The data are measurements of treatment vs control. Sample size (n) is 3 and the data include both positive and negative values and zeros.
To use logRR (log response ratio), a transformation is required (adding the absolute minimal negative value, and assigning an arbitrarily small value instead of zero). I understand that these transformations are not recommended. Alternatively, Hedges' g can be used without any transformations.
The problem arises from the high variance (due to low sample size) in some cases, where the Hedges' g (that include SD in the denominator) is much lower than logRR, although its error estimate (for example, confidence interval) is larger. Then, a different interpretation can take place - small effect with low uncertainty using Hedges' g, and large effect with high uncertainty using logRR.
Attached is an example of the two estimators for the same data.
What would be the best practice?
Small N designs are tough. But, the first article on AIDS started with a few case-reports. Wishing you good findings in your work on oceans!
I've used the non-parametric method MRPP with success once--in analysis of a factorial design with only one subject per cell:
- Gisondi, M.A., Smith-Coggins, R., Harter, P.M., Soltysik, R.C., & Yarnold, P.R. (2004). Assessment of resident professionalism using high-fidelity simulation of ethical dilemmas. Academic Emergency Medicine, 11, 931-937.
These two PDFs introduce aspects of MRPP:
- http://www.umass.edu/landeco/teaching/multivariate/readings/McCune.and.Grace.2002.chapte24.pdf
- http://www.umass.edu/landeco/teaching/multivariate/schedule/discriminate1.pdf
Thank you, Paul.
I skimmed through your paper and the material on MRPP, while this method seems to be a good way to compare the dis/similarity between groups, in my analysis I would like to show both the magnitude and direction of an effect. Does MRPP analysis indicate direction?
You are welcome, Tamar
Yep. Here is a more beefy citation (discussing effect direction, magnitude, p-value), with worked examples and providing other resources:
- https://pubs.usgs.gov/of/2005/1353/pdf/OF2005-1353.pdf
The USGS uses these methods to study relatively rare phenomena like volcanic eruptions and earthquakes. You should also be able to find articles relevant to your application(s) using search engines such as google scholar.
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