Hi, I do not have the perfect answer to your question, but have a look at this paper (and the papers citing it). It discusses the issue of normal distribution in psychological variables

http://psycnet.apa.org/psycinfo/1989-14214-001

Hi, warm thanks for your answer.

It is not what I was searching for but it is full of clues regarding to my problematic.

I also think that, the reason why most of the variables found not to be "normal" in this paper is because they are scores created by humans and don't come from natural mechanisms like cellular division which tend follow a log-normal distribution.

(Please note that, as regards psychometric scores, the main issue might be if wheter those scores are quantitative)

I don't think that an exhaustive list of the distributional features of biological variables exists. Usually, at the class of medical statistics, they tell you that "most of the biological variables can be assumed to be normally distributed in the general population" (and in my experience this is more or less true, with a few exceptions like lipidic metabolism). So, the point is: are you working on a general population? For instance: it is known that height and weight are normally distributed in the general population. But if you consider the sub-population of basket players, it might be not true (or maybe it will, but quite obviously with a different mean&SD... who knows!)

Anyway, it is not clear to me what you're looking for as regards the "additive and multiplicative effect" stuff, so I don't know if my answer will be useful...

In my experience, variables observed in natural systems (biology, climate, etc.) tend to exhibit right-skewed distributional shapes. Aitchison and Brown (1957) give many examples for the (right-skewed) lognormal distribution.

The origin of right-skewness may lie in multiplicative interactions of the "building microvariables". In my feeling, one should not necessarily go so far and assume a priori a certain distributional shape (or employ a table for that) because there exist different types of right-skewed distributions (e.g., Generalized Extreme Value Distribution).

Evidently, an assessment based on explorative data analysis (studying the distributional shapes by means of histograms or kernels) should complement the consultation of a theoretical table of distributional shapes.

Cheers, Manfred

P.s.: The reference and some of the mentioned techniques are mentioned, for example, in my book on climate time series analysis.

http://www.manfredmudelsee.com/book/index.htm

Thank you all for your answers.

Please excuse my late reply, I've been heavily busy these days.

Marco Gnesi, your comment on the sub-groups is a very important detail and just made me realize why I have extreme kurtosis values in my analyses. The reason is because all of the mice we analyse have the same age and the same weight and even though these aren't the analyzed variables, they can have a serious impact on the variables' distribution (heavy tail distribution).

It's now too late to take new mice, the data comes from the past 20 years so we have to deal with what we have BUT we can also assess normality of a distribution if the only reason is a moderately high kurtosis.

If you want to have a closer look to additive/multiplicative effects which are underlying possible mechanisms for each variable, look at this seminar:

http://stat.ethz.ch/~stahel/talks/lognormal.pdf

Manfred Mudelsee, thank you for your links, I have checked them and unfortunaly none of my biological variables were found in the list but the article was very interesting.

Do you have a concrete exemple of this multiplicative interaction of "building microvariables" ? It is a bit subjective to me. I have proportionate errors in mind but it's still abstract to me.

And I completely agree on graphs to rely on, like the Residuals vs Predicted values of raw data which can give clues on log-normal distribution (if residuals are more variable at high values).

Hi Yacine,

happy I've been of some help :) anyway, if the problem is that your distribution is leptocurtic it is not such a big problem as if it is asymmetric...

Dear Yacine, I am sorry that I cannot offer biological expertise. Multiplicative interaction: if X is Gaussian and Y is Gaussian, then X*Y is not Gaussian (it is chi-squared), and so on: X * Y * Z --- things get more complex, become analytically intractable; it appears that the resulting product becomes (in many situations) rather skewed. This underlines the importance of doing an explorative data analysis. Beest, Manfred

Hello,

It depends Marco, if you want to assess the impact of violation of normality for one-way ANOVAs, extreme kurtosis have more impact on power than skewed distributions.

Thank you for your explaination Manfred. I am going to ask pharmacians of my laboratory for mechanisms underlying the results of each biological variable.

Still, it is not a golden rule to tell a variable has multiplicative effects (log-normal) if it comes from a multiplicative formula but it is known that it won't yield to a gaussian distribution, is this right ?

Once again, thank you both for your answers

Hi Yacine,

- good point, I didn't think about those cases in my previous comment... sorry

- I would say no. Biological variables might me a bit tricky sometimes, and obviously the effect being additive or multiplicative depends on the biological features behind the particular variable that you've measured...