Hi Alessandro!

You should use a linear mixed model, with random effects for site and day.

Try using the lme4 package from R.

The following documentation may help you: http://cran.r-project.org/doc/contrib/Fox-Companion/appendix-mixed-models.pdf

All the best!

Before you think about modelling - plot the data!

Before we may think about your model, we also need to see such plots.

Jochen has made a good point. Danilo's suggestion to treat Site as a random variable may be problematic as the sample size is just 2 if I got Alessandro right! With Day this looks fine - one would however need to choose an appropriate correlation model to account for the dependence between repeated measure - perhaps AR1.

Hey everybody these are my wind data (see attached file).

So u can see I have 2 treatments (W and E) and for each treament I have no stress (N) and  stress (Y).

My question is: are the two treatments W and E different concerning wind when the stress was N and after when the stress was Y? It is a really simple design but I had really different opinions abóut how to analyse this dataset:

- some collegues told me that: since I did collect only 1-value per day (so no more replicates per time), I do not have to consider time as random effect variable. For example this is the answer to my mail from a collegue of mine:

"Hey Ale,

You can only ever put in a repeated random factor into an analysis if you have repeated observations of each level of that factor within each treatment.

So for example: you have your time factor. Your different levels of your time factor are 24hr, 48hr etc. Right now, for your data, you only have one observation of each level (24hr, 48hr) within each treatment. If you had multiple observations of each level (24hr, 48hr) then you could put in time as a factor. So even though, yes, the oxygen levels may be related to each other over time, your experimental design right now does not allow you to test that"

- some others told me to consider them as time-related (so time as fixed effect)

Which one is right?

Best

Ale

from what I see in your data, I would suggest you consider an interrupted time series analysis. This will allow you to compare between treatments, accounting for autocorrelation. Take a look at the paper I provide a link to below. I also wrote a program in Stata called -itsa-  that will perform the analysis for you

Article Applying a propensity-score based weighting model to interru...

Dear Ariel,

                thank you very much for your suggestion. But do you think that with the "interrupted time series analysis" I can compare also my 2 sites in both the 2 conditions (bef and Aft the stress?). My main aim is, infact, to show that before the stress the 2 sites where identical from a physico-chem point of view.

And another thing: I´m not really familiar with STATA and in our Institution (IGB, berlin) they dont have any license is there a way to to the same with R?

Best wishes

Ale

Absolutely! The design of the ITSA is such that you can compare the pre-period, the post-period, and the difference between the pre-post period for one or more treatment groups. So in this case, you could see if the groups were the same on both level and trend in the "pre" period, if they were the same or different on level and trend in the "post-period".

I don't use R, so I don't know what is available there. I am attaching a paper (it's currently waiting publication) that I wrote on the implementation of -itsa- in Stata. This should give you an idea of how it can be used.

Ale,

I agree with Ariel, you need consider time-series analysis.  Form the plots, it is clearly, the records are not independent, the autocorrelation is higher, I think the auto correlation coefficient  is over 0.6 to 0.7. This violated the assumtion for using a linear regression modeling. Your data is a time-series data.  You may use auto regression model. In SAS, proc autoreg can hadle it. The AUTOREG procedure estimates and forecasts linear regression models for time series data when the errors are autocorrelated or heteroscedastic. (the varaice is not a cinstant) The autoregressive error model is used to correct for autocorrelation, and the generalized autoregressive conditional heteroscedasticity (GARCH) model and its variants are used to model and correct for heteroscedasticity. You can include the predictors, which you used in the linear model and correct the auto-error.  You can choose the lags using nlag=k to correct auto-correlation up to k days. I think any powerful statistical software  can handle the auto-correlated erros, not only SAS does that.