Maybe you can try to analysis the residual of SLA (LAI, biomass allocation)~size to light and species. I'm not very sure.

It is probable you can use a simple ANOVA analisys and a Tukey test. You just have to be careful with the independence of the variables

Actually, this study shoud be a three-way ANOVA design, considering all three factors (light level, tree species and tree size) as you mentioned. However, tree size may be a factor that  has been neglected in the study. I think you can make sure whether tree size has effects on the variables you measured. That is to say, a simple supplement experiment may be needed to find out whether tree size will make a difference. If it is not the case, then two-way ANOVA (light level, tree species) can be used in your study. However, if it is the case, then I think re-designing the experiment to three factors (light level, tree species and tree size) may be better.

Best regard!

I would suggest to use a one way ANOVA analysis with species as a main factor, and tree size and/or light level should be used as a co-variance rather than the main factors.

Hello Ardalan - I conducted a similar study many years ago.  I found that the species differences were so large, that I could not reliably analyze the light levels statistically so I did all of the analyses separately by species.  I used initial size at the time the treatments were implemented as a co-variant to account for the size difference effects within a species and light level was the main effect.  Because I had 8 light levels, I also fit models to the treatment means to look for significant trends with light level.  I have attached the 3 papers published from my study in case you want to read them for more details of what I did.  Cheers, Kurt

You may try with ANOVA under split plot design by considering light levels as main treatments. 

Dear Kurt W. Gottschalk

Thank you so much for your description. My study is in a natural forest and in a natural conditions, so I couldn't control the light condition and also I don't know (I don't have) initial size.

Since you have light measurements for every tree, one approach could be to not use the parametric light level categories at all but do a regression analysis of actual light versus each of the other variables.  Again I would recommend dong this by species.  You can then test the regression coefficients for their significance in addition to evaluating the regression fit. This has the advantage of not increasing variation in each light level category by the variation in actual light levels within that category but using that actual light information to its fullest.

Dear Kurt W. Gottschalk

Thank you so much again. I have done it before, but there is a problem here and the problem is different size again. Most of my variables do not show a trend versus of different amount of light and I know that the source of this problem is different tree size.

Dear Ardalan Daryaei  

you can design your experiment according to Factorial experiment with two factors : species ( three levels ) and light level ( three level ) performed in  Randomized completely Block Design ( RCBD ) with many observation  , using the size of tree as a block ( you can make many categories for the tree sizes ) to isolate its effect from the experimental error

you say that the size affects the results (although you do not have the size) but that you

want to ignore that. why?

when species effects are different it is often a good idea to analyze species separately as kurt mentioned.

your explanation is not very clear in that you have light levels and % light by tree. are these understory trees?

also analysis a blocked or split plot depends upon the physical layout which you have not mentioned.

Dear Carl W. Mize

I have the current sizes but I don't have initial size. For example for leaf biomass allocation, bigger trees have lower leaf allocation and smaller trees have more leaf biomass allocation. So I want to know the impact of light and species on leaf allocation, therefore I want to ignore the size.

I am exactly studying on understory trees.

you don't want to ignore something that will affect the results.

you could use final size instead of initial.  initial would be better but the change should not be too large and initial and final should be very highly correlated.  treat size as a covariate as various people have commented.  by adjusting you get a better estimate of the other affects.

But that is the crux of your problem.  You are looking at variables where understory tree size is by far a more important component of the variation than is species or light. So in order to get at those smaller influences you have to remove the size influence.  There are basically two ways to do that.  One way which was mentioned by another answer is to block your observations by size classes, so that all of the trees of similar size are in one block or replication, then you will have a significant block response in the ANOVA which will remove that variation and allow you to test for light or species differences.  The second way as mentioned before is use one tree size variable - say height - as a covariate to reduce the variation due to size.  this can be done either in CANOVA or regression. 

agreed. 

blocking in size seems more problematic.

Dear Ardalan

As it was rightly mentioned by Kurtz the tree size (height and Crown area or width ) could influence the light availability, biomass allocation in the trees etc. Hence, it is better to go for  Analysis of Covariance by taking tree size as the covariant.  

Thank you dear all for your suggestions.

Dear Ardalan

I think there is a specific statistical model for this purpose. You can use a mixed effects model in which you have fixed effects (factors you are interested in) and random effects (factors with influence but not the object of you study. The approach is like a common linear model with ML fit. More details in:

Pinheiro J, Bates D, DebRoy S, Sarkar D & R Core Team (2015). nlme: Linear and Nonlinear Mixed Effects Models. R package version 3.1-120, http://CRAN.R-project.org/package=nlme.

hi, Ardalan.The size affects the results. So,you can ignore that. I think  You can use a mixed effects model to analyze your data with tree size being a covariant.