1. What statistical analysis can we use for a low sample size (n=3): between 2 groups and between more than 2 groups
2. If we take two samples and run them in technical replicates of say 6, can my n be considered as n=12 (2 samples x 6 = 12)
3. What is the best method to calculate sample size, in case of rare samples
Hello Elizabeth,
In general, unless differences are quite large, there is no statistical test that offers much statistical power with samples of 3 cases per group. The overall principle here is, more observations = better ability to detect differences (if they exist).
So, you can increase observations by: (a) using more cases (bigger sample size); and/or (b) observing the cases more times (as in a repeated measures design.
If it were possible to observe the same cases under both conditions (randomizing the order of group/treatment exposure), the resultant test (via repeated measures) is almost always more sensitive than the between-subjects group/treatment alternative.
Finally, the choice of what test is best depends on the nature of the dependent variable, the specific research question, and how data were collected.
Good luck with your work.
David Morse is right. Nonparametric sign test (permutation calculations) works sometimes.
Sometimes bootstrap techniques can help in case of small samples but for n=3 there seems almost no chance at all...
David Morse Babak Jamshidi Kathrin Möllenhoff , Thank you for the inputs. Since we deal with rare samples (non-diseased knee joint cartilage samples), it difficult to increase the number of cases. However repeated measures is possible.
In such a case
Based on available literature and assumption on the expected values, I tried to calculate the probable SD and keeping the alpha error at 5% and power at 80%, my study shows that I require a minimum no of 12.
This is based on the following formulae (attached file)
To procure 12 samples is difficult, could I instead take 2 samples, conduct them in technical replicates of 6 each and consider all the values obtained as 12?
Thank you in advance
Elizabeth
Hello again Elizabeth,
If measuring the same cases on multiple occasions does not affect the response variable in any way (e.g., through fatigue, participant reluctance to "do that again," or some combinatorial effect of time period x events followed by time period y events), then you can use a repeated measures approach.
However, the resultant responses are no longer independent (e.g., a participant that measures/scores high on the DV at time x is more likely to score high, comparatively, at time y), you'll need to use a RM paradigm for evaluating the relative power of your design. G*power allows for this (https://www.psychologie.hhu.de/arbeitsgruppen/allgemeine-psychologie-und-arbeitspsychologie/gpower). Alternatively, you could run simulations to determine the relative power (https://webpower.psychstat.org/wiki/, or https://aaroncaldwell.us/SuperpowerBook/).
Good luck with your work.
@david morse, thank you for the information and links, will try using the RM paradigm. Regards
Why statistical inferences for two to three observations? You can easily measure using the range which is also not required. In case these observations are being measured in decimals and each decimal is sensitive then you need some tools.
Another approach is to generate samples as mentioned by you but it won’t be of much help. Working with artificial data means several assumptions.
If the objective of your study is to compare 2 or 3+ groups, then you'll need more than 3 samples. Or you have some ground proof that a single sample is all you need and offcourse, if your aim is to compare measurement variation.
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