Statistical Significance for 3 samples

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SUMMARY

The discussion focuses on determining the statistical significance of three independent samples using One-Way ANOVA, specifically addressing the challenge of unequal standard deviations among the samples. The participant notes that their sample standard deviation ratios exceed the acceptable threshold of 2, complicating the application of ANOVA. They seek alternative statistical tests or variations of ANOVA that do not require the assumption of equal population standard deviations. The conversation highlights the need for robust statistical methods when standard deviation assumptions are violated.

PREREQUISITES
  • Understanding of One-Way ANOVA
  • Knowledge of statistical significance and confidence intervals
  • Familiarity with standard deviation and its implications in statistical tests
  • Basic concepts of sample sizes and their impact on statistical analysis
NEXT STEPS
  • Research Welch's ANOVA for handling unequal variances
  • Explore the Brown-Forsythe test as an alternative to One-Way ANOVA
  • Learn about the Kruskal-Wallis test for non-parametric analysis of multiple samples
  • Study the implications of sample size on statistical power and significance
USEFUL FOR

Statisticians, data analysts, researchers conducting experiments with multiple independent samples, and anyone needing to assess statistical significance without the assumption of equal variances.

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

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