 & 24 & 1.8021 & & \
\hline & & & & & \
\hline \text { Total } & 86.7192 & & & & \
\hline
\end{array}$$ The overall sample size is:
A)7.
B)25.
C)32.
D)impossible to determine as given.

Quizplus · Accepted Answer

The total degrees of freedom (df) can be determined by adding up the df for each source of variation. In this case, Medication type has 1 df, Patient age group has an unknown df (which we can determine later), and Interaction has 3 df. The Error df is given as 24. Thus, the total df is:

1 + df for Patient age group + 3 + 24 = total df
28 + df for Patient age group = total df

The total SS is given as 86.7192. If we divide this by the total df, we get the Mean Square Error (MSE):

MSE = 86.7192/total df

The MSE is also given as 1.8021 for the Error source of variation. Thus:

MSE = 1.8021

We can use this to solve for the df for Patient age group:

25.0938/df for Patient age group = 8.3646

df for Patient age group = 2.997 ≈ 3

Thus, the total df is:

1 + 3 + 3 + 24 = 31

And the overall sample size is:

n = total df + 1 = 32.

Here Is an Excel ANOVA Table for an Experiment That