A beverage distributor wanted to determine the combination of advertising agency (two levels) and advertising medium (three levels) that would produce the largest increase in sales per advertising dollar. Each of the advertising agencies prepared ads as required for each of the media-- newspaper, radio, and television. Twelve small towns of roughly the same size were selected for the experiment, and two each were randomly assigned to receive an advertisement prepared and transmitted by each of the six agency-medium
combinations. The dollar increases in sales per advertising dollar, based on a 1-month sales period, are shown in the table.

$$\begin{array}{l}
\text {\quad\quad\quad\quad\quad\quad\quad\quad\quad Advertising Medium }\
\begin{array} { l | c | c | c }
& { \text { Newspaper } } & \text { Radio } & \text { Television } \
\hline \text { Agency 1 } & 15.3,12.7 & 17.4,20.1 & 16.2,12.7 \
\text { Agency } 2 & 22.4,18.9 & 24.3,28.8 & 9.4,12.5
\end{array}
\end{array}$$ The SPSS analysis is shown below.

$* * *$ A N A L YSIS OF V ARIANCE***
SALES
BY AGENCY
MEDIUM
$\begin{array} { c l c c c r } & \text { Sum of } & & \text { Mean } & & \begin{array} { r } \text { Signif } \ \text { of F } \end{array} \ \text { Source of Variation } & \text { Squares } & \text { DF } & \text { Square } & \text { F } & \ \text { Main Effects } & 238.299 & 3 & 79.433 & 13.934 & .004 \end{array}$ $$\begin{array} { c r r r r r }
\text { AGENCY } & 39.967 & 1 & 39.967 & 7.011 & .038 \
\text { MEDIUM } & 198.332 & 2 & 99.166 & 17.395 & .003 \
\text { AGENCY*MEDIUM } & 77.345 & 2 & 38.672 & 6.784 & .029 \
& & & & & \
\text { Explained } & 315.644 & 5 & 63.129 & 11.074 & .005 \
\text { Residual } & 34.205 & 6 & 5.701 & & \
\text { Total } & 349.849 & 11 & 31.804 & &
\end{array}$$ (Note: SPSS uses "Explained" instead of "Treatment" in the factorial analysis. Also, SPSS uses "Residual" instead of "Error.") Would you test the main effects factors, agency and medium, in this example? Explain why or why not.

Question

A beverage distributor wanted to determine the combination of advertising agency (two levels) and advertising medium (three levels) that would produce the largest increase in sales per advertising dollar. Each of the advertising agencies prepared ads as required for each of the media-- newspaper, radio, and television. Twelve small towns of roughly the same size were selected for the experiment, and two each were randomly assigned to receive an advertisement prepared and transmitted by each of the six agency-medium
combinations. The dollar increases in sales per advertising dollar, based on a 1-month sales period, are shown in the table.

$$\begin{array}{l}
\text {\quad\quad\quad\quad\quad\quad\quad\quad\quad Advertising Medium }\
\begin{array} { l | c | c | c } 
&   { \text { Newspaper } } & \text { Radio } & \text { Television } \
\hline \text { Agency 1 } & 15.3,12.7 & 17.4,20.1 & 16.2,12.7 \
\text { Agency } 2 & 22.4,18.9 & 24.3,28.8 & 9.4,12.5
\end{array}
\end{array}$$ The SPSS analysis is shown below.

$* * *$ A N A L YSIS OF V ARIANCE***
SALES
BY AGENCY
MEDIUM
$\begin{array} { c l c c c r } & \text { Sum of } & & \text { Mean } & & \begin{array} { r } \text { Signif } \ \text { of F } \end{array} \ \text { Source of Variation } & \text { Squares } & \text { DF } & \text { Square } & \text { F } & \ \text { Main Effects } & 238.299 & 3 & 79.433 & 13.934 & .004 \end{array}$ $$\begin{array} { c r r r r r } 
\text { AGENCY } & 39.967 & 1 & 39.967 & 7.011 & .038 \
\text { MEDIUM } & 198.332 & 2 & 99.166 & 17.395 & .003 \
\text { AGENCY*MEDIUM } & 77.345 & 2 & 38.672 & 6.784 & .029 \
& & & & & \
\text { Explained } & 315.644 & 5 & 63.129 & 11.074 & .005 \
\text { Residual } & 34.205 & 6 & 5.701 & & \
\text { Total } & 349.849 & 11 & 31.804 & &
\end{array}$$ (Note: SPSS uses "Explained" instead of "Treatment" in the factorial analysis. Also, SPSS uses "Residual" instead of "Error.") Would you test the main effects factors, agency and medium, in this example? Explain why or why not.

Quizplus · Accepted Answer

The Answer of A beverage distributor wanted to determine the combination of advertising agency (two levels) and advertising medium (three levels) that would produce the largest increase in sales per advertising dollar. Each of the advertising agencies prepared ads as required for each of the media-- newspaper, radio, and television. Twelve small towns of roughly the same size were selected for the experiment, and two each were randomly assigned to receive an advertisement prepared and transmitted by each of the six agency-medium
combinations. The dollar increases in sales per advertising dollar, based on a 1-month sales period, are shown in the table.

$$\begin{array}{l}
\text {\quad\quad\quad\quad\quad\quad\quad\quad\quad Advertising Medium }\
\begin{array} { l | c | c | c } 
&   { \text { Newspaper } } & \text { Radio } & \text { Television } \
\hline \text { Agency 1 } & 15.3,12.7 & 17.4,20.1 & 16.2,12.7 \
\text { Agency } 2 & 22.4,18.9 & 24.3,28.8 & 9.4,12.5
\end{array}
\end{array}$$ The SPSS analysis is shown below.

$* * *$ A N A L YSIS OF V ARIANCE***
SALES
BY AGENCY
MEDIUM
$\begin{array} { c l c c c r } & \text { Sum of } & & \text { Mean } & & \begin{array} { r } \text { Signif } \ \text { of F } \end{array} \ \text { Source of Variation } & \text { Squares } & \text { DF } & \text { Square } & \text { F } & \ \text { Main Effects } & 238.299 & 3 & 79.433 & 13.934 & .004 \end{array}$ $$\begin{array} { c r r r r r } 
\text { AGENCY } & 39.967 & 1 & 39.967 & 7.011 & .038 \
\text { MEDIUM } & 198.332 & 2 & 99.166 & 17.395 & .003 \
\text { AGENCY*MEDIUM } & 77.345 & 2 & 38.672 & 6.784 & .029 \
& & & & & \
\text { Explained } & 315.644 & 5 & 63.129 & 11.074 & .005 \
\text { Residual } & 34.205 & 6 & 5.701 & & \
\text { Total } & 349.849 & 11 & 31.804 & &
\end{array}$$ (Note: SPSS uses "Explained" instead of "Treatment" in the factorial analysis. Also, SPSS uses "Residual" instead of "Error.") Would you test the main effects factors, agency and medium, in this example? Explain why or why not.

A Beverage Distributor Wanted to Determine the Combination of Advertising