# Transformation to improve normality

• Jan 31st 2013, 07:56 PM
rav8
Transformation to improve normality
Hi, I have a problem with some data that I am trying to analyse in a Repeated Measures design.

I have 5 conditions (variables), 13 subjects, data points ranging from about -40.0 to +40.0

Both the Kolmogorov-Smirnov and Shapiro-Wilk tests are significant for some of the variables. Some of the variables are negatively skewed while others are positively skewed.

I have tried log, sqrt, and inverse transforms (after adding a constant), however it depends on the direction of the skew as to whether I reflect them or not to get the best result.

e.g. for the negatively skewed variable, i can improve normality by multiplying by -1, adding a constant to return the set to positive values, and then taking the log transform. However this makes the positively skewed values worse.

I can't do different transforms on different variables and then do a repeated measures ANOVA.

How can I address this problem?

Thanks in advance for any assistance!
• Jan 31st 2013, 08:41 PM
chiro
Re: Transformation to improve normality
Hey rav8.

Do you have to transform these? Have you considered non-parametric varieties of tests and statistics for your problem?
• Jan 31st 2013, 08:59 PM
rav8
Re: Transformation to improve normality
Quote:

Originally Posted by chiro
Hey rav8.

Do you have to transform these? Have you considered non-parametric varieties of tests and statistics for your problem?

Hi, thanks for your reply. Yes, I could use non-parametric stats, however I always feel more comfortable using parametric - I know this isn't terribly rational! I'm not really a stats person at the best of times...

If I don't have any luck transforming them, I won't have much choice I guess!
• Jan 31st 2013, 09:40 PM
chiro
Re: Transformation to improve normality
What kind of applications, tests, and inferences did you have in mind?
• Feb 2nd 2013, 01:50 AM
rav8
Re: Transformation to improve normality
I just want to do a repeated measures anova with some posthocs...
• Feb 2nd 2013, 05:39 PM
chiro
Re: Transformation to improve normality
I took a look at repeated and it said that along with independent samples and normality, it also requires sphericity on top of this.

This is just my opinion but I would look either look into non-parametric variants of the test, or if the normality and sphericity values are only just significant enough, then use the ANOVA with a much higher confidence level (instead of 95% make it say 97% or 98%).

Make sure you check sphericity in your statistics package and if the two tests (sphericity and normality) are too significant, then you should be looking at non-parametric variants without question.
• Feb 3rd 2013, 04:25 PM
rav8
Re: Transformation to improve normality
Quote:

Originally Posted by chiro
I took a look at repeated and it said that along with independent samples and normality, it also requires sphericity on top of this.

This is just my opinion but I would look either look into non-parametric variants of the test, or if the normality and sphericity values are only just significant enough, then use the ANOVA with a much higher confidence level (instead of 95% make it say 97% or 98%).

Make sure you check sphericity in your statistics package and if the two tests (sphericity and normality) are too significant, then you should be looking at non-parametric variants without question.

Hi, thanks for your comments, sphericity is OK with this data - it's just the normality.

Does anyone have any other transform suggestions? Otherwise I might have to go with non-parametric :(