Pseudoreplication: When n Is Smaller Than It Looks

Pseudoreplication treats dependent measurements as independent units in an analysis. Several leaves from a plant or cells from a well can share conditions. These measurements may add information about that unit, but they do not create new independent treatment assignments. Identify the assignment level and relevant sources of dependence before choosing the analysis.

Technical repeats remeasure the same specimen or preparation; subsamples measure parts within it. Biological samples are distinct specimens or separately prepared cultures and can share a donor or batch. Separate treatment assignments do not remove shared-source variation. Average suitable repeats into a unit summary, or use a hierarchical model that retains measurements and accounts for grouping.

Changing an analysis to account for dependence can change its uncertainty without changing the estimated treatment difference. A result may then cease to meet the planned significance threshold. That does not prove the treatment effect is zero. Report the estimate, uncertainty, assignment units and model rather than treating significance as a verdict on whether an effect exists.

For independent observations, the standard error of a mean is estimated by s divided by the square root of n. Positive within-unit correlation can make a calculation using every reading as independent underestimate that error. Not all error bars show standard errors: they may show standard deviations, confidence intervals or another quantity. Check the definition before interpreting their width.

Repeated readings within independently assigned patients form a hierarchy. An analysis can use patient summaries or model variation between patients and dependence within patients. The choice depends on the response and question. Retain unit identifiers. Pooling every reading as an independent patient ignores the design, while discarding whole groups is not a general solution.

A figure legend should distinguish assigned units from measurements. Many points from a few animals show nesting, but do not by themselves prove an invalid analysis. Check what n counts, what each point represents and how error bars were calculated. A report may show all readings while correctly using animals as the independent treatment units.