Design of experiments chooses experimental units, treatments, replication, blocks in experimental design and randomization so that scientifically useful treatment contrasts can be estimated with meaningful standard errors. Allocation determines which measurements supply independent treatment information.
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.
A factorial design includes every combination of specified factor levels. Balanced replication permits separate estimation of marginal effects and interaction terms. The factor allocation, not the number of subsamples, determines the appropriate error term for each effect.
A crossover design assigns each subject a sequence of treatments in successive periods. Subject blocking can reduce between-subject variation; balanced sequences can separate treatment from period effects. A carryover effect or irreversible change can invalidate a simple within-subject comparison.
A carryover effect is an effect of a previous treatment on a later response. Balanced transitions help prevent a treatment from being preceded disproportionately by one particular alternative, but do not ensure that carryover effects vanish or are separately identifiable in every model.
A completely randomized design assigns treatments directly to available experimental units using complete randomization, without blocking. Fixed group sizes can be enforced. The residual then includes uncontrolled between-unit variation.
A block groups experimental units expected to have similar background responses. Comparing treatments within blocks can reduce the variance of an estimator. Block allocation must be specified before responses are used to evaluate treatment effects.
A block design assigns treatments to experimental units partitioned into blocks. Its incidence counts record how often treatment occurs in block . Balance and connectedness determine which treatment contrasts are estimable and how much adjustment for blocks costs.
A row-column design has two crossed partitions of experimental units into rows and columns. Equal treatment proportions in every row and every column make treatment contrasts orthogonal to both centered block spaces. A repeated three-treatment arrangement in a six-by-six array can give a balanced example.
A randomized complete block design places every treatment in every block, with a common replication pattern, and uses independent within-block randomization. The usual basic version has one occurrence of each treatment per block; equal repeated occurrences give a replicated complete-block version. Such equal-proportion designs are orthogonal block designs.
An orthogonal block design has centered treatment-indicator vectors orthogonal to centered block-indicator vectors on the experimental units. With treatment replication , block size and total , this is equivalent to . It permits additive block adjustment without changing treatment estimates.
Replication in experimental design assigns a treatment to multiple independently allocated experimental units. Repeated measurements on one unit can improve measurement precision without providing independent treatment replication.
A replicate is an independently allocated instance of a treatment on an experimental unit. Independent replicates permit estimation of response variation; subsamples within one unit do not supply additional independent treatment replication.
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.
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.
Articles by others on the same topic
Design of Experiments (DOE) is a systematic method used in statistics for planning, conducting, analyzing, and interpreting controlled tests to evaluate the factors that may influence a particular outcome or response. It is commonly applied in various fields, including agriculture, engineering, pharmaceuticals, and social sciences, to understand the relationships between different inputs (factors) and outputs (responses).