I am going to perform a regression analysis with one dependent and three independent variables but the sample size is really small (n=11), as a rule of thumb I need at lease 20 per variables. I am just wondering if there is any alternative test. our study is not a survival study. Can I use cox regression?
Difficult problem. Are you sure that the variables are/appear to be normally distributed? In any case I would start with non-parametric regression of each variable and the dependent one (Kendall's rank correlation test). Can be done in SPSS. Then think!
Dear Robin and others,
Thank you for your comment. I performed Kendall's rank correlation.
results:
dependant - variable 1 : 0.611*
dependant-variable 2 : 0.298
dependant - variable 3: 0.564*
*: significant.
I also performed regression analysis, R square: 0.9. and dependant variable is significantly correlated to variable 1 and not to 2 and 3. which is desirable for me. However due to small sample size, I have doubts on the results. there is no previous studies testing our hypothesis in the same way.
What about post hoc power analysis for multiple regression? any idea?
Hello Amir. With that sample size and number of variables, you are severely over-fitting your model. See Mike Babyak's (non-technical) article for a nice discussion of over-fitting.
http://www.cs.vu.nl/~eliens/sg/local/theory/overfitting.pdf
Dear Bruce,
Thank you for your comment. Interesting article. Do you think of any alternative test? Unfortunatelly, no further data are available. I also performed post hoc analysis that showed a power of 98% and 69% at a probability level of 0.01 and 0.001. However there are some contraversies regarding this calculation in the literature.
Thank you Chan for your comment,
I actually wanted to see the effect of two confounders. maybe a correlation analysis can be a supplement to the analysis. really confused!!!
regards
Your sample size is far too small to support multivariable analysis, Amir. You cannot get (statistical) blood out of (such) a (small) turnip. [See link below for an explanation of that statement!]
http://www.wisegeek.com/what-does-it-mean-to-get-blood-from-a-turnip.htm
Amir -
Might you treat what you have as a kind of pilot study? A pilot study is often a good idea for working out what you need to do or examine, obtaining information such as an estimate for standard deviations to help determine sample size needs. I do not know how, or even if, this might apply to anything you are doing, but thought it might. Might you be able to use what you have to plan further study?
Because of interactions between regressors, looking at one regressor at a time can often be misleading, but might you here look at one at a time to see if one does substantially better than the others? Also, if this agrees with subject matter theory, might you collect more of the more important variable data?
But to learn more about your regressors with the tiny bit of data you have, you might try scatterplots of one pair at a time. Spurious results may be obtained. As Bruce said, your small sample can't give you but so much information. But you might see some possibly promising avenues to pursue, or of one regressor is highly predictive of another, even though a small sample, but hopefully not so small as to be coincidental, and if subject matter theory agrees, perhaps you could drop one of those independent variables.
Just some speculations in an area/subject matter for which I am largely inexperienced.
But as Bruce said, it seems that you want to extract a good deal more information from your data than your data can reasonably support. If relationships are not very, very strong, you really won't have anything.
Cheers - Jim
PS - I thought the saying was "blood from a stone," but don't know why. :-)
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