1. After ANOVA
If your F < F critical: Null not rejected, stop right now!!
If your F > F critical: Null rejected, now figure out which of the multiple means differ from which others
Use multiple comparison test (many available)
2 kinds of MCT
 comparisons between all pairs of means
 comparisons between a control and all other means

2. For all possible pair-wise comparisons
Multiple Comparison Tests
Tukey Test
H0: A = B
For all possible pair-wise comparisons
Number of comparisons of K, 2 at a time =
k (k-1) 2

3. --Arrange the means in order of increasing magnitude
Conclusions depend on order in which pairwise comparisons considered
Largest to smallest, then largest to next smallest…..
Then second largest to smallest………
--Calculate q for each pair of means
XbarB- XbarA
q = SE s2
Within groups MS from ANOVA = n
# data in A & B
See modification for unequal sample size pg 212 Zar

4. Other MCT available (see hand out)
Tukey’s:
--controls for experiment-wise error rate
--is conservative (less likely to find difference)
--rarely criticized
Dunnett’s test:
--designed to compare control to all other groups
--not interested in all comparisons
--SAS assumes first treatment level is control
Scheffe’s test:
--best for “multiple contrasts”
--ex. want to compare level 1, 2, & 3 to level 4

5. Normally pick one data start;
infile 'C:\Documents and Settings\cmayer3\My Documents\teaching\Biostatistics\Lectures\exam 1 anova.csv' dlm=',' DSD;
input trtmt $ nampeat;
options ls=80;
proc print;
data two; set start;
proc glm;
class trtmt;
model nampeat=trtmt;
means trtmt/tukey bon scheffe duncan snk;
run;
Normally pick one

6. The SAS System
15:11 Tuesday, October 4, 2005
The GLM Procedure
Class Level Information
Class Levels Values
trtmt dark highligh lowlight
Number of Observations Read
Number of Observations Used
Dependent Variable: nampeat
Sum of
Source DF Squares Mean Square F Value Pr > F
Model
Error
Corrected Total
R-Square Coeff Var Root MSE nampeat Mean
Source DF Type I SS Mean Square F Value Pr > F
trtmt
Source DF Type III SS Mean Square F Value Pr > F
Output gives type I and type III SS, use type 3 insensitive to model order (same for simple models)

7. Output for Tukey– all tests gave same results in this case
The SAS System
15:11 Tuesday, October 4, 2005
= The GLM Procedure
Tukey's Studentized Range (HSD) Test for nampeat
NOTE: This test controls the Type I experimentwise error rate, but it generally
has a higher Type II error rate than REGWQ.
Alpha
Error Degrees of Freedom
Error Mean Square
Critical Value of Studentized Range
Minimum Significant Difference
Means with the same letter are not significantly different.
Tukey Grouping Mean N trtmt
A lowlight A
B A highligh B
B dark
Output for Tukey– all tests gave same results in this case
Now must interpret
Low differs from dark, high not differ from dark………. Conclusion, any light at all affects feeding level not important
Sometimes lines over treatments
Letters used to show diffs