A reading specialist would like to know whether the page layout has any consistent effect on children's reading speed. He printed the same story in three types of page layout (one-column, two-column, and three-column) and then randomly assigned 15 children to each group. The time each child took to finish reading is recorded and compared using the one-factor ANOVA model. Complete the following ANOVA summary table using $\alpha$= .05. Based on the results, does page layout have an effect on the speed of reading?

$\begin{array}{lccccc}
\hline \text { Source } & S S & d f & M S & F & \text { Critical Value and Decision } \
\hline \text { Between } & & & 9 & 1.8 & \
\text { Within } & & & & & \
\text { Total } & & & & & \
\hline
\end{array}$

Question

A reading specialist would like to know whether the page layout has any consistent effect on children's reading speed. He printed the same story in three types of page layout (one-column, two-column, and three-column) and then randomly assigned 15 children to each group. The time each child took to finish reading is recorded and compared using the one-factor ANOVA model. Complete the following ANOVA summary table using

\alpha

= .05. Based on the results, does page layout have an effect on the speed of reading?

\begin{array}{lccccc}\hline \text { Source } & S S & d f & M S & F & \text { Critical Value and Decision } \\\hline \text { Between } & & & 9 & 1.8 & \\\text { Within } & & & & & \\\text { Total } & & & & & \\\hline\end{array}

$\begin{array}{lccccc}
\hline \text { Source } & S S & d f & M S & F & \text { Critical Value and Decision } \
\hline \text { Between } & & & 9 & 1.8 & \
\text { Within } & & & & & \
\text { Total } & & & & & \
\hline
\end{array}$

Quizplus · Accepted Answer

The Answer is There are 3 different types of page layout, so J = 3. There were 15 children in each group, so n = 15.
N = 3*15 = 45.
df_betw = J - 1 = 3 - 1 = 2, df_with = N - J = 45 - 3 = 42, df_total = N - 1 = 45 - 1 = 44.
Because F = MS_betw/MS_with, MS_with = MS_betw/F = 9/1.8 = 5.

SS_betw = MS_betw*df_betw = 9*2 = 18, SS_with = MS_with*df_with = 5*42 = 210, SS_total = SS_betw+ SS_with = 18 + 210 = 228.

Critical value _.05F_2,42 = 3.22. Because F = 1.8 < critical F value, we fail to reject H₀ and conclude that page layout does not have a significant effect on the speed of reading.

\begin{array}{lrrrcc}\hline ext { Source } & S S & {\boldsymbol{d f}} & {M S} & F & ext { Critical Value and Decision } \\hline ext { B etween } & 18 & 2 & 9 & 1.8 & .05 F_{2,42}=3.22 \ ext { Within } & 210 & 42 & 5 & & ext { Fail to reject } H 0 \ ext { Total } & 228 & 44 & & & \\hline\end{array}

A Reading Specialist Would Like to Know Whether the Page α\alphaα

A Reading Specialist Would Like to Know Whether the Page $\alpha$