Statistical Significance for 3 samples

[NSX]

Hello all,

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 if the ratio of the largest to the smallest sample standard deviation is less than 2, called the rule 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

 

[EnumaElish]

I think there is a version of ANOVA that is a generalization of the t-test with unequal variances.

 

[tacman]

Hello there,

Thank you for sharing your question and concerns about finding the statistical significance for 3 independent samples. You are correct in your understanding that ANOVA is typically used for comparing means of more than 2 samples. However, as you mentioned, one of the assumptions of ANOVA is that the standard deviations of the populations are equal. This assumption is important because it affects the accuracy and validity of the results.

If the standard deviations are not equal, there are alternative tests that can be used, such as Welch's ANOVA or the Kruskal-Wallis test. These tests do not require the assumption of equal standard deviations and are more appropriate when the data violates this assumption. Additionally, these tests can be used for small sample sizes, such as the ones you have (4, 3, and 3).

In summary, there are alternative tests that can be used for finding the statistical significance of 3 independent samples when the assumption of equal standard deviations is not met. I would recommend consulting with a statistician or conducting further research to determine which test would be most appropriate for your specific data and research question.

Best of luck with your analysis!