Experimental unit 2026-10-07
An experimental unit is a unit to which a treatment is assigned under the experimental allocation. A whole orchard can be an experimental unit even when responses are recorded separately on its trees. Different factors in a split-plot design can have different experimental units.
This produces a split-plot design: assign spray to whole orchards, with six sprayed and six unsprayed, then independently randomize ten trees to each pruning method inside every orchard. Orchards remain experimental units for spray; individual trees become experimental units for pruning. Pruning contrasts and the spray-by-pruning interaction term now lie in the within-block ANOVA stratum, while spray is tested between orchards.
The between-orchard ANOVA stratum has eleven statistical degrees of freedom, split into one for spray and ten for error. The within-orchard ANOVA stratum has 348, split into two for pruning, two for the interaction term and 344 for error. This pooling of within-orchard error is appropriate under the stated compound-symmetry covariance model; additional orchard-specific pruning variation would need its own variance component rather than this simplified error model.
The shared orchard effect cancels in a pruning difference within an orchard. Its variance is , so averaging across twelve orchards gives
The spray contrast still compares means of six orchards per group, each based on 30 trees, so its estimated variance remains . For a difference of pruning differences between the two spray groups, each group's pruning difference has estimated variance , and the resulting interaction contrast has estimated variance , compared with in the original allocation.
Splitting pruning within orchards improves pruning and interaction precision without extra trees, and gives spray a less sparse error estimate; it does not reduce the spray contrast's variance. This option requires tree-level pruning to be practical without interference between neighboring trees. The numerical gains, like those in the other options, assume the current variance components remain applicable next year.
Split-plot design 2026-10-07
A split-plot design randomizes one factor to whole plots and another to subplots within each whole plot. Whole-plot treatment effects and subplot treatment effects therefore use different error ANOVA strata. Whole plots provide replication for the first factor; their subplots do not supply extra independent whole-plot replication. Within-whole-plot comparisons can remove a shared additive whole-plot variance component.