Hello,
I have a dataset in which we were measuring vegetation height near some Burrowing Owl burrows. Many of the sites were surrounded by bare ground, so our vegetation heights were zero. This has skewed our data and I have tried normalizing them using square root and log(x+1) transformations, with little success (i.e., still not normally distributed). Is there really anything I can do to data such as these to make them normally distributed? Thanks everyone for your input, in advance.
Lots of techniques for zeroes (e.g., zero-inflated models, censored models, two step models [first predict zero, then amount]). You should consider these. First though, why do you want to transform the variable? Why do you think height would or should be normally distributed for these plants?
Nicholas Ryan Peterson, what are you trying to model? If you are trying to model vegetation height by some predictor variables, Daniel Wright answer seems reasonable. However, my assumption is that you are not modeling vegetation height, rather something to do with the Burrowing Owls or their burrows. If you could provide a little more insight to what you are trying to accomplish, I'd be happy to provide some advice.
Am not clear about your research aim, if you are looking at the vegetation heights influencing some number of Burrowing, (i.e., Owl burrows) then a commonly used likelihood-based model to accommodate to a censored sample is the Tobit model (censored data modeling). For instance, consider
Y_i* = β0+ β1X_i + ε_i , where ε_i ~ N(0,σ2)
Y_i : presence and number of burrows at i-th area vegetation.
X_i: the i-th area vegetation height.
*Mapped vegetation plot/the type (and measuring the standard heights) are the units.
* If natural habitation of this owls include bare grounds (natural, artificial or seasonal) then categorizing or limiting to exclude non favourable places shouldn't be wrong, their will be homogeneous characteristics (vegetation growth) , and the error should follow normal distribution.
The normal distribution is not the holy grail! I agree with Ibiloye Christian: what is the ultimate aim of you research, what are your research questions.
Without an explication of this, there is just not an answer to your question, as there is not really something as " your question".
Daniel Wright, thanks for the follow-up. I'm really just looking at whether sites used by Burrowing Owls had vegetation heights that were significantly different from nearby, unused sites (these are measured at a microhabitat scale, so no overlap in areas being measured). I do not suppose that vegetation height should be normally distributed, that is a good point. I am thinking that a nonparametric test, perhaps Wilcoxon rank-sum test, may be the best approach for comparing vegetation heights at used vs. unused sites.
Be it microhabitat (i.e. fine-scale) and bioclimatic (i.e. coarse-scale) analyses, a clearly identified niche differences between microhabitat/species and clear pairs (used microhabitat and unused sites (median of heights of the surrounding grasses?) are necessary before you apply the right non parametric test (Wilcoxon rank/sign test) i.e., the condition for it's use is satisfied and your research question is answered!
Goodluck Nicholas Ryan Peterson .
I'd consider the Wilcoxon rank-sum test as a last resort (if one-to-one transformations, ranking [not one-to-one] is at least better than binning into categories, but as described here, https://statmodeling.stat.columbia.edu/2015/07/13/dont-do-the-wilcoxon/ , even if ranking there are better alternatives). THere are problems when you have ties, also, and problems with what is being tested. See here:
Divine, G. W., Norton, H. J., Barón, A. E., & Juarez-Colunga, E. (2018). The
Wilcoxon?Mann?Whitney procedure fails as a test of medians. The American Statistician, 72,
278-286. doi: 10.1080/00031305.2017.1305291
ps. @Nicholas, I see you are in CA. I'm in Big Bear at the moment.
What is the reason that you want to transform it? Because if it is for regression/anova/t-test purposes, it is a misunderstanding that your dependent variable has to be normally distributed (it are the errors that have to be normally distributed).
See e.g. https://data.library.virginia.edu/normality-assumption/#:~:text=No%2C%20you%20don't%20have,No%20way!&text=Yes%2C%20you%20should%20check%20normality%20of%20errors%20AFTER%20modeling.
But I agree that you have a problem of abundant zeros, so look at tobit/heckman/hurdle (see also comment of Daniel Wright).
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