ANOVA Table Post Hoc Analysis
Tukey Simultaneous Comparison T-Values $($

question 143

Multiple Choice

ANOVA table
$\begin{array}{lrrrr}\hline\text { Source } & S S & d f & M S & F &p \text {-value }\\\hline \text { Treatment } & 6.000 & 3 & 1.9998 & 18.85&3.4E-05\\\hline\text { Error } & 1.486 & 14 & 0.1061 & \\\hline\text { Total } & 7.485 & 17 & &\end{array}$
Post hoc analysis
Tukey simultaneous comparison t-values $($ d.f. $=14)$
$\begin{array}{ccccc}&\text { Brand 3 }   \text { Brand 2 }  \text { Brand 4 }  \text { Brand 1 } \\&\quad1.40 \quad 2.28 \quad 2.58 \quad 2.95\\\begin{array}{ll}\text { Brand 3 } & 1.40 \\\text { Brand 2 } & 2.28 \\\text { Brand 4 } & 2.58 \\\text { Brand 1 } & 2.95\end{array}&\begin{array}{|l|l|l|l|}\hline & & & \\\hline 4.27 & & & \\\hline 5.38 & 1.35 & & \\\hline 7.09 & 3.07 & 1.63 &\quad\quad \\\hline\end{array}\end{array}$
The Excel/Mega-Stat output given above summarizes the results of a one-way analysis of variance in an attempt to compare the performance characteristics of four brands of vacuum cleaners. The response variable is the amount of time it takes to clean a specific size room with a specific amount of dirt.

-At a significance level of 0.05,the null hypothesis for the ANOVA F test is rejected.Analysis of the Tukey's simultaneous confidence intervals shows that at the significance level (experimentwise) of 0.05 we would conclude that,in regards to average time,

• A)all four brands of vacuum cleaners differ from each other in terms of their performance.
• B)brand 1 differs from brand 2,and brand 2 differs from brand 3 while the rest of the vacuum cleaner pairs do not differ from each other in terms of their performance.
• C)brand 1 differs from brand 2,and brand 3 differs from brands 1,2 and 4,while the rest of the vacuum cleaner pairs do not differ from each other in terms of their performance.
• D)only brand 3 differs from the other three brands (brands 1,2 and 3),while the rest of the vacuum cleaner pairs do not differ from each other in terms of their performance.
• E)none of the four brands of vacuum cleaners differ from each other in terms of their performance.

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