With three observations per group I would not worry too much about variance. With that sample size you probably don't have enough power for a hypothesis test.. I would recommend plots of each group and compare them to answer your research questions. Best wishes David Booth

It is hard to find any known pattern in 3 data. If you subtract the data of each group from its mean, you have 18 data. It is possible to check its normality (or being of other distributions).

If you want to use nonparametric tests, you are right but your threshold p-value must be more than 0.10.

To be precise: A large p-value for Levene's test does not say that the variances are equal. It just says that there's not good evidence to conclude that the variances are different. With only three observations per group, the test probably lacks power to confidently detect the differences in variances.

In general, it's a bad idea to use hypothesis tests to assess normality or homoscedasticity as a prelude to conducting another analysis.

( See:

https://www.r-bloggers.com/2011/10/normality-tests-don%E2%80%99t-do-what-you-think-they-do/ ,

https://www.researchgate.net/post/Are_tests_of_normality_basically_useless ).

Instead, what you did is more helpful: looking at the variances, or looking at a plot.

If the variance of one group is four times that of another group, I would not assume the variances are equal.

If you are interested in comparing means, you might use Welch's anova, or a permutation test. Or perhaps Kruskal-Wallis with Dunn test (1964) post-hoc.

I'll add one more comment to those above. Unless you are working with variables no one has ever studied before, you have access to information about those variables beyond what can be gleaned from your small sample. That is one of the key points in this BMJ Stats Note by Bland & Altman.

Article Practice Statistics Notes Analysis of continuous data from s...

HTH.

You can as well replicate those sample 1000 times using bootsrap method and get qurtiles

If you are thinking of using a nonparametric test, I think you should explore Kruskal Wallis test

Levene's test is used to check that variances are equal for all samples when your data comes from a non-normal distribution. And as per my knowledge, Non-parametric tests will be best suited for non-normal distribution.

Prashant Kumar , are you saying that if one has sampled from (approximately) normal populations, Levene's test cannot be used? If so, I disagree, but would love to see whatever resources you have to support that claim.

While we're on the topic, I don't think it is very wise to rely on statistical tests of the assumptions of other tests, and I include both statistical tests of normality and tests of homogeneity of variance. That topic has been discussed many times here on RG and elsewhere.

Bruce Weaver Sir, I had carefully used the word "best suited".

Will be happy to hear better answers here.

This is getting off topic, but I was curious about the advice about using Bartlett's test when the sampled population is normal (which is quite common on the internet). Has anyone seen any good write-up on this ? ... I ran some simulations. I kept it simple, and they're not good enough to be considered authoritative. In particular, I wasn't sure how to model the non-normal, unequal variance samples. But attached is an example of the distributions I used. And attached is an summary table. The values are the proportion of p