# Transformation to improve normality

#### rav8

##### New Member
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!

#### Karabiner

##### TS Contributor
Why don't you just use the Friedman test?

With kind regards

K.

#### rav8

##### New Member
Why don't you just use the Friedman test?

With kind regards

K.
Thanks, but I would prefer to do parametric if I can transform this data successfully...

#### noetsi

##### No cake for spunky
Tukey created a list of powers and roots to transform data and a logic when to use it. He referred to it as a ladder. One of the things that it deals with is skew. I don't know if this helps in your case but you might want to look at this article (it talks about skewness at the bottom). You will have to follow it up with a more comprehensive review of this method (which can be found in many text although I don't have one at hand) or likely on line as this is a well known mechanism.

http://onlinestatbook.com/2/transformations/tukey.html

#### Karabiner

##### TS Contributor
Thanks, but I would prefer to do parametric if I can transform this data successfully...
I see. There is someone pointing with a gun at you.

#### noetsi

##### No cake for spunky
Parametric analysis is commonly desirable in organizations because its easier to explain and because its well accepted. Managers like means

#### rav8

##### New Member
Parametric analysis is commonly desirable in organizations because its easier to explain and because its well accepted. Managers like means
spot on

#### noetsi

##### No cake for spunky
Its never very hard to tell the statisticians from the lowly data analyst on this board