In section\(13.2\) we considered two hypothetical examples to explain the logic behind one-way ANOVA. Now you are to further examine those examples.

a. Refer to Table \(13.1\) on page \(528\). Perform a one-way ANOVA on the data and compare your conclusion to that stated in the corresponding "what does it mean"? box. Use \(\alpha =0.05\).

b. Repeat part (a) for the data in Table \(13.2\) on page \(528\).

The data given is

Calculate the SST, SSTR and SSE using given relation

\(SST=\sum x^{2}-\frac{(\sum x)^{2}}{n}\)

\(SST=7272-\frac{(270)^{2}}{24}=1197\)

\(SSTR=\frac{\sum (x_{i})^{2}}{n_{i}}-\frac{\sum (x)^{2}}{n}\)

\(SSTR=\frac{120^{2}}{6}+\frac{150^{2}}{6}-\frac{(270)^{2}}{12}=75\)

\(SSE=SST-SSTR=1122\)

Then,

\(df_{T}=k-1=4-1=3\)

\(df_{E}=n-k=24-4=20\)

\(MSTR=\frac{SSTR}{df_{T}}=\frac{75}{1}=75\)

\(MSE=\frac{SSE}{df_{E}}=\frac{1122}{10}=112.2\)

\(F=\frac{MSTR}{MSE}=\frac{75}{112.2}\approx 0.67\)

Then make an ANOVA table.

At the \(5%\) significance level data do not provide the sufficient evidence because p-value fail to reject null hypothesis.

\(P>0.05\Rightarrow\) Fail to Reject \(H_{0}\)

Program:

Query:

• First, we have defined the samples.
• Calculate the value of SST and SSTR.

• Then calculate the SSE.