If you are going to compare means then you need sufficient data to compute means in the first place. This is true regardless of test method. Your second post would suggest one of the following: you are working with a problem that is very rare in the population, you didn’t do a search for prior art to understand the issues concerned with your choice of groups (enrollment times, exclusion criteria, etc) or you are under pressure to “produce something”.
Reasons for sparse population of groups aside, if you have to produce something you will have to get out the old paper and pencil and grind it out by hand. One possible approach would be the following:
First – take those groups that have more than one sample and run an ANOVA on them – you will, of course, want to test for variance equality. If the variances are equal – generate an estimate of the pooled variance, pretend the numbers corresponding to your groups with a single sample are mean values and then manually run post-hoc pairwise “means” tests using the actual mean values for those groups with actual means and the pretend mean values for those groups with a single entry.
You will have to invoke a multiple comparison correction and since the actual calculations for this, given your circumstances, would be of dubious value the simplest approximation to this would be a simplified Bonferroni correction – take the number of comparisons you want to run (you will have to decide this before you run the tests) generate the individual p-values for each of the pairwise tests and multiply that value by the number of predetermined comparisons.
If the variances are unequal you could again pool their values and run the above or you could be conservative and use only the largest variance for your calculations. Given that you are pretending that a single measure is representative of the group mean the latter choice could be viewed as a way for compensating for this rather large assumption.
If the variances are unequal you could also run Welch’s test for unequal variance for those groups with more than one value. The problem would be how to manually modify the test to run such a test for single entry groups – I suppose there might be some kind of workaround but if it exists it something of which I’m not aware.
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