Please help me with multiple comparisons - (stats)

[mintsharpie]

Please help me with multiple comparisons - urgent (stats)

Hello, I just have a quick question understanding multiple comparisons and I'd appreciate any help because I'm on the verge of failing :uhh: 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=...sg=AFQjCNENKSsWfC1UN4CdwHObbCR7NAkXpw&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 $\mu_A = \mu_B$ is true then the contrast $1 \mu_A + (-1) \mu_B = 0$. 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.

 

[blue_raver22]

Hello there,

I understand that you are struggling with understanding multiple comparisons in statistics and are feeling overwhelmed. Don't worry, I am here to help you.

Multiple comparisons refer to the process of comparing more than two groups or treatments in a study. In your example, the psychologist is comparing four different drugs to see which one is most effective in treating patients. The table with contrasts is used to compare each group to the control group. The 1s, -1s, and 2s represent the weights given to each group in the comparison. For example, in the first contrast, group 1 is given a weight of 1 and the control group is given a weight of -1. This means that group 1 is being compared to the control group, with group 1 being given more importance in the comparison.

To fill in the table, you need to determine the weights for each group based on the research question. In this case, the research question is about the effectiveness of the new drug compared to the other drugs and the control group. So, the weight for group 1 would be 1, and the weights for groups 2 and 3 would be -1, since they are being compared to group 1. The weight for the control group would be -2, as it is being compared to all three drug groups.

Once you have filled in the table, you can use it to determine the critical values for the post hoc test. The critical values can be found in a table or calculated using a statistical software. You would then compare the calculated value to the critical value to determine if there is a significant difference between the groups.

I hope this explanation helps you better understand multiple comparisons. Remember, it is important to carefully read and understand the research question in order to determine the appropriate weights for the comparison. Don't hesitate to seek help from your instructor or a tutor if you are still struggling. Good luck on your test!