MANE 6313
Week 4, Module E
Student Learning Outcome
Analyze simple comparative experiments and experiments with a single factor.
Module Learning Outcome
Interpret multiple comparisons of treatments.
Contrasts
-
A hypothesis from a linear combination of the parameters \(C=\sum_{i=1}^ac_iy_{i.}\) with the constraint that \(\sum_{i=1}^ac_i=0\)
-
Can be extended to multiple comparisons using orthogonal contrasts
Multiple Comparisons
-
Used to test \(H_0:\mu_i=\mu_j\) for all \(i\neq j\)
-
Only used if \(H_0\) is rejected
-
There are four methods presented in the textbook
-
LSD method
-
Duncan's multiple range test
-
Newman-Keuls test
-
Tukey's test
-
-
All methods control family-wise error rate not individual error rate
-
Read the section on "which method do I use?"
Review Mortar Example
"Fancy" Dot Plot of Mortar Example
- requires ggPlot2 package
Dot Plot without Messages
- Add "messages=FALSE" to "{r}"
Tukey Multiple Comparison Example
Tukey Multiple Comparison - Graphical
Other Multiple Comparison Techniques
- R supports the following other methods
- FisherLSD in package MAIT
- Duncan.test in package agricolae
- SnkTest in package PMCMRplus
- The methods shown above will not be demonstrated in this class