Pseudo-replication refers to the use of inferential statistics to test for treatment effects with data from experiments where either the treatments are not replicated (though samples may be) or replicates are not statistically independent. Replication is the repetition of an experimental condition so that the variability associated with the phenomenon can be estimated. Replicates must be distinguished from experimental samples. If there is pseudo-replication (i.e. samples are compared rather than true replicates), then application of any statistical test will only show non-independent variation within the single replicate, rather than among replicates. For example, multiple plots within one local marine area are actually related samples but could erroneously be tested as replicates. In this example, true replicates would constitute multiple different widely spaced marine areas within which plots are sampled.

Avoiding pseudo replication in regression modelling could be done by applying mixed model regression, which has random and fixed effects (a standard regression only has fixed effects). The replicates are considered as random effects, but the overall variability in the data is still incorporated :)

See: Methods in Enzymology

Volume 384, 2004, Pages 139–171

Mixed-Model Regression Analysis and Dealing with Interindividual Differences

Thank you for your quick response Andrew.

You're welcome Andry :)