# Am I Log Normalizing correctly?

I have searched the other questions about log normalization and all assume a level of understanding that I don't have.

I have some ecological data and I am told that it needs to be log transformed. My dependent variables are relative densities of compounds found in the plants, and the independent variables have to do with location (A or B), distance from a trail (on a trail or not on a trail), and a number of covariants like pH and soil moisture. I have done ANCOVA's with the two independent variables adding the different covariants. However, I apparently need to log normalize the data

As I understand it, I need to take either the base ten or base e log of my variables. I can do that fine for the relative densities as they are numerical, but what do I do when my independent variables are categorical like location A v. B? Also, what do I do with the covariants, all of which are numerical?

• Could you tell us on what basis you need to "log normalize the data"? Certainly you don't need to take logarithms of all the numbers in sight! – whuber Apr 9 at 18:05

ANOVA, MANOVA and ANCOVA assume normally distributed residuals of the data. They are parametric methods, so before performing them, you should check whether your data matched the assumptions made.

So what log-tranforming does is it stabilizes log-normally distributed data. If your data has a distribution like this and is positively skewed, then log-transforming the data makes it more normally distributed. Then it's better suited for analysis of this kind.

Now you can think again on which columns you should perform this. Explore the characteristics of your data before diving head in.

Please note that I am also not an expert on this thematic and read the comments to my answer.

• Your premises are incorrect. ANOVA assumes something about the distributions of the error terms but not about the data themselves. Indeed, when there are significant differences between groups the data will be decidedly non-normal. In the second paragraph you seem to confuse "shifted to the left and skewed" with right (positively) skewed; but, regardless, the conclusion is incorrect. – whuber Apr 9 at 19:42
• The most fundamental issue is the importance of distinguishing the responses from the errors. The distribution of the responses is of no direct interest and almost useless for analysis. In particular, it is of little to no use in helping you select an appropriate procedure or model (whether parametric or not). – whuber Apr 9 at 19:50
• In relation to your opening paragraph - in approximate order of importance: (i) the raw distribution of the response variable may be quite irrelevant, since no assumption relates to it (whuber covers this one); (ii) while there is an assumption about the error term, a formal test of the assumption is not a particularly good idea. e.g. see here (in particular, I recommend the brief answer by Harvey Motulsky); (iii) the choice between parametric and nonparametric has little to do with whether or not you have normality ... ctd – Glen_b -Reinstate Monica Apr 10 at 0:09
• ctd ... - firstly note that "parametric" and "normal" are not synonyms (a normal model is merely one example of a parametric assumption). Secondly, in some situations a person may very reasonably use a nonparametric procedure even when normality is a perfectly adequate assumption; or may well use a parametric procedure -- just not necessarily one that assumes normality -- when normality is not an adequate assumption. Finally, one might look to robust methods, for example. $\:$ The rest of the answer looks okay (I have some minor quibbles) – Glen_b -Reinstate Monica Apr 10 at 0:10
• Re the edit: you make an interesting claim, but its correctness depends on what you mean by "lognormally distributed data." Would that refer to the raw response or to the error terms? The interpretation of this phrase determines how one might proceed to "explore the characteristics of [the] data," so it is important. – whuber Apr 10 at 12:39