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I need to find the statistical significance (95% confidence interval) for 3 independent samples. From what I understand, in order to find the statistical significance for more than 2 samples, ANOVA (ANalysis Of VAriance) is employed.

ANOVA fits in nicely with what I want to do, in particular, One-Way ANOVA, but I have a problem with the third assumption of ANOVA:

Equal standard deviations:

The standard deviations of the populations under consideration are equal. As a rule of thumb, this assumption is satisfied ifthe ratio of the largest to the smallest sample standard deviation is less than 2, called therule of 2.

Introductory Statistics, Neil A. Weiss. 1997

I'm having a problem because some of my samples' ratios are as high as 2.981. Thus, I was wondering what to do if I want to find the statistical significance of 3 independent samples, yet the standard deviations of these 3 samples exceed those allowed by ANOVA? In addition, I do not think that my scenario is such that the standard deviations of the population under consideration are equal.

My sample sizes are 4, 3, and 3 respectively if that helps.

In summary, are there any tests or variations of ANOVA for statistical significance such that this third assumption is not required? i.e. standard deviation of the population does not have to be equal.

Thanks