StATS: Analysis of Means answers to on your own exercises (created 2007-03-06)

On the web page

you were asked to calculate ANOM charts for two different data sets.

The first data set is reproduced below.

A 14 39
B 60 20
C 26  9
D  9 12
E 36 21
F 53 18

The summary statistics are

  Mean Var   Stdev
A 26.5 312.5 17.68
B 40.0 800.0 28.28
C 17.5 144.5 12.02
D 10.5   4.5  2.12
E 28.5 112.5 10.61
F 35.5 612.5 24.75

The average of the individual means is 26.4 and the average of the individual variances is 331.1. The square root of this value is 18.2 which represents the pooled standard deviation.

In this example, I is 6 and N is 12. The critical value h is 3.62. The upper decision limit is

26.4+3.62*18.2*√5/18=61.4

The lower decision limit is less than zero. Since negative values are impossible in this setting, you should not plot this value. Here is a graphical display.

The second data set represents proportions and is reproduced below.

25 23 22 18 24 30 22 28 29 15
19 35 33 35 33 17 19 19 40 26

The average of these 20 proportions is 0.26. In this example, I=20 and N=2000. The critical value h is 3.02. The upper and lower decision limits are

0.26-3.02*√(0.26*0.74)*√(19/2000)=0.13
0.26+3.02*√(0.26*0.74)*√(19/2000)=0.39

Here is a graphical display of the individual proportions and the decision limits.

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.