Table 5.32: Summary Statistics
Keyword |
Description |
---|---|
CSS |
Corrected sum of squares |
CV |
Coefficient of variation |
GEOMEAN |
Geometric mean |
KURTOSIS | KURT |
Kurtosis |
MAX |
Largest value |
MEAN |
Sample mean |
MIN |
Smallest value |
MODE |
Most frequent value |
N |
Sample size |
NEXCL |
Number of observations excluded by MAXNBIN= or MAXSIGMAS= option |
NMISS |
Number of missing values |
NOBS |
Number of observations |
RANGE |
Range |
SKEWNESS | SKEW |
Skewness |
STD | STDDEV |
Standard deviation |
STDMEAN | STDERR |
Standard error of the mean |
SUM |
Sum of the observations |
SUMWGT |
Sum of the weights |
USS |
Uncorrected sum of squares |
VAR |
Variance |
Table 5.33: Percentile Statistics
Keyword |
Description |
---|---|
P1 |
1st percentile |
P5 |
5th percentile |
P10 |
10th percentile |
Q1 | P25 |
Lower quartile (25th percentile) |
MEDIAN | Q2 | P50 |
Median (50th percentile) |
Q3 | P75 |
Upper quartile (75th percentile) |
P90 |
90th percentile |
P95 |
95th percentile |
P99 |
99th percentile |
QRANGE |
Interquartile range (Q3 - Q1) |
Table 5.34 lists keywords for distribution-free confidence limits for percentiles requested with the CIPCTLDF option.
Table 5.34: Keywords for Distribution-Free Confidence Limits for Percentiles
Keyword |
Description |
---|---|
P1_LCL_DF |
1st percentile lower confidence limit |
P1_UCL_DF |
1st percentile upper confidence limit |
P5_LCL_DF |
5th percentile lower confidence limit |
P5_UCL_DF |
5th percentile upper confidence limit |
P10_LCL_DF |
10th percentile lower confidence limit |
P10_UCL_DF |
10th percentile upper confidence limit |
Q1_LCL_DF | P25_LCL_DF |
Lower quartile (25th percentile) lower confidence limit |
Q1_UCL_DF | P25_UCL_DF |
Lower quartile (25th percentile) upper confidence limit |
MEDIAN_LCL_DF | Q2_LCL_DF | P50_LCL_DF |
Median (50th percentile) lower confidence limit |
MEDIAN_UCL_DF | Q2_UCL_DF | P50_UCL_DF |
Median (50th percentile) upper confidence limit |
Q3_LCL_DF | P75_LCL_DF |
Upper quartile (75th percentile) lower confidence limit |
Q3_UCL_DF | P75_UCL_DF |
Upper quartile (75th percentile) upper confidence limit |
P90_LCL_DF |
90th percentile lower confidence limit |
P90_UCL_DF |
90th percentile upper confidence limit |
P95_LCL_DF |
95th percentile lower confidence limit |
P95_UCL_DF |
95th percentile upper confidence limit |
P99_LCL_DF |
99th percentile lower confidence limit |
P99_UCL_DF |
99th percentile upper confidence limit |
Table 5.35 lists keywords for percentile confidence limits computed assuming normality requested with the CIPCTLNORMAL option.
Table 5.35: Keywords Percentile Confidence Limits Assuming Normality
Keyword |
Description |
---|---|
P1_LCL |
1st percentile lower confidence limit |
P1_UCL |
1st percentile upper confidence limit |
P5_LCL |
5th percentile lower confidence limit |
P5_UCL |
5th percentile upper confidence limit |
P10_LCL |
10th percentile lower confidence limit |
P10_UCL |
10th percentile upper confidence limit |
Q1_LCL | P25_LCL |
Lower quartile (25th percentile) lower confidence limit |
Q1_UCL | P25_UCL |
Lower quartile (25th percentile) upper confidence limit |
MEDIAN_LCL | Q2_LCL | P50_LCL |
Median (50th percentile) lower confidence limit |
MEDIAN_UCL | Q2_UCL | P50_UCL |
Median (50th percentile) upper confidence limit |
Q3_LCL | P75_LCL |
Upper quartile (75th percentile) lower confidence limit |
Q3_UCL | P75_UCL |
Upper quartile (75th percentile) upper confidence limit |
P90_LCL |
90th percentile lower confidence limit |
P90_UCL |
90th percentile upper confidence limit |
P95_LCL |
95th percentile lower confidence limit |
P95_UCL |
95th percentile upper confidence limit |
P99_LCL |
99th percentile lower confidence limit |
P99_UCL |
99th percentile upper confidence limit |
Table 5.36: Robust Statistics
Keyword |
Description |
---|---|
GINI |
Gini’s mean difference |
MAD |
Median absolute difference about the median |
QN |
, alternative to MAD |
SN |
, alternative to MAD |
STD_GINI |
Gini’s standard deviation |
STD_MAD |
MAD standard deviation |
STD_QN |
standard deviation |
STD_QRANGE |
Interquartile range standard deviation |
STD_SN |
standard deviation |
Table 5.37: Hypothesis Testing
Keyword |
Description |
---|---|
MSIGN |
Sign statistic |
NORMALTEST |
Test statistic for normality |
PNORMAL |
Probability value for the test of normality |
SIGNRANK |
Signed rank statistic |
PROBM |
Probability of greater absolute value for the sign statistic |
PROBN |
Probability value for the test of normality |
PROBS |
Probability value for the signed rank test |
PROBT |
Probability value for the Student’s t test |
T |
Statistics for Student’s t test |
Table 5.39: Capability Indices and Confidence Limits
Keyword |
Description |
---|---|
CP |
Capability index |
CPLCL |
Lower confidence limit for |
CPUCL |
Upper confidence limit for |
CPK |
Capability index |
CPKLCL |
Lower confidence limit for |
CPKUCL |
Upper confidence limit for |
CPL |
Capability index CPL |
CPM |
Capability index |
CPMLCL |
Lower confidence limit for |
CPMUCL |
Upper confidence interval for |
CPU |
Capability index CPU |
K |
Capability index K |
Table 5.40: Specification Limits and Related Information
Keyword |
Description |
---|---|
LSL |
Lower specification limit |
USL |
Upper specification limit |
TARGET |
Target value |
PCTGTR |
Percent of nonmissing observations that exceed the upper specification limit |
PCTLSS |
Percent of nonmissing observations that are less than the lower specification limit |
PCTBET |
Percent of nonmissing observations between the upper and lower specification limits (inclusive) |
You can request parametric density estimates with all plot statements in the CAPABILITY procedure (CDFPLOT, COMPHISTOGRAM,
HISTOGRAM, PPPLOT, PROBPLOT, and QQPLOT). You can display parameters and statistics associated with these estimates in an
inset by specifying a distribution keyword followed by secondary keywords in parentheses. For example, the following statements
create a histogram for Strength
with a fitted exponential density curve:
proc capability data=Wire; histogram Strength / exp; inset exp(sigma theta); run;
The secondary keywords SIGMA and THETA for the EXP distribution keyword request an inset displaying the values of the exponential scale parameter and threshold parameter . You must request the distribution option in the plot statement to display the corresponding distribution statistics in an inset. Specifying a distribution keyword with no secondary keywords produces an inset displaying the full set of parameters for that distribution. See Output 5.15.1 for an example of an inset with statistics from a fitted normal curve.
The following table describes the available distribution keywords. Note that some keywords are not available with all plot statements.
Table 5.41: Density Estimation Primary Keywords
Keyword |
Distribution |
Plot Statement Availability |
---|---|---|
BETA |
beta |
all but COMPHISTOGRAM |
EXPONENTIAL |
exponential |
all but COMPHISTOGRAM |
GAMMA |
gamma |
all but COMPHISTOGRAM |
GUMBEL |
Gumbel |
all but COMPHISTOGRAM |
IGAUSS |
inverse Gaussian |
CDFPLOT, HISTOGRAM, PPPLOT |
LOGNORMAL |
lognormal |
all but COMPHISTOGRAM |
NORMAL |
normal |
all |
PARETO |
generalized Pareto |
all but COMPHISTOGRAM |
POWER |
power function |
all but COMPHISTOGRAM |
RAYLEIGH |
Rayleigh |
all but COMPHISTOGRAM |
SB |
Johnson |
HISTOGRAM |
SU |
Johnson |
HISTOGRAM |
WEIBULL |
Weibull |
all but COMPHISTOGRAM |
WEIBULL2 |
2-parameter Weibull |
PROBPLOT, QQPLOT |
Table 5.42 lists the secondary keywords available with each distribution keyword listed in Table 5.41. In many cases, aliases can be used (for example, ALPHA in place of SHAPE1).
Table 5.42: Density Estimation Secondary Keywords
Secondary |
||
---|---|---|
Keyword |
Alias |
Description |
Secondary Keywords Available with the BETA Keyword |
||
ALPHA |
SHAPE1 |
First shape parameter |
BETA |
SHAPE2 |
Second shape parameter |
SIGMA |
SCALE |
Scale parameter |
THETA |
THRESHOLD |
Lower threshold parameter |
MEAN |
Mean of the fitted distribution |
|
STD |
Standard deviation of the fitted distribution |
|
Secondary Keywords Available with the EXPONENTIAL Keyword |
||
SIGMA |
SCALE |
Scale parameter |
THETA |
THRESHOLD |
Threshold parameter |
MEAN |
Mean of the fitted distribution |
|
STD |
Standard deviation of the fitted distribution |
|
Secondary Keywords Available with the GAMMA Keyword |
||
ALPHA |
SHAPE |
Shape parameter |
SIGMA |
SCALE |
Scale parameter |
THETA |
THRESHOLD |
Threshold parameter |
MEAN |
Mean of the fitted distribution |
|
STD |
Standard deviation of the fitted distribution |
|
Secondary Keywords Available with the GUMBEL Keyword |
||
MU |
Location parameter |
|
SIGMA |
SCALE |
Scale parameter |
MEAN |
Mean of the fitted distribution |
|
STD |
Standard deviation of the fitted distribution |
|
Secondary Keywords Available with the IGAUSS Keyword |
||
MU |
Mean parameter |
|
LAMBDA |
Shape parameter |
|
MEAN |
Mean of the fitted distribution |
|
STD |
Standard deviation of the fitted distribution |
|
Secondary Keywords Available with the LOGNORMAL Keyword |
||
SIGMA |
SHAPE |
Shape parameter |
THETA |
THRESHOLD |
Threshold parameter |
ZETA |
SCALE |
Scale parameter |
MEAN |
Mean of the fitted distribution |
|
STD |
Standard deviation of the fitted distribution |
|
Secondary Keywords Available with the NORMAL Keyword |
||
MU |
MEAN |
Mean parameter |
SIGMA |
STD |
Scale parameter |
Secondary Keywords Available with the PARETO Keyword |
||
ALPHA |
Shape parameter |
|
SIGMA |
SCALE |
Scale parameter |
THETA |
THRESHOLD |
Threshold parameter |
MEAN |
Mean of the fitted distribution |
|
STD |
Standard deviation of the fitted distribution |
|
Secondary Keywords Available with the POWER Keyword |
||
ALPHA |
Shape parameter |
|
SIGMA |
SCALE |
Scale parameter |
THETA |
THRESHOLD |
Threshold parameter |
MEAN |
Mean of the fitted distribution |
|
STD |
Standard deviation of the fitted distribution |
|
Secondary Keywords Available with the RAYLEIGH Keyword |
||
SIGMA |
SCALE |
Scale parameter |
THETA |
THRESHOLD |
Threshold parameter |
MEAN |
Mean of the fitted distribution |
|
STD |
Standard deviation of the fitted distribution |
|
Secondary Keywords Available with the SB Keyword |
||
DELTA |
SHAPE1 |
Shape parameter |
GAMMA |
SHAPE2 |
Shape parameter |
SIGMA |
SCALE |
Scale parameter |
THETA |
THRESHOLD |
Threshold parameter |
MEAN |
Mean of the fitted distribution |
|
STD |
Standard deviation of the fitted distribution |
|
Secondary Keywords Available with the SU Keyword |
||
DELTA |
SHAPE1 |
Shape parameter |
GAMMA |
SHAPE2 |
Shape parameter |
SIGMA |
SCALE |
Scale parameter |
THETA |
Location parameter |
|
MEAN |
Mean of the fitted distribution |
|
STD |
Standard deviation of the fitted distribution |
|
Secondary Keywords Available with the WEIBULL Keyword |
||
C |
SHAPE |
Shape parameter c |
SIGMA |
SCALE |
Scale parameter |
THETA |
THRESHOLD |
Threshold parameter |
MEAN |
Mean of the fitted distribution |
|
STD |
Standard deviation of the fitted distribution |
|
Secondary Keywords Available with the WEIBULL2 Keyword |
||
C |
SHAPE |
Shape parameter c |
SIGMA |
SCALE |
Scale parameter |
THETA |
THRESHOLD |
Known lower threshold |
MEAN |
Mean of the fitted distribution |
|
STD |
Standard deviation of the fitted distribution |
The secondary keywords listed in Table 5.43 can be used with any distribution keyword but only with the HISTOGRAM and COMPHISTOGRAM plot statements.
Table 5.43: Statistics Computed from Any Parametric Density Estimate
Secondary |
|
---|---|
Keyword |
Description |
CP |
Capability index |
CPK |
Capability index |
CPL |
Capability index CPL |
CPM |
Capability index |
CPU |
Capability index CPU |
ESTPCTLSS |
Estimated percentage less than the lower specification limit |
ESTPCTGTR |
Estimated percentage greater than the upper specification limit |
K |
Capability index K |
The secondary keywords listed in Table 5.44 can be used with any distribution keyword but only with the HISTOGRAM plot statement (see Example 5.15).
Table 5.44: Goodness-of-Fit Statistics for Fitted Curves
Secondary |
|
---|---|
Keyword |
Description |
CHISQ |
Chi-square statistic |
DF |
Degrees of freedom for the chi-square test |
PCHISQ |
Probability value for the chi-square test |
AD |
Anderson-Darling EDF test statistic |
ADPVAL |
Anderson-Darling EDF test p-value |
CVM |
Cramér-von Mises EDF test statistic |
CVMPVAL |
Cramér-von Mises EDF test p-value |
KSD |
Kolmogorov-Smirnov EDF test statistic |
KSDPVAL |
Kolmogorov-Smirnov EDF test p-value |
Table 5.45 lists primary keywords available only with the HISTOGRAM and COMPHISTOGRAM plot statements. These keywords display fill areas on a histogram. If you fit a parametric density on a histogram and request that the area under the curve be filled, these keywords display the percentage of the distribution area that lies below the lower specification limit, between the specification limits, or above the upper specification limit. If you do not fill the area beneath a parametric density estimate, these keywords display the observed proportion of observations (that is, the area in the bars of the histogram).
You should use these options with the FILL, CFILL=, and PFILL= options in the HISTOGRAM and COMPHISTOGRAM statements and with the CLEFT=, CRIGHT=, PLEFT=, and PRIGHT= options in the SPEC statements. See Output 5.16.1 for an example.
Table 5.45: Curve Area Keywords
Keyword |
Alias |
Description |
---|---|---|
BETWEENPCT |
BETPCT |
Area between the specification limits |
LSLPCT |
Area below the lower specification limit |
|
USLPCT |
Area above the upper specification limit |
You can request nonparametric kernel density estimates with the HISTOGRAM and COMPHISTOGRAM plot statements. You can display
statistics associated with these estimates by specifying a kernel density keyword followed by secondary keywords in parentheses.
For example, the following statements create a histogram for Strength
with a fitted kernel density estimate:
proc capability data=Wire; histogram Strength / kernel; inset kernel(c amise); run;
The secondary keywords C and AMISE for the KERNEL keyword display the values of the standardized bandwidth c and the approximate mean integrated square error.
Note that you can specify more than one kernel density estimate on a single histogram. If you specify multiple kernel density estimates, you can request inset statistics for all of the estimates with the KERNEL keyword, or you can display inset statistics for up to five individual curves with KERNELn keywords, as in the following example:
proc capability data=Wire; histogram Strength / kernel(c = 1 2 3); inset kernel2(c) kernel3(c); run;
Three kernel density estimates are displayed on the histogram, but the inset displays the value of c only for the second and third estimates.
Table 5.46 lists the kernel density keywords. Table 5.47 lists the available secondary keywords.
Table 5.46: Kernel Density Estimate Primary Keywords
Keyword |
Description |
---|---|
KERNEL |
displays statistics for all kernel estimates |
KERNELn |
displays statistics for only the nth kernel density estimate |
|
Table 5.47: Secondary Keywords Available with the KERNEL Keyword
Secondary Keyword |
Description |
---|---|
TYPE |
kernel type: normal, quadratic, or triangular |
BANDWIDTH |
bandwidth for the density estimate |
BWIDTH |
alias for BANDWIDTH |
C |
standardized bandwidth c for the density estimate: |
where n = sample size, bandwidth, and |
|
Q = interquartile range |
|
AMISE |
approximate mean integrated square error (MISE) for the |
kernel density |