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In combinatorial mathematics, a block design is an incidence structure consisting of a set together with a family of subsets known as blocks, chosen such that frequency of the elements [clarification needed] satisfies certain conditions making the collection of blocks exhibit symmetry (balance).
Block Design is a statistical technique used primarily in the field of experimental design. It involves the arrangement of experimental units into groups, or blocks, that are similar to one another.
Blocking is a technique for dealing with nuisancefactors. A nuisance factor is a factor that has some effect on the response, but is of no interest to the experimenter; however, the variability it transmits to the response needs to be minimized or explained.
In that sense, blocking is a so-called variance reduction technique. Typical block factors are location (see example above), day (if an experiment is run on multiple days), machine operator (if different operators are needed for the experiment), subjects, etc.
In the statistical theory of the design of experiments, blocking is the arranging of experimental units in groups (blocks) that are similar to one another. Typically, a blocking factor is a source of variability that is not of primary interest to the experimenter.
What is a Block Design? Block designs are viewed in different ways by combinatorialists and statisticians. To a statistician, a block design is a set of ``plots'' or ``experimental units'' which carries a partition into ``blocks'', and a function from this set to the set of ``treatments''.
Chapter 12. Block Designs. Often there are covariates in the experimental units that are known to affect the response variable and must be taken into account. Ideally an experimenter can group the experimental units into blocks where the within block variance is small, but the block to block variability is large.
