# Significant difference between two non normal and inhomogene groups

I've done some measurement of tissue rigidity. So I did 1.000 measures with healthy (n=300) and ill (n=700) people.

Now I want to find out if there is a significant different value of the measured tissue rigidity for the ill people compared to the healthy people. Otherwise this measure method would give no benefit.

My data has no normality, so I choose a Mann Whitney U-Test.

But also my data is inhomogene (levene and also complete different histograms). So if I do the Mann Whitney I do get a p = .000

So I am not quite sure...

1. how to interpret the inhomogene data
2. if I can still use the MW U-Test (is it really significant)
3. if there is another way to test if there is a significant difference between those two groups. Looking at my data shows me that there is obviously a difference between the values (as they are much more higher), but I need to test it statistically correct...

You have three options for transforming and modeling your data readily available to you:

1. Conduct a Box-Cox analysis (the link uses the linearity plot method, but any implementation of the transformation will do).
2. Use the regression line from a Quantile-Quantile Plot (QQ Plot) of log transformations of your two sets of data.
3. Use the regression line from a Spread vs. Level Plot conducted by plotting $\log\tilde{x}$ on the $x$-axis and $\log IQR$ on the $y$ axis.

For methods 2 and 3, the slope of the regression line can be used to define the transform (power) that should be used to transform your data.

Transformation  Power   Slope of plot
Cube            3           -2
Square          2           -1
No change       1            0
Square root     .5          .5
Log             0           1
Rec. root       -.5         1.5
Reciprocal      -1          2

• Only if I understand it correctly? I have to transform my data? – user3142695 Mar 10 '17 at 18:18
• I would start with the option to transform your data. There are other options if that fails, but you will have the most options available if transformation works. – Tavrock Mar 10 '17 at 18:31
• Hmm... no, transformation didn't work for my data... – user3142695 Mar 10 '17 at 21:06
• Can you provide some plot of what your data does look like? Even if I were to suggest another distribution, there are a lot of non-normal distributions to pick from and a simple plot can help a lot with that process. – Tavrock Mar 10 '17 at 23:08
• My Data looks like this: gdurl.com/wqDY . As you can see the control group has less values and the main group has a lot of higher values, so there is a difference, but I need to prove it statistically. Also you can see that this is non-normal (which is no problem), but also inhomogene – user3142695 Mar 11 '17 at 8:56