Standard Article

Incomplete Block Designs

Natural Resources and Agriculture

  1. Walter T. Federer1,
  2. Nam-ky Nguyen2

Published Online: 15 SEP 2006

DOI: 10.1002/9780470057339.vai005

Encyclopedia of Environmetrics

Encyclopedia of Environmetrics

How to Cite

Federer, W. T. and Nguyen, N.-k. 2006. Incomplete Block Designs. Encyclopedia of Environmetrics. 3.

Author Information

  1. 1

    Cornell University, NY, USA

  2. 2

    Scoresby Business Centre, Victoria, Australia

Publication History

  1. Published Online: 15 SEP 2006


The subject of statistics deals with variability and how to deal with it. In the planning and conduct of an environmental or ecological investigation, the items used to control variability are (a) refinement of experimental technique, (b) selection of homogeneous material and/or environments, (c) grouping (blocking, stratifying) material into homogeneous subgroups (blocks, strata), and (d) measurement of related variables and use of covariance. There are many ways of blocking (arranging) the experimental units (EUs) in a comparative experiment with v treatments. If the sample of EUs is from a homogeneous population, then no blocking is required and a completely randomized experiment design (ED) of the v treatments randomly allotted to the rv EUs is used. The replicate number (sample size) for each treatment is r unless unequal replication is desired. If homogeneous blocks of size v are available to accommodate all v treatments, a randomized complete block ED (all v treatments in each block, not necessarily an equal number of times) is used. In many situations, the block size, k, is less than v and an incomplete block ED (not all treatments in each of the blocks) is used.