I am currently in the process of transforming some of my data; mental health questionnaire scores, which are positively skewed due to a number of participants scoring 0. Referring to Tabachnick and Fidell (2007), if this is the case you can use a Log10 transformation (Newvar = Log10 (X + C), where C is the constant with the lowest score +1).
However, after transforming my data, I've found it is no more normally distributed than it was before. My question is, do I now just use my untransformed data in my analysis, because it isn't any better than the transformed data? I'm not sure what the general rule is to follow when this happens.
Please help!
Your data don't need to be normally distributed, and with a cluster of zero scores there's no reason to assume that any transformation will make a difference. You have zero-inflated data. You can think of your data like this:
The zeros are a different group: the people who score zero are well. It's not appropriate to ask what factors reduce their mental health because they don't exhibit reduced mental health.
In this case, you have a Heckman model . The first part of the model (called the selection part) asks what are the predictors of a non-zero score. IN other words, what factors predict psychological unwellness.
The second part (the regression part) asks what are the predictors of the magnitude of the score in people who don't score zero. In other words, among those who are unwell, what factors predict the severity.
You probably need to disentangle these two questions in your analysis, judging from your description of your data.
Hi Hope,
I have two general comments for you to consider. You mentioned that your data are positively skewed. However, I noticed that your method of transformation was reflecting your data (taking the lowest score and adding 1). But this is generally used in case of negatively skewed distributions as opposed to positive ones. As such, using a log transformation (or try a square root transformation) alone should suffice.
The second, and more important point is that I wonder why you are transforming your data. Many people erroneously assume that their individual variables must be normally distributed lest they violate a statistical assumption. But the actual assumption is not normality of the the individual variable but rather normality of the residuals. For example, if you run a basic regression analysis and include a residual scatterplot in the output, you can check whether or not the residuals are normally distributed. Often, you will discover that an individual variable can be non-normally distributed yet residuals be normal when regressed upon another variable of interest.
Cheers.
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