if we suppose that you have k groups, N is the total sample size for all groups, then n-k  should exceeds zero. Otherwise, there is no minimum size for each group except you need 2 elements for each to enable calculating the variance, but this is just a theoretical criteria.

However, to use ANOVA you need the check the Normal distribution for each group, so the higher size of your groups sizes, the more opportunity to have the Normal distribution.

Hi,

I wonder if ANOVA is what you want. I suspect you want to infer the expected differences between the three groups (aka "compare the group means"). This is achieved by t-tests, whereas ANOVA is a tool to compare nested models with different numbers of predictos (in your case possibly a model with "group" as a predictor against a model without "group" as predictor - that's upposedly not what you are mainly interesed in).

If t-tests are the right tool depends on the combination of sample size and the kind of the response variable (=what you measured), precisely its (assumed) distribution, and the purpose of your analysis. There is no answer that would be generally right. Most people would agree that for n>100 per group the distribution of the response is irrelevant in most practical cases. The more symmetric the distribution of the response values is, the smaller sample sizes are accepable. "Acceptable", however, is no strict mathematical criterion. It is a judgement call, considering the aim of the analysis.

Some response variables call for different analyses, different error models. Examples are binary values, proportions, counts, or rates. For some response variables a "difference in means" is not a sensible statistic. Examples are all variables where the expected difference depends on the mean (a quite common fact for biological variables). In such cases is makes more sense to analyze relative changes (what are differences on the log scale!).

Although I do not know precise guidance for the number of cases needed, I would like to highlight one important issue. With bigger samples you have increased chances to detect medium or small effect sizes that otherwise may be masked when the sample is too small. Please reflect if this is important in your context. Good luck. 

Numerous clinical studies are in print with small sample sizes like yours.  But an appropriate power analysis based on prior evidence would offer guidance as to the size of the effect you are anticipating -- and thus the required number of cases in each group needed to have a reasonable chance of seeing such an effect.  Note that inequality of sample sizes is not an issue.  Note too that the t-test recommended above is not appropriate here, and no, ANOVA is not restricted to nested models.  (The commentator may be referring, correctly, to a fundamental difference between the functions "aov" and "anova" in the statistical language R.)

You might best start your statistical appraisal with a check of your data distributions for normality, as the ANOVA can be sensitive to statistical outliers.  If normally distributed, and assuming each group is independent, a 1-way ANOVA would be entirely suitable, followed by post-hoc testing to compare each group against the other.  In the face of non-normality you would want to consider robust statistical solutions.

David, could you give me a hint where and how ANOVA can apply to non-nested models?

I would also be happy if you could specify what is learnt from the result of a 1way-ANOVA what is *not* conveyed by the post-hoc tests. To my understanding the ANOVA is not required at all (the post hoc tests do control the FWER if desired), and in the majority of papers writing that they did ANOVA never report anything of this (no sum of squares, no variances, no F-values, nothing).

I also don't understand how you can say that t-tests are not appropriate but at the same time suggest post-hoc tests, that are likely all based on the t-test (however with pooled estimates for teh satndard error and adjusted degrees of freedom).

PS: I was not referring to some R function speciality, I was referring to the logig behind the underlying F-test.

The number per group is not the first question.

First, we should consider the extent of the effect that we are interested. Second, we should estimate the variance of the experiment (i.e. pilot plans). Finally, based on the extent of the effect, the variance and the power desired, we could calculate the sample size.

After performing the experiment, the assumptions should be verified.

Inequality of sample sizes is not an issue but groups of the same size could help. An exception could be the control group, if we want estimate more precisely the experimental error.

Thank you for all your responses- very helpful.

Sinead

If I want to use one way ANOVA for my analysis, what should have to be the minimum number for my sample size?? Thank you very much in advance!

depends on what effect you want to be able to detect with what probability and what confidence you like to heve in that decision.

All of your friends provided useful information. But it's important to note that so much emphasis on G POWER software will make us mistaken. For example, sometimes our research sample includes specific groups. (For example, a specific psychiatric disorder with very low prevalence). In this case, note that you need a smaller sample size for a statistical test, such as ANCOVA. In summary, consider the specific circumstances of any research.

You can estimate the effect of size on your results. When you obtain ANOVA results, see the sum of square results. Calculate the sum of squares between groups/ total sum of the square. According to Cohen's (1988, pp.284-7), if the value 0.01 the effect is small, 0.06; the effect is medium, and 0.14; the effect is large.