The following notation is used in this section:
|
jth response in the ith group |
k |
number of groups |
|
sample size of ith group |
N |
total sample size |
|
expected value of a response in the ith group |
|
standard deviation of a response |
|
average response in the ith group |
|
weighted average of k group means |
|
sample variance of the responses in the ith group |
|
mean square error (MSE) |
|
degrees of freedom associated with the mean square error |
|
significance level |
|
critical value for analysis of means when the sample sizes are equal |
|
critical value for analysis of means when the sample sizes are not equal |
By default, the central line on an ANOM chart for means represents the weighted average of the group means, which is computed as
You can specify a value for with the MEAN= option in the XCHART statement or with the variable _MEAN_
in a LIMITS= data set.
In the analysis of means for continuous data, it is assumed that the responses in the ith group are at least approximately normally distributed with a constant variance:
When the group sizes are constant (), then and the decision limits are computed as follows:
Here the mean square error (MSE) is computed as follows:
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 ith group are computed as follows:
Here the mean square error (MSE) is computed as follows:
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, n is the observed sample size in the balanced case.
Specify k with the LIMITK= option or with the variable _LIMITK_
in a LIMITS= data set. By default, k 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.