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 response |
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average response in |
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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 |
A box-and-whisker plot is displayed for the measurements in each group on the ANOM boxchart. Figure 4.9 illustrates the elements of each plot.
The skeletal style of the box-and-whisker plot shown in Figure 4.9 is the default. You can specify alternative styles with the BOXSTYLE= option; see the entry for the BOXSTYLE= option in Dictionary of Options: SHEWHART Procedure.
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 BOXCHART 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 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 (1981, 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 Fritzsch and Hsu (1997), Nelson (1982b, 1991), and Soong and Hsu (1997).
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.