Thread: Multivariate Regression - I think!

1. Unfortunately, the sample size issue far out-weighs any consideration of normality or homogeneity of variance.

ANOVAs are pretty robust to departures from normality or to non-homogeneity of variance, but if gender is an independent variable in the study, then 20 vs 30 is a big enough difference to be concerned about - it will confound your results, to a degree - in other words, what you see as a gender difference or interaction with another factor may really only be due to the fact that there are more females than males...

Either you need to:

(1) get 10 more males to participate, or
(2) randomly throw out 10 female data points, or
(3) work directly with a statistician who can help you with weighting the male data points* - which makes the analysis more difficult, or
(4) do separate analyses for each gender, and if you see any gender differences, you'll only be able to make general comments, and propose a further study to work them out

*if you look in SPSS Help, they may tell you how to make adjustments to the "regular" ANOVA if you have unequal sample sizes
* the following link describes some SPSS options for dealing with unequal sample sizes:
http://www2.chass.ncsu.edu/garson/PA765/anova.htm

2. Hey, that's a great resource, thanks.

So even if the assumptions of normality and homogeneity of variance are fulfulled, the data will still be biased towards a larger sample size? I must have misunderstood my text. Is there an approximate cutoff for an acceptable ratio, i.e. 0.75 isn't close enough, but 0.80 is?

Also, am I correct in saying that a ceiling effect is a problem due to a deviation from normality? So the only things things I need to look out for are such deviations from these assumptions (for the purpose of noting, I mean, not to prevent the use of the robust ANOVA).

Thanks again,
Iain

3. Actually, I looked back through the earlier postings in this thread, and maybe the unequal sample sizes won't be that big of an issue - gender is your only independent variable, with BMI as a covariate, so maybe it won't be a big deal. It would be a big deal if you had another indepenent variable in there...

I wouldn't worry too much about ceiling effects - I mean, the normal distribution goes to infinity in both directions - hardly anything we measure in real life does that, but the normal distribution is still a decent model...and ANOVA is robust to departures from normality...

The unequal sample sizes don't really "bias" things - it causes confounding (a situation where the effect of one variable isn't a "clean" estimate of the effect - other things or other variables are playing into it).

4. I do actually have another IV: a Visual Condition (control / media) :0( This stuff is really very intricate (read difficult!). There's just so much knowledge I just don't have.

I'll have to work on gleaning a few more male participants from somewhere, and just have to throw away the surplus female participants.

Thanks,
Iain

5. Exploring the interaction

Ok, I think I may be being stupid here - I've done nothing but stats for the last few days, so I think the mind's starting to slow.

I have two tests with significant interaction effects but no main effects - one is a two-way ANOVA (sex x visual condition), the other a 3x2x2 repeated measures ANOVA (question (Ideal, SIdeal, OSIdeal) x sex x visual condition).

Am I right in saying that I now need to do post-hoc tests to find where the differences lie? i.e. in the two-way ANOVA, it could be that just one of the sexes changes across conditions, or both do right? I tried to do a bonferroni, (and a tukey for kicks - these were the tests I recognised), but the interface doesn't give me the option to do a test on 'question' in the repeated measures interaction, and when I try to do it on sex or visual condition in the two-way ANOVA, it says it can't because they only have two levels.

I really think I'm being a dunce here, sorry - if you could point me (again!) in the right direction, I'd appreciate it.

Thanks,
Iain

6. You should be able to do the post-hoc tests you described - I'm not sure why it's giving you problems...

7. Research leads me to beleive that what I'm looking for is a test of 'simple main effects' - that is, testing for a significant differences across one factor within each level of the other factor. For example, in my 2-Way ANOVA, I have a sex*condition interaction, but no significant main effects. If I run a 'simple main effects' test, this tests for significant differences across cond within each level of sex - in other words, whether males differ across condition and whether females differ across condition.

Does this sound correct? The output makes sense - the steeper line in the interaction plot is males, and in the simple main effects test, males but not females come out to significantly differ across condition.

In what way is a 'simple main effects' test different from doing a t-test for each sex across condition?

Many thanks,
Iain

8. I don't think they're different at all.