I am teaching myself to use and apply statistics to a big database.
I have 2 groups that I wish to compare, healty controls (HC) and patients (P).
The sizes are HC= 84, P= 196.
Each group has many different clinical data collected as continous variables, such as weight, BMI, size of theire frontal lobe, etc.
Given the central limit theorem, I would have thought that I could just assume normality. I corroborated this graphically with histograms, and noticed that in many cases the distribution was not normal. So I performed a shapiro-wilk test, confirming that several variables of both patients and controls had non-normal distribution.
This outcome made me more confused, because now I would like to compare the 2 groups, but they have different distributions.
How should I statistically approch this?
For example, I would like to test if the size of the frontal lobe is statistically different in patients than in controls. BUT the distributions looks like this: