XCHART Statement: ANOM Procedure
Constructing ANOM Charts for Means
The following notation is used in this section:
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number of groups |
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sample size of |
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total sample size |
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expected value of a response in the |
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standard deviation of a response |
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average response in the |
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weighted average of |
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sample variance of the responses in the |
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mean square error (MSE) |
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degrees of freedom associated with the mean square error |
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significance level |
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critical value for analysis of means when the sample sizes |
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critical value for analysis of means when the sample sizes |
th response in the 
are equal 
Central Line
By default, the central line on an ANOM chart for means represents the weighted average of the group means, which is computed as
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You can specify a value for 
with the MEAN= option in the XCHART statement or with the variable _MEAN_ in a LIMITS= data set.
Decision Limits
In the analysis of means for continuous data, it is assumed that the responses in the 
th group are at least approximately normally distributed with a constant variance:
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When the group sizes are constant (
), then 
and the decision limits are computed as follows:
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Here the mean square error (MSE) is computed as follows:
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For details concerning the function 
, see Nelson (1982a, 1993).
When the group sizes are not constant (the unbalanced case), 
and the decision limits for the th group are computed as follows:
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Here the mean square error (MSE) is computed as follows:
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This requires that 
be positive. A chart is not produced if 
but MSE is equal to zero (unless you specify the ZEROSTD option). For details concerning the function 
, see Nelson (1991).
You can specify parameters for the limits as follows:
Specify
with the ALPHA= option or with the variable _ALPHA_ in a LIMITS= data set. By default, = 0.05. 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. By default, 
is the observed sample size in the balanced case. Specify
with the LIMITK= option or with the variable _LIMITK_ in a LIMITS= data set. By default, is the number of groups. Specify
with the MEAN= option or with the variable _MEAN_ in a LIMITS= data set. By default, is the weighted average of the responses. Specify
with the MSE= option or with the variable _MSE_ in a LIMITS= data set. By default, is computed as indicated above. Specify
with the DFE= option or with the variable _DFE_ in a LIMITS= data set. By default, is determined as indicated above.