Use logarithmic or linear values when performing correlation and ANOVA? The data was collected using a logarithmic scale: scores (explanatory variable) are collected with values from 0-5. A score of 3 is 10x the value of a score of 2.
I wasn't sure if using either the log scale (0-5) or a "linearalized" scale (0-100000), when performing corr. or ANOVA, was correct, so I tried both. Unsurprisingly, the scale I choose affects whether correlations are found or not, and whether variances are found or not.
Which scale should I use in my analysis? Or what questions do I need to answer to help me decide which scale I should use in my analysis?
Thanks very much!
 A: An ANOVA doesn't require normally distributed data, but normally distributed residuals. That is, a normally distributed dependent variable conditional on the predictors in the model. However, you refer to the transformed variable as a "explanatory variable." I take that to be an independent variable, and thus it does not need to be transformed to fit into the assumptions of an ANOVA framework.
A: As far as I remember, ANOVA requires you to have normally distributed data. Hence if your dataset is not normally distributed, you'd use a transformation. I've just read a paper that had a good review of data transformation techniques (even though probably quite unrelated to your topic): http://www.degruyter.com/view/j/cclm.2010.48.issue-11/cclm.2010.319/cclm.2010.319.xml
If you don't have access to full text, here's a summary by myself:


*

*Plot a histogram of your data. Start with your raw data, then log-transformed data, and then after each transformation. Overlay the Gaussian bell-shape if you can, but you should be able to judge visually which transformation brings you closest to the normal shape.

*Some transformations to try: x^3, X^2, sqrt(x), log(x)

*If these do not work, try adding or subtracting a constant "a": (x-a)^3, ..., log(x-a), etc.

*If you need to judge formally (not just visually) which transformation works best, use skewness (should be between -0.15 and 0.15) and curtosis (should be between 2.7 and 3.3).


Hope this helps.
