Please help me with multiple comparisons - urgent (stats)

mintsharpie

Hello, I just have a quick question understanding multiple comparisons and I'd appreciate any help because I'm on the verge of failing I'm reviewing for a test, and reading over questions and their corresponding answers in the back of the textbook. The question I'm stuck on deals with a psychologist testing the claim made by a drug company that a drug would help patients.

To do this, they selected 20 patients from their hospital, and randomly assigned them to one of four groups - group 1 receiving the new drug, group 2 receiving a different drug, group 3 receiving a different drug, and group 4 as the control group. Here is the answer given in the textbook:



I understand the first part, and how SSE is calculated and everything, but the second table with the contrasts totally baffles me. I have no idea how that table was filled in, or how I would be able to fill it in on a test if I had a different example. How were those 1s, -1s, and 2s determined? What do they mean and how were they calculated? In addition, once I go on to the appropriate post hoc test - in this case, Dunn - how do I utilise the table in terms of critical values?

Please help me, I'm so very lost!

Stephen Tashi

I'm not an expert on this, but I was curious enough about the table to look up "Dunn Test" and found: http://www.google.com/url?sa=t&rct=j...NAkXpw&cad=rja

In the slide "What is a contrast anyway", it is explained that a contrast is a linear combination of means. For example, if the hypothesis [itex] \mu_A = \mu_B [/itex] is true then the contrast [itex] 1 \mu_A + (-1) \mu_B = 0 [/itex]. So I suspect the table gives you the coefficients (such as 1 and -1) that are involved in the contrast being tested. I don't know anything else about the subject.

mintsharpie

I'm so confused, and I don't understand this at all

ssd

This is an "analysis of one way classified data".
In design of experiments you see it as CRD (completely randomized design).
The analysis is very straight forward.

Xi = ith observation
Ti= i th row total, G = sum of Ti. Then SS(T)= Sum(Ti*Ti/Ni)-cf, has df=4-1=3
where, cf= (G*G/N), Ni= values in i th row, N = sum of Ni.
SST= Sum(Xi*Xi)-cf, has df= 20-1=19.
SSE= SST-SS(T), has df=19-3=16.
F= MS(T)/MSE ~ F (3,16) (=> F distribution with 3,16 df)
MS(T)=SS(T)/3, MSE=SSE/16. Critical region:F> F(a,3,16). a=0.05 or 0.01 as you choose. Find F(a,3,16)
from Biometrica tables.