I need to analyse differences in distribution and variance in 2 populations whose variable samples are not normally distributed. Each population represents a kind of biological sample (X), and each sample represents a molecular variable assessed (Y), as "levels of something, as protein, RNA" decide by yourself.
I already performed Kolmogorov-Smirnov test and Levene's test to assess differences in distribution and variance of samples in each population. Now, I need to add another variable in my analysis (for instance, age), to assess if age influences sample distrubution.
In conclusion, I want to add another variable to my bivariate analysis. I know that I need to move to multivariate analysis, but I do not know how to move. I don't have the time to do a course in statistics, neither I want to lose my mind on an hundred of formulas. So please, do you know some test that could help me? Or some easy free software?
convoluted but just a suggestion. Run X on age and use the residual from the regression as (new X) and using your Y carry out the same kolmogorov-smirnov test as before. I look forward to having others respond.
Thank you both for the answer. Jacek, the paper you suggested me is perfect. However, do you know if there is a software that I can use to construct probability densities, define Discriminant functions, compute cumulative distribution function and significance function?
You can use multiple regression analysis. Spss software help you.
I agree with Dr. Tabatabaee. You could use multiple reg. analysis. Please go to the "Help" section on SPSS software for running this type of analysis.
At the beginning of my analysis I performed Shapiro-Wilk test, and I know that one of my populations is not normally distributed. Therefore, I must use non-parametric tests.
I do not have access to SPSS (I do not own that software, neither my institution). I tried to use the Jackec paper, but I think it's too difficult for me and I can not guarantee the result.
Thank you very much for your help. At the end, I solved my problem in this way. Just tell me if it is ok.
My purpose is to check if the biological differences among sample populations is related to advanced age of patients by which the sample is taken. For advanced age, we commonly refer to "more than 37 age". This simplified my analysis, because I can assign to each sample one of two conditions: (1) young age, (2) advanced age.
So I compared, for each couple of populations, if there was an enrichment of advanced age samples. I did a simple chi-square test!
I did not find any statistical relevance among each population's couple, so I assume that advanced age is not statistically relevant in my analysis.
Is it correct?
Correct, but you may have an important loss of power by this methodology, so not to find an age effect may not be conclusive without careful power analysis.
You may have surprises in testing normality before adjusting for covariates (like age), because effect of this covariate will distort the distribution, so it may be interesting to try a multiple regression including age (either as is or classified as you did) and check the normality of the residuals... You may have luck and have normal residuals, or at least normal enough to be confident in the results...
If you have any hypothsis about age grouping you can categorize age and analys your data by MANNOVA models.
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