# Response variable with exponential distribution - how to analyse?

I would like to analyse the following data:

• Number of observations: 430 trees
• 1 response variable: diameter growth of trees
• 2 categorical factors: tree species (9 levels) and treatment (2 levels)

The response variable seems to have an exponential distribution (density, density of log-transformed growth).

This plot suggests that tree species has a strong influence on dbh growth, and this plot that treatment hasn't. For some species, there seems to be an interaction between species and treatment.

I would like to analyze influence of species, treatment and interaction between species ~ treatment. If the response variable was normally distributed, I guess an ANOVA would be adequate. However, due to the exponential distribution, I am unsure about how to proceed further.

I made an ANOVA (aov(dbh.growth ~ species * treat, data=df) that showed significant Pr(>F) values for both factors + interaction (see analysis plots), but are the results usable?

What possibilities are there for factor analysis with exponentially distributed data?

Are there any transformations I might use the transform the data to a normal distribution?

Thanks for any help... I'm really stuck here. ;)

• I don't see exponential distributions here. The plots indicate you have mixtures of distributions, each of which may be symmetric or close to it. So the first thing to do is a robust ANOVA (such as median polish) and investigate its residuals. This may show that ANOVA is fine. Otherwise, it will suggest ways to re-express the data that leave symmetrically distributed residuals. – whuber Sep 19 '11 at 14:41

You could try a parametric survival regression with no censoring and an assumed exponential distribution: survreg(Surv(dbh.growth) ~ species * treat, data=df,dist="exponential")