Analysis of means compares the absolute deviations of group means from their overall mean, an approach that was initially studied by Laplace in 1827. Halperin et al. derived a version of this method in the form of a multiple significance test in 1955. Ott developed a graphical representation for the test and introduced the term “analysis of means” in 1967. Refer to Ott (1967) and Ott (1975).

P. R. Nelson (1982a) and L. S. Nelson (1983) provided exact critical values for ANOM when the groups have equal sample sizes. P. R. Nelson (1991) developed a method for computing exact critical values for ANOM when the group sample sizes are not equal. Refer to Nelson, Coffin, and Copeland (2003) for more information on the use of ANOM in engineering experimentation.