1. Studentized Range Statistic
similar to t
Independent Groups
Largest mean
Smallest mean
If means are selected randomly t is approx. If not – correct p of Type I error why?
Example
8.2
11.8
critical value
= 3.77
Fail to Reject

2. Solving for smallest significant difference
When to use ?
When you expect:
Otherwise use F

3. Newman-Kewls Uses 1. Arrange in ascending order 2. Steps from to =
8.2
11.8 2.
Steps from to =
e.g.
&
smallest difference required was 6.61
If 2 steps
smallest significant difference

4. N-K 3. Treatment Matrix T1 T2 T3 r 3.6 3 6.61 2 5.41 4.
3.6 3
6.61 2
5.41 4.
Significant Difference Pattern T1 T2 T3

5. Example 2 3 9 10

6. Read Right to Left UNTIL 1. The row is completed 2.
A nonsignificant difference is found 2.
Reaching a column which was nonsignificant on the previous row

7. T1 T2 T3 T4 T5 r 1 7 8 5
4.04 6 4
3.79 3
3.44 2
2.86 T1 T2 T3 T4 T5 *

8. Unequal n’s
Tukey-Kramer
Replace
with

9. Behrens-Fisher * *
Each particular pairing of means must be examined with a different critical value and their own
Thus, the smallest significant difference will vary even for a given

10. Tukey's HSD Tukey's WSD N-K except
If there are 4 means, all differences are treated as 4 steps.
Tukey's WSD
r = # of steps between the two
means to be compared.

11. Tukey's HSD Use largest for all pairwise comparisons T1 T2 T3 T4 T5 17 8 5
4.04 6 4
3.79 3
3.44 2
2.86

12. Dunnett’s control vs. treatments
(even if a priori)
run standard
and use
or, solve for critical difference (CV)
Go to Table for *

13. Sheffé’s test Linear contrast MS(contrast)
It sets the family-wise Type-I Error rate ( in our case) for ALL possible linear contrasts, not merely the pair-wise comparisons.
Linear contrast
MS(contrast)
MS(error)
Evaluate at (k-1) critical value for (df treatment(k-1)), df error
Don’t use when only doing pair-wise, because it will be overly conservative.

14. Post Hoc – Sheffé test To evaluate 1)
consult F table and find critical value F.05 (k-1, dferror) (CV) 2)
multiply CV by (k-1). (new CV)
k = # of conditions
FW will now be held at 0.05