Hello,
I have a very basic question regarding the normal distribution assumptions. My data contains clinical variables in which some show moderately normal distribution, most of them are left skewed. Kruskall-Wallis showed significant p value for all variables rejecting the null hypothesis. I want to perform a correlation analysis and build a regression model adjusting covariates. I came across that regression is a parametric test. How to then go for my data processing?
shall I transform the non-normal variables and continue with regression?
or shall I transform the entire data frame with all variables?
or shall I use a non-parametric tests? I am not sure what instead of linear regression i could use?
your help will be greatly appreciated here
Thank-you,
Ordinary linear regression assumes normality of residuals, not the independent variables. But that aside, it is up to you, you can either
1) log-transform (or inverse for extreme cases) and do your analysis, or
2) Use non-parametric tests, like Spearman instead of Pearson for correlations. There is really no such thing as a non-parametric linear regression as it assumes a linear relationship between IV and DV, but there are non-parametric methods that you can use as alternatives when assumptions are violated, such as generalized additive models (GAM) or quantile regressions. But plot your data first, does the relationship even look linear? If not maybe look into other models
Choose a non-parametric regression method when data does not fit a specific parametric model, and select kernel regression for smooth estimates, k-nearest neighbors (KNN) regression for local adaptability, spline regression for flexible curve fitting, or random forests for handling high-dimensional and complex interactions.
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