= Replication in experimental design
= Replication
{synonym}
<Replication in experimental design> repeats a <treatment> on multiple independent <experimental units>, so that variation between those units can inform a <treatment contrast> and its <standard error>. Repeated measurements on one <experimental unit> can improve measurement precision without providing additional independent <treatment> <replication>. The <experimental unit> is identified by where the <treatment> is applied, rather than by how many responses are recorded.<Experimental unit (NC3Rs Experimental Design Assistant)>[Experimental unit, “Why is the experimental unit important?” and “Know your experimental unit”, revised 31 October 2023]{ref}
For a constructed example, grow one <plant> in each of eight separate pots. Apply <treatment> A to four pots and <treatment> B to four pots, without sharing drainage water between pots. Measure the <length> of three <leaves> per pot. The pot is the <experimental unit>; the <leaf> is the <observational unit>. There are four <treatment> <replicates> per group, eight <experimental units> overall, and $8\cdot3=24$ measurements. The three <leaves> in one pot are <nested measurements>, because they share the same <plant> and <treatment> application. The setup assumes that pots do not affect one another; simply putting them in separate containers does not establish statistical <independence>.
\Image[/experimental-replication-pots-and-leaves.png]
{title=Constructed two-<treatment> design: eight pot <experimental units> contain twenty-four <leaf> <observational units>}
{description=Each outlined pot receives one <treatment> application and supplies three <nested measurements>. A pot label marks an <experimental unit>, not a measured response value.}
<Randomization> chooses which <experimental units> receive which <treatments>; <replication> supplies multiple <experimental units> receiving the same <treatment>. These solve different problems. In the balanced allocation above, choose the four A pots uniformly among the $\binom84=70$ possible <subsets>. A particular pot has <probability> $1/2$ of receiving A. Given that one pot receives A, a second receives A with <conditional probability> $3/7$, rather than $1/2$. Thus the assignments are not <independent random variables>, even though the <experimental units> can supply independent responses conditional on those assignments in a suitable <statistical model>.
An actual <ecology> experiment illustrates why the distinction matters. In <Stuart H. Hurlbert>'s account, twelve experimental ponds initially received zero, fifty or 450 <fish>, with five, four and three ponds respectively. Preparation included assessing variation between ponds before introducing <fish>; allocation considered both location and existing differences between ponds. The zero-<fish> ponds supplied the <scientific control>. These were repeated <treatment> applications to ponds, not twelve samples from one pond.<Pseudoreplication and the Design of Ecological Field Experiments by Stuart H. Hurlbert>[Pseudoreplication and the Design of Ecological Field Experiments, pp. 194–195, combined or hybrid allocation approach and the Hurlbert–Mulla experiment]{ref}
The original article followed the southern California ponds for ten months. Its readouts included <zooplankton> populations and total <phytoplankton>; it reported decreases in some <zooplankton> populations and increased total <phytoplankton>.<Impacts of mosquitofish (Gambusia affinis) predation on plankton communities by Stuart H. Hurlbert and Mir Subhan Mulla>[Impacts of mosquitofish (Gambusia affinis) predation on plankton communities, abstract, Hydrobiologia 83, pp. 125–151, August 1981]{ref} Repeated sampling within a pond helps describe its response through time, while ponds supply <treatment> <replication>. Unequal group sizes and initial pond variation matter for the <statistical model>; the <treatment> counts alone do not establish equal <variances> or independent responses.
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