**StATS: Analysis of Means calculations (created 2007-03-02)**.

Analysis of Means (ANOM) are available for a wide range of data sets, and it is impossible to summarize all the applications of ANOM here. The goal on this web page is to illustrate a few of the calculations.

The simplest application of ANOM is a balanced single factor study. A single factor represents measurements done across individuals or sometimes machines, or other conditions). Let I represent the number of individuals being studied and let N represent the total number of observations. If there are m observations per individual, then N=mI.

For each individual, calculate a mean and a variance. The formula for upper and lower decision limits in this setting is

where

As a classroom exercise, a group of three volunteers (labeled A, R, and V to protect their anonymity) were asked to take turns hitting a target with a hand launched foam rocket.

The equipment | Shooting at the target | Measuring the result |

Since the group was small, I asked each team member to shoot twice with their dominant hand and twice with their non-dominant hand. For each shot, the distance from the target was measured in centimeters. Here is the data (D=dominant hand, N=non-dominant hand).

`A-D 14 39`

A-N 60 20

R-D 26 9

R-N 9 12

V-D 36 21

V-N 53 18

The means, variances, and standard deviations are:

` Mean Var Stdev`

A-D 26.5 312.5 17.68

A-N 40.0 800.0 28.28

R-D 17.5 144.5 12.02

R-N 10.5 4.5 2.12

V-D 28.5 112.5 10.61

V-N 35.5 612.5 24.75

The overall mean is 26.42 and the pooled standard deviation is 18.20. The ANOM limits are

`26.4 - 3.724 * 18.2 * sqrt(5/12) = -17.3 (round this to zero)`

26.4 + 3.724 * 18.2 * sqrt(5/12) = 70.1

Here is a graph of the results:

[[This page will show some of the calculations needed for an ANOM chart]]

This page was written by Steve Simon while working at Children's Mercy Hospital. Although I do not hold the copyright for this material, I am reproducing it here as a service, as it is no longer available on the Children's Mercy Hospital website. Need more information? I have a page with general help resources. You can also browse for pages similar to this one at Category: Analysis of means.