# Analysis of Means - Explained

What is Analysis of Means?

# What is Analysis of Means (ANOM)?

Analysis of means is a systematic statistical procedure used in depicting significant differences among groups of information in a visual form. It is active mostly in quality control. ANOM methodology compares the average of each group to the mean of the overall process to discover statistical differences of significance.

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## How is Analysis of Means Used?

It allows data to be graphically visualized. The technique was developed in 1967 by R. Ellis Ott, who observed statisticians were not challenged with comprehension of the analysis of variance. Edward G. Schilling extended the concept further in 1973 by allowing ANOM to be used with a large number of statistical tests based on the assumption of normality and connected data in a way that the mean and variances of the number of successes in repeated trials of a binomial experiment when only two outcomes are possible does not apply. ANOM is a graphical likeness of analysis of variance which is a statistical procedure for deciding the amount of similarity or difference between two groups of data used to evaluate the balance of population averages. The graph shows the decision limits, total mean, and mean for each determinant. If a point in the chart falls outside of the decision limit for any given factor, it shows there is an important difference between the factor's mean value and the population mean, which is the average of all elements that meet the criteria of selection for a group. Mean analysis is the same as the analysis of variance but can be used for both normal distribution, which is a bell-shaped symmetrical curve representing the number of times a given sum of objects or events occur in a data set and binomial distribution, which is the number of times one of two possible outcomes occurs in a set of data. ANOM is equal to the null hypothesis of the analysis of variances (ANOVA) which states all factors are the same in averages. When it comes to the alternative hypothesis of analysis of means, it indicates that the mean value of an element is not the same as the population mean. However, the alternative hypothesis of ANOVA states not all factor means are equal. Because of this difference, the ANOM and ANOVA can end up with different conclusions. For example, if the averages of one factor group is higher than the population mean, and the other group is lower, then the F test which is a statistical test that determines if two populations with normal distribution have identical variances or standard deviation, for ANOVA will show there are differences, but the F test for ANOM will show none. In another example, if a one-factor level has a mean different than the other means, the analysis of variances F test may not show a difference, but for analysis of means, it could explain a variation of the group from the population mean.