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 BOXCHART Statement

Constructing Box Charts

The following notation is used in this section:

 process mean (expected value of the population of measurements) process standard deviation (standard deviation of the population of measurements) mean of measurements in i th subgroup ni sample size of i th subgroup N the number of subgroups xij j th measurement in the i th subgroup, j = 1,2,3 ... , ni xi(j) j th largest measurement in the i th subgroup: weighted average of subgroup means Mi median of the measurements in the i th subgroup: average of the subgroup medians: median of the subgroup medians. Denote the j th largest median by M(j) so that . eM(n) standard error of the median of n independent, normally distributed variables with unit standard deviation (the value of eM(n) can be calculated with the STDMED function in a DATA step) Qp(n) 100p th percentile (0

Elements of Box-and-Whisker Plots

A box-and-whisker plot is displayed for the measurements in each subgroup on the box chart. Figure 32.12 illustrates the elements of each plot.

Figure 32.12: Box-and-Whisker Plot

The skeletal style of the box-and-whisker plot shown in Figure 32.12 is the default. You can specify alternative styles with the BOXSTYLE= option; see Example 32.2 or the entry for the BOXSTYLE= option.

Control Limits and Central Line

You can compute the limits in the following ways:

• as a specified multiple (k) of the standard error of (or Mi) above and below the central line. The default limits are computed with k=3 (these are referred to as limits).
• as probability limits defined in terms of , a specified probability that (or Mi) exceeds the limits

The CONTROLSTAT= option specifies whether control limits are computed for subgroup means (the default) or subgroup medians. The following tables provide the formulas for the limits:

Table 32.23: Control Limits and Central Line for Box Charts
 CONTROLSTAT=MEAN CONTROLSTAT=MEDIAN LCLX = lower limit LCLM = lower limit Central Line Central Line UCLX = upper limit UCLM = upper limit

Table 32.24: Probability Limits and Central Line for Box Charts
 CONTROLSTAT=MEAN CONTROLSTAT=MEDIAN LCLX = lower limit LCLM = lower limit Central Line Central Line UCLX = upper limit UCLM = upper limit

In the preceding tables, replace with if you specify MEDCENTRAL=AVGMEAN in addition to CONTROLSTAT=MEDIAN. Likewise, replace with if you specify MEDCENTRAL=MEDMED in addition to CONTROLSTAT=MEDIAN. If standard values and are available for and , replace with and with in Table 32.23 and Table 32.24.

Note that the limits vary with ni. The formulas for median limits assume that the data are normally distributed.

You can specify parameters for the limits as follows:

• Specify k with the SIGMAS= option or with the variable _SIGMAS_ in a LIMITS= data set.
• Specify with the ALPHA= option or with the variable _ALPHA_ in a LIMITS= data set.
• Specify a constant nominal sample size for the control limits with the LIMITN= option or with the variable _LIMITN_ in a LIMITS= data set.
• Specify with the MU0= option or with the variable _MEAN_ in a LIMITS= data set.
• Specify with the SIGMA0= option or with the variable _STDDEV_ in a LIMITS= data set.

Note: You can suppress the display of the control limits with the NOLIMITS option. This is useful for creating standard side-by-side box-and-whisker plots (in this case, the STDDEVIATIONS option is also recommended).

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