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¶
-
Bartlett's Test
-
Relies on the assumption of Normality
-
Levene's Test
-
More robust to departures of Normality
-
R performs both tests!
Bartlett's Test Example Problem¶
The source for problems 12. 10 and 12.30 is Ostle, Turner, Hicks and McElrath[^1]
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¶
[^1]: Ostle, Turner, Hicks and McElrath. (1996). Engineering Statistics: The Industrial Experience. Duxbury Press.