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Multiple group designs

Sampling methodology

Typical response variables in epidemiological studies are the incidence rate of a particular disease or overall mortality rate. In ecological studies mortality rate may also be measured as well as true aggregate variables such as density of species diversity. The main explanatory variable will determine which groups will be included in the study. For example if that variable is ethnic composition, then replicate groups of different ethnic composition would be chosen. If that variable is farm management system, then you will need to select replicates of each of the different systems.

The sampling frame and sampling methodology must then be defined for each level. In medical epidemiology the primary sampling unit is commonly an administrative unit, for example districts or countries. In ecology the sampling unit is more likely to be a habitat unit such as a game reserves or woodland. Each group comprises a cluster using sampling terminology. One could select a simple random sample of clusters from each 'treatment' level - for example a random sample of organic farms compared to a random sample of conventional farms. Or one could form them into matched pairs and take a random sample of pairs. If at all possible one should avoid the temptation of using haphazard or convenience sampling, although this may be unavoidable if access to some clusters is denied. One should never only sample one cluster from each category.

Sampling of individuals to measure the response variable should also be done using probability sampling - although in medical studies existing records for the whole population can sometimes be used. All potentially confounding variables should also be measured. This applies at both at the group level and (if appropriate) the individual level. This is easier said than done since you will not know about some of the potentially confounding variables. But ignoring the possibility of their existence will not make them go away!

Analytical methods

It is important to avoid pseudoreplication in the analysis. The t-test (after an appropriate transformation) is generally considered a fairly robust way to test for differences between 'treatment' means - whether of proportions, rates or densities. Alternatively some form of nested ANOVA would be appropriate. Modelling approaches, such as multiple regression or multivariate logistic regression can be used to take account of confounding factors. Another option now is multilevel modelling.




Multiple time period designs

Sampling methodology

We will focus on a before-after control-impact design given the inadequacies of the simple before-after design. The main explanatory variable will be determined by the nature of the intervention. Whether the number of levels can be varied over time usually depends on whether the intervention is under the control of the researcher or not. For a simple BACI design, a single control or reference group should be selected . For a multiple BACI design select several reference areas at random from a set of suitable areas. Convenience selection is very unwise because of the risk of bias. Of course, if it is feasible to replicate intervention areas as well as well as reference areas, you should always randomly allocate treatment and thus carry out an experimental rather than observational study.

For spatial replication, probability sampling should be used to obtain samples in both reference and intervention areas. If two stage sampling is used (for example use of traps or distance sampling), probability sampling should always be used for the first stage. Second stage sampling should be unbiased, or (if this is not possible) the degree of bias should be independently assessed. For temporal 'replication' (remembering such samples are unlikely to be independent), take multiple repeated samples at regular intervals (systematic sampling) before and after the intervention. All potentially confounding variables should be monitored over time and space including weather factors and human interventions.

Analytical methods

For a simple BACI design one approach is to calculate the difference between the reference and intervention site at each time of sampling and then use a paired t-test to compare the mean difference before intervention with mean difference after intervention. Alternatively a non-parametric test or a permutation test can be used. These tests only establish there is a difference between time periods - not between 'treatments'. For a multiple BACI design use analysis of variance or generalized linear modelling to investigate whether there is a greater difference between the intervention and reference areas than there (generally) is between the controls. Strictly speaking this still only shows there is a difference between time periods, but you will have somewhat more justification to propose a causal role for the intervention. Covariance analysis can be used to adjust for confounding factors.