similar to t

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 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
Arrange in ascending order
1.

8.2 8.2 11.8
Steps from to
2.

e.g.
smallest difference required was 6.61
If 2 steps
smallest significant difference
4
N-K
3.
Treatment Matrix
T1 T2 T3 r
T1 0 3.6 3 6.61
T2 3.6 2 5.41
T3
Significant Difference Pattern
4.
T1 T2 T3
T1
T2
T3
5
Example

2 3 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
T1 1 1 7 8 5 4.04
T2 0 6 7 4 3.79
T3 6 7 3 3.44
T4 1 2 2.86
T5
T1 T2 T3 T4 T5
T1
T2
T3
T4
T5
8
Unequal ns
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
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
T1 1 1 7 8 5 4.04
T2 6 7 4 3.79
T3 6 7 3 3.44
T4 1 2 2.86
T5
12
Dunnetts control vs. treatments
(even if a priori)
run standard
and use
or, solve for critical difference (CV)
Go to Table for

13
Sheffés test
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
Dont 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