1. ## Orthogonal Contrasts

What are orthogonal contrasts?

2. ## Re: Orthogonal Contrasts

What exactly do you want to know?

I could be snarky and just answer that they're contrasts that are orthogonal to one another but I don't think that's what you're looking for.

3. ## Re: Orthogonal Contrasts

I'll add something that will at least hopefully get this moving in the right direction...

Do you know what a contrast is?

Do you know what it means for two vectors to be orthogonal?

4. ## Re: Orthogonal Contrasts

Thanks for the reply! I just found it in my textbook... sorry. Is there a way to delete threads?

5. ## Re: Orthogonal Contrasts

Well I could delete the thread for you. Or I could let it be lost in the sands of time. But I don't really see a reason to delete it.

6. ## Re: Orthogonal Contrasts

Actually, I've never really dealt with contrasts. I'm interested in any explanation. Granted, I could just do my own web search. I'm lazy. And I know what orthogonality is. And I know what contrasts, are. What's an orthogonal contrast? Got an example? When it is appropriate?

7. ## Re: Orthogonal Contrasts

A contrast is just a linear combination of the model parameters where the coefficients of the combination sum to 0. A set of orthogonal contrasts is just a set of contrasts where each pair of contrasts in the set is orthogonal to one another. This is nice because we get some nice properties. In particular orthogonal contrasts are uncorrelated with one another and if we're assuming normality in our model this means that the tests of the contrasts are independent of one another. For example in a balanced 2-way anova the test of main effects and the interaction form a set of orthogonal contrasts.

8. ## The Following User Says Thank You to Dason For This Useful Post:

bryangoodrich (12-06-2011)

9. ## Re: Orthogonal Contrasts

Great explanation. Now what kind of exam question can I expect to see related to this?? haha

10. ## Re: Orthogonal Contrasts

One of the problems with orthogonal contrasts is that the some of the hypotheses considered may be useless because you're forcing the vectors to be indepenent of each other.

For example, consider a balanced One-Way ANOVA with 6 groups. One could easily construct 2^(6-1) -1 = 31 sets of orthogonal contrasts (without duplication) to exhaust the all of the Sums of Squares Between these groups. They certainly have the nice properties of orthogonality --- but many of these hypotheses may be completely uninterpretable.