This section provides the computational details for constructing an ANOM chart for the lth factor in an experiment involving two factors (l = 1 or 2). It is assumed that there is no interaction effect. See Example 4.5 for an illustration.
The following notation is used in this section:

kth response at the ith level of factor 1 and the jth level of factor 2, where 

number of groups (levels) for the lth factor, 

number of replicates in cell 
N 
total sample size 

variance of a response 

average response in cell 

average response for ith level of factor 1 

average response for jth level of factor 2 



sample variance of the responses for the ith level of factor 1 and the jth level of factor 2 

mean square error (MSE) in the twoway analysis of variance 

degrees of freedom associated with the mean square error in the twoway analysis of variance 

significance level 

critical value for analysis of means in a oneway layout for groups (treatment levels) when the sample sizes for each level are constant and is the degrees of freedom associated with the mean square error; see the section Constructing ANOM Charts for Means. 
The points on the ANOM chart for factor 1 represent , and the points on the ANOM chart for factor 2 represent , .
The central line on the ANOM chart for the lth factor is the overall weighted average . Some authors use the notation for this average.
It is assumed that

where the quantities are independent and at least approximately normally distributed with

The correct decision limits for a given factor in a twoway layout are not computed by default when the lth factor is specified as the groupvariable in the XCHART statement, since the mean square error and degrees of freedom are not adjusted for the twoway structure of the data. Consequently, and must be precomputed and provided to the ANOM procedure, as illustrated in Example 4.5.
In the case of a twoway layout with equal group sizes (), the appropriate decision limits are:






where the mean square error (MSE) is computed as in the ANOVA or GLM procedure:

and the degrees of freedom for error is . For details concerning the function , see Nelson (1982a, 1993).
You can provide the appropriate values of MSE
and by
specifying with the MSE= option or with the variable _MSE_
in a LIMITS= data set
specifying with the DFE= option or with the variable _DFE_
in a LIMITS= data set
In addition you can:
Specify with the ALPHA= option or with the variable _ALPHA_
in a LIMITS= data set. By default, .
Specify a constant nominal sample size for the decision limits in the balanced case with the LIMITN= option or with the variable _LIMITN_
in a LIMITS= data set.
Specify with the LIMITK= option or with the variable _LIMITK_
in a LIMITS= data set.
Specify with the MEAN= option or with the variable _MEAN_
in a LIMITS= data set.