anombal

Analysis of Means (ANOM) is a statistical procedure for troubleshooting industrial processes and analyzing the results of experimental designs with factors at fixed levels. ANOM is an alternative to ANOVA for a fixed effects model. Unlike ANOVA only determines if there is a significant difference between the treatment means, ANOM identifies the means that are significantly different. For it is considered a class of multiple comparasions procedure. ANOM not only answers the question of whether or not there are any differences among the factor levels, but when there are differences, it also tell us which levels are better and which are worst.

It compares the absolute deviations of group means from their overall mean, an approach that was initially studied by Laplace in 1827. Halperin et al. (1955) derived a version of this method in the form of a multiple significance test in 1955. Ott (1967, 1975) developed a graphical representation for the test and introduced the term 'analysis of means'. Nelson (1982) and Nelson (1983) provided exact critical values for ANOM when the groups have equal sample sizes (balanced).

According to Nelson et al. (2005), basically, an ANOM is the generation of a decison chart similar in appearance to a control chart. It has a centerline, located at the overall mean, rate or proportion, and upper and lower decision limits. The group means, rate or proportions are plotted, and those that fall beyond the decision limits are said to be significantly diferent from the overall value. These differences are statistical diferences, if they exist. Then, ANOM allows one to easily evaluate the practical differences.

This m-file considers that all the factor levels have equal sample size (balanced), and with the known assumption that the errors e_ij are approximately normally distributed and that the populations all have approximately the same variance (homoscedasticity).

Here, we use the statistical fundamentals and procedure given by Nelson et al. (2003, p.250-251).

Inputs:
X - data matrix (Size of matrix must be n-by-2; data=column 1, sample=column 2).
a - significance level (default = 0.05).

Outputs:
- Complete Analysis of Means
- ANOM chart