There is extensive literature describing the pros and cons of BACI, but in the most basic form the statistical model is:

Y=mu_before/after+mu_treatment/control+mu_before*treatment and the appropriate test is for a significant interaction.

A good plot of the treatment and control means pre and post is perhaps the best way to visualize this test. You are looking for non-parallel lines as an indication of significant interaction.

If multiple time steps are available this model can be extended to look for change in slope over time pre/post or tests looking for recovery to an appropriately defined asymptote over time.

Most of the controversy over BACI is about whether all environmental factors are adequately controlled or if lurking factors may cause rejection when in fact there has been no "treatment" effect.

There is extensive literature describing the pros and cons of BACI, but in the most basic form the statistical model is:

Y=mu_before/after+mu_treatment/control+mu_before*treatment and the appropriate test is for a significant interaction.

A good plot of the treatment and control means pre and post is perhaps the best way to visualize this test. You are looking for non-parallel lines as an indication of significant interaction.

If multiple time steps are available this model can be extended to look for change in slope over time pre/post or tests looking for recovery to an appropriately defined asymptote over time.

Most of the controversy over BACI is about whether all environmental factors are adequately controlled or if lurking factors may cause rejection when in fact there has been no "treatment" effect.

I fully agree with John. I am afraid that a BACI but even an M-BACI (Multiple Before/After Control/Impact) design have the same subjectivity problems like BACI for the selection of 'reference-control' sites in environmental designs because there is no control of past and present environmental variable effects and history is of paramount importance in the environmental sampling design . In an experiment, instead, where you can control some environmental variables. you can balance unknown factors by randomly selecting groups of organisms for treatment and control.

Always choose the MBACI design over BACI:

Regardless if you are working with a field survey or an experiment, try to replicate your sites or treatments by including at least 2 "control" and "impact" sites separated in space, and sample them before and after. Such an M-BACI (Multiple Before/After Control/Impact) design is much more trustworthy than a simple BACI design, and can be tested using "site" as a nested, random factor in your analysis.

Actually the selection of [unaffected] reference sites in BACI as well as in MBACI for environmental studies is assumed to be a random sample from a population of sites as in design-based approaches (Underwood 1992). However, this assumption is not true, even approximately, and not plausible as a model. It is a subjective guess by the assessor, and thus invalid for inference. It has also been suggested that null hypothesis significance tests approaches can be appropriate in experimental studies but should not be used in observational studies because variance in the data set has not been generated by experimental manipulation, leaving inference vulnerable to unconsidered confounding factors. In addition, data treatments following BACI sampling designs are often suggested involving permutations (e.g. permanova) between environmental variables and biota assuming that species can be permutated across samples independently of their often strict ecological linkages evolved in time with specific habitats. Also this assumption is not true (with the only exception for ubiquitous species, but are there really any?), and thus invalid for inference. The risk in this case is to destroy the inherent and rich ecological information of temporary or long lasting interdependence of biota with contextual habitats.

Thanks Giovanni for your hints. By the way do you think it could be formally possible to select randomly a reference site, basing on existing information? For example, selecting non-polluted site from a population of geographic coordinates with known low concentrations of pollutants.

Hi Paolo, I am afraid that the only "true" reference site will be exactly the same site along with relative biota before the pollution event. Just because you are looking for a bio-ecological response to impacts, only in that case the "before" and "after" the pollution event would have the same history behind and you would be sure to deal with the same community of organisms you are checking for change. Anyhow, in case of lichens like you use, I think that you could approach the problem by preparing, for instance, your biological material in controlled and standardized conditions and then expose it, for example, to atmospheric pollution. In this case you are formally allowed to compare what you have seen "after" with what you prepared "before". The same standardized procedure could be adopted by other researchers allowing a much wider generalization of results. However, in this case you have to consider the confounding effect of exposure to the "new" environmental conditions apart from pollution. But you can address this last point by placing part of your biological material in selected unpolluted sites as you mentioned. In any case, formally, you could not select randomly communities found in the field and use them as reference since usually you know almost nothing about the history behind such communities and the biophysical complex of factors that have been and are still acting on them possibly affecting community response to treatment.