MANE 6313
Week 4, Module D
Student Learning Outcome
Analyze simple comparative experiments and experiments with a single factor.
Module Learning Outcome
Assess the assumption of equal variances in one-way analysis of variance.
Test for Equality of Variances
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Bartlett's Test
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Relies on the assumption of Normality
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Levene's Test
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More robust to departures of Normality
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R performs both tests!
Bartlett's Test Example Problem
The source for problems 12. 10 and 12.30 is Ostle, Turner, Hicks and McElrath1
Box Plots
Analysis of Variance
Residual Plot
Bartlett's Test
\[
\begin{eqnarray*}
H_0&:&\sigma^2_1=\sigma^2_2=\cdots=\sigma^2_a\\
H_1&:&\mbox{above not true for at least one }\sigma^2_i
\end{eqnarray*}
\]
Levene's Test
\[
\begin{eqnarray*}
H_0&:\sigma^2_1=\sigma^2_2=\cdots=\sigma^2_a\\
H_1&:\mbox{above not true for at least one }\sigma^2_i
\end{eqnarray*}
\]
R Demonstration
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Ostle, Turner, Hicks and McElrath. (1996). Engineering Statistics: The Industrial Experience. Duxbury Press. ↩