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An observational unit is the object or occasion supplying a recorded response. Several observational units can belong to one experimental unit; counting them as independent treatment replicates creates pseudoreplication.

The experimental unit is a volunteer on a particular afternoon, since that volunteer-session receives a program assignment. There are 36 such experimental units; a volunteer is a repeated block, rather than a unit that receives only one program throughout the experiment.

The observational unit is the individual completed sketch, equivalently the session's single recorded count of correctly represented features. The separate map features contribute to that response variable; they are not independently randomized replicates. Nor are repeated sessions on one volunteer independent subjects.

First agree the scientific question and primary response variable. Ask the vet about the disease's course, the proposed mechanism and duration of each treatment, the eligible population, baseline severity, and what outcome and follow-up time would represent worthwhile improvement. Is the disease transmissible, is recovery reversible, and can treating one cow affect another's outcome? These answers determine whether a crossover design is credible, whether the experimental unit should be a cow or a whole herd, and whether individual randomization would leave interference between groups. Agree welfare and rescue arrangements with the vet when deciding which comparisons are feasible; the statistical plan cannot determine these from an unfamiliar disease name.

Second agree feasible allocation and adequate independent replication. Discuss numbers of available cows and herds, variation in the chosen outcome, a scientifically meaningful treatment difference, and the desired statistical power. Use these to plan sample size, rather than choosing a number solely from convenience. Discuss herd, lactation stage and initial severity as potential blocks in experimental design, then specify randomization, comparable management, concealed allocation and blinded outcome assessment where feasible. Repeated milk or health records from the same cow are observational units, not extra independent experimental units; pseudoreplication would give misleading standard errors. Availability of enough independent cows or herds, together with expected variation, governs the precision actually achievable.

Both factors are assigned at orchard level. Therefore the experimental units are the twelve orchards; the trees are observational units within them. The six combinations form a balanced factorial design, replicated twice. The orchard ANOVA stratum has $12-1=11$ statistical degrees of freedom. Spray uses $2-1=1$, pruning uses $3-1=2$, and their interaction term uses $(2-1)(3-1)=2$, leaving six for error.

Dividing each treatment sum of squares in ANOVA by its statistical degrees of freedom and using $1440/6=240$ as the denominator gives all missing entries:

The unrounded F-test statistics are $998/240=4.15833\dots$, $560/240=2.33333\dots$ and $202/240=0.841667\dots$. The within-orchard tree mean square in ANOVA, 180, is not the treatment error denominator: using it would confuse subsampling with independent replication. The tree ANOVA stratum has $12(30-1)=348$ statistical degrees of freedom; $1+11+348=360$ is the uncorrected total, and the corrected total is 359.

A replicate is an instance of a treatment on a distinct experimental unit. Independent replicates permit estimation of response variation between experimental units; subsamples within one experimental unit do not supply additional independent treatment replication. In the pot example, another pot receiving A supplies another A replicate, while another leaf from an existing A pot supplies another observational unit.

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.^[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 $8\cdot 3=24$ 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.

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 $\left(\genfrac{}{}{0ex}{}{8}{4}\right)=70$ 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.^[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.^[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.