APA Dictionary of Psychology

a study in which participants are first divided into blocks (relatively homogeneous subsets) according to some characteristic (e.g., age) that is not a focus of interest and are then assigned to the different treatments or conditions in such a manner that each treatment appears once in each block. Thus, the number of participants in each block must equal the number of experimental conditions. For example, the following arrangement of four treatments (A, B, C, D) and 16 individuals (from four age groups) is a complete block design:
\begin{matrix} &&\mathrm{Treatment} \\ \mathrm{Block \#} &&\\ \mathrm{1 \; (children)} &&A\;\;\;\;\;\;B\;\;\;\;\;\;C\;\;\;\;\;\;D\\ \mathrm{2 \; (adolescents)} &&B\;\;\;\;\;\;C\;\;\;\;\;\;D\;\;\;\;\;\;A\\ \mathrm{3 \; (young adults)} &&C\;\;\;\;\;\;D\;\;\;\;\;\;A\;\;\;\;\;\;B\\ \mathrm{4 \; (older adults)} &&D\;\;\;\;\;\;A\;\;\;\;\;\;B\;\;\;\;\;\;C\\ \end{matrix}
By ensuring that the “nuisance” characteristic (here, age) is equally represented across all conditions, complete block designs reduce or eliminate its contribution to experimental error. Compare incomplete block design. See also block design; randomized block design.