Selecting the best statistical analysis I'm going to begin an experiment about drying leaves. I want to learn about how some special kind of leaves are going to dry themselves in 2 different situation. A group of them will stay in a high density, and the another group I will spread out in a bigger area (for example, 1 m2 for the first, and 3 m2 for the second). Of course, I will repeat this experiment several times. In the end, I will get:


*

*Individual weight of the leaves (selecting samples) in the beginning

*Individual weight along 4 days

*Individual weight in the end

*Nutritional composition in the start and in the end


I am remembering my knowledge in stats and R, but I am still lost. My question is, which is the best comparison method to analyse this data? I want to know:


*

*How the humidity content change along the days

*To dry this kind of leaves, which drying area is better?

*Is it statistical significance between both method about losing water and nutrient content?


Kind regards!
Alex.
 A: It is possible you are trying to cram too much into one design.
Here is a somewhat simplified version: 
Consider three effects:


*

*Density (fixed effect $\delta$ at two levels High and Low)

*Leaves (random effect $L$ at $n$ levels)

*Times [fixed effect $\tau$, three levels (0, 4, Last), nested within Leaves].
These specifications to the model
$$Y_{ijk} = \mu + \delta_i + L_j + \tau(L)_{k(j)} + \{\delta*L\}_{ij}
+ e_{ijk},$$
where $e_{ijk} \stackrel{iid}{\sim} \mathsf{Norm}(0, \sigma).$
Lower-case Greek letters represent fixed effects, upper-case Latin
letters respresent random effects, parentheses indicate nesting; 
$Y_{ijk}$ are measurements of weight and $e_{ijk}$ are normally
distributed random effects. [Parentheses are read as 'of ' not 'within'.] 
The only interaction effect supported
is between Density and Leaf, a three-way interaction for density,
Leaf and time would be confounded with the error term, and there
cannot be an interaction between an effect $\tau$ and an effect $L$
within which it is nested. 
[Many software packages have proprietary
notations for indicating fixed and nested effects; for example
Minitab declares random effects separately and indicates nesting
within the model by parentheses.]
You might do separate ANOVAs for humidity and nutritional content.
Alternatively, do a multivariate ANOVA [MANOVA] with weight, humidity, and
nutritional content as data dimensions.
This type of design is sometimes called 'partially hierarchical'
and sometimes called 'repeated measures'. But the terminology
'repeated measures' has been used in so many different ways in
different fields of study as to have become almost useless.
Whatever model you use, you must account for the fact that the
same leaves are measured at three times, but that the leaves
at High density are not the same as those at Low density.
