Hi all,
I hope someone can help, I am a post-graduate student doing my thesis in Psychology. I am conducting a research project where I have measured participants (n = 316) on the Illinois Rape Myth Acceptance Scale.
As expected it is positively skewed. The composite is 1.660 for skew and 3.611 for kurtosis. When I transform the composite with a log10 transformation, skew is .588 and kurtosis is -.234.
The composite score will be used as an IV in a regression (there are also a few other IVs).
I expect the higher someone scores on the IRMA, the less they will recommend that the hypothetical victim (vignettes) should officially report an assault. I also expect these participants to attribute higher responsibility to the victim than the perpetrator for an assault.
As I plan to use the data in this way, would it be incorrect to transform the composite score so my IV is more normally distributed? Especially as I am interested in the views of what would be the outliers?
Hello Gabrielle,
It's not essential that each IV be normally distributed. (It is true, however, that if two variables have different marginal distributions, the absolute value of the maximum possible Pearson correlations will be < 1; so having different distributions does attenuate the maximum possible correlation.)
In regression, the concern of normality applies to the model residuals (after fitting the model). So, look at these. You may well find that model residuals are "better behaved" when you do transform scores on one or more of the model variables, but hold off until you check.
Good luck with your work.
Gabrielle -
If you stated exactly what your dependent variable will be, I did not note it, but I am under the impression that it will be similarly skewed, and you really should not transform that independent variable. I've done a lot of work in official statistics with a highly skewed IV and a like DV, such that the appropriate regression is not just linear, but actually described by a straight line, and though you have other IVs to consider, I expect that you will find this appropriate.
David is correct that the assumption of "normality" just applies to the estimated residuals (or consider the random factors of the estimated residuals in weighted least squares regression). It is also not a strict requirement.
The unconditional distributions of the variables are not a problem, but may determine what type of regression you use.
I suggest that for multiple regression you use a "graphical residual analysis" to evaluate model fit, and a "cross-validation" to study whether you have overfit to your particular sample. Note that a graphical residual analysis is also the first step toward considering heteroscedasticity, which is often to be expected. ("Essential heteroscedasticity is a feature, not a bug." Some model and/or data issues may effectively increase or decrease heteroscedasticity, however.)
Transformation of variables is probably substantially overused, I think, and I doubt that it is appropriate here.
Cheers - Jim
PS - With regard to outliers, you do not want to delete data just because it is inconvenient. Remember that approximately 2% of your y-values SHOULD fall outside of a 98% prediction interval. A 'true outlier' (a datum which does not belong to the subject population), however, may fall well within such limits. If you have a suspected outlier which would distort your results, you should investigate, if possible. If you find an explanation as to how the data could have been collected incorrectly (in my case, energy data could have been reported in the wrong units, for example), then you might be able to justify removing such data. You might want to have an appendix showing what happens if certain data are or are not used. But you should not be too quick to just throw away data that does not give you what you want to see. - An expert in data quality once noted to me that there is no real substitute for collecting data well from the beginning.