Can you do a t-test or ANOVA between 2 or 3 groups respectively if one of those groups has a sample size of 2? Are the results interpretable in the same way as with larger sample sizes(n=4,5,6?). If you can provide any references to read more about very small sample size statistics, that would be helpful.
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The discussion at http://stats.stackexchange.com/a/1836 concerns the related situation of a t-test with a group of 1. References are provided. Also related are http://stats.stackexchange.com/a/83199 and http://stats.stackexchange.com/a/20337. – whuber Mar 18 '14 at 20:20
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possible duplicate of Is there a minimum sample size required for the t-test to be valid? – gung - Reinstate Monica Mar 18 '14 at 20:33
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What is the minimum viable cell size for a 2x2 ANOVA is relevant (& potentially a duplicate) as well. – gung - Reinstate Monica Mar 18 '14 at 20:35
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1There's also a discussion of a two-sample t-test with n=1 vs n=3 here; caveats are discussed. So not only is it possible, it's been discussed multiple times here on CV. With an ordinary ANOVA with 3 groups I think your smallest feasible n's would be 1,1 and 2 (in any order) - one of them needs 2 to calculate a standard deviation; any fewer - (1,1,1) - would require nifty tricks like those mentioned in comments under one of @whuber's links which make it not ordinary. – Glen_b Mar 18 '14 at 22:52