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

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

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

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

Example 2 3 9 10

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

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 *

Unequal n’s Tukey-Kramer Replace with

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

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.

Tukey's HSD Use largest for all pairwise comparisons T1 T2 T3 T4 T5 1 7 8 5 4.04 6 4 3.79 3 3.44 2 2.86

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

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.

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