We have a rodent data set including both sexes, and two genotypes - WT and mutant. The WT data is mostly consistent with tight standard deviations, whereas the mutant data is highly inconsistent with variable standard deviations. For statistical analysis of this data set, my understanding is that I can run the Levene's test to check for homoscedasticity, and then run a Two way Welch-ANOVA (if this exists) to check for significant differences. Is this approach correct? I am interested in highlighting the fact that the mutants are inconsistent by comparing the standard deviations with a statistical test. The n is equal for both sets.
Swati,
If your sample size is small OR your both samples or one of them is heavily skewed, then Levene's Test works well.
An F-test for testing equality of variances wil have more power than Levene's Test, if data is symmetric (better said, is normally distributed)
An ANOVA test is for testing the differences in means in 3 or more independent populations. If you have two 2 independent populations, then the ANOVA test is just a T-test.
You would run a TWO-way ANOVA if you have two factors of interest, in your case (Sex and Genotype)
Also to run ANOVA tests, you would have to check to be sure your data satifies the assumptions. Some being; data is from a normal population(distribution) / sample size is large, population varainces are equal; independent samples etc.
Can you throw more light on your goal again?
Hope this helps.
Hi,
Levene's test will show that the distributions in your samples are the same or different. For example, if one part is normally distributed and the other one is uniformly distributed or simply skewed. ANOVA might show that there is difference between samples. I think you need both tests: you cannot perform ANOVA if the samples have different directions. But you actually need to find differences in variance caused by the group belonging.
I hope I understood your issue correctly...
Best,
Eugene
Good Morning! I did t test because my samples were relatively small and these articles did to give more support in my thesis defended in 2015.
Thanks for the collaboration.
Hi Daniel, thank you for your reply! As you correctly pointed out -my dataset has two factors of interest - gender and genotype. My mutant mice are highly erratic and unable to follow a consistent pattern as compared to my wild-type mice who are quite consistent. I would like to quantify the erraticity in my mutant mice by running a statistical test on the standard deviations thereby showing that my mutants are inconsistent. Would it be valid to run an ANOVA on the standard deviations from both sets (I get a significant difference between the standard deviations when I do this)?
Hi Eugene, thank you for your reply. You have understood my issue correctly. I need to compare the variances/stdevs of both sets and show that there is a difference between the way my wild-types and mutants behave.
You should perform a homogeneity test of variance (Levene's test) and it should be NOT significant. When not significant then your small sample is not an issue. If significant - there are other tests for this case.
Hi Eugene, I am told that the ANOVA is fairly robust even when the assumptions are violated. Is this true? Also I am seeing some responses that say Levene's test increases your overall alpha error and is a generally bad idea?
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