What is "pseudoreplication"

n. (context statistics especially in biology ecology English) The exaggeration of the statistical significance of a set of measurements resulting from treating the data as independent observations when they are in fact interdependent.

Pseudoreplication, as originally defined, is a special case of inadequate specification of random factors where both random and fixed factors are present. The problem of inadequate specification arises when treatments are assigned to units that are subsampled and the treatment F-ratio in an analysis of variance ( ANOVA) table is formed with respect to the residual mean square rather than with respect to the among unit mean square. The F-ratio relative to the within unit mean square is vulnerable to the confounding of treatment and unit effects, especially when experimental unit number is small (e.g. four tank units, two tanks treated, two not treated, several subsamples per tank). The problem is eliminated by forming the F-ratio relative to the correct mean square in the ANOVA table (tank by treatment MS in the example above), where this is possible. The problem is addressed by the use of mixed models.

Hurlbert reported "pseudoreplication" in 48% of the studies he examined, that used inferential statistics. When time and resources limit the number of experimental units, and unit effects cannot be eliminated statistically by testing over the unit variance, it is important to use other sources of information to evaluate the degree to which an F-ratio is confounded by unit effects.