The UNIVARIATE Procedure
- Overview
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Getting Started
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Syntax
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DetailsMissing ValuesRoundingDescriptive StatisticsCalculating the ModeCalculating PercentilesTests for LocationConfidence Limits for Parameters of the Normal DistributionRobust EstimatorsCreating Line Printer PlotsCreating High-Resolution GraphicsUsing the CLASS Statement to Create Comparative PlotsPositioning InsetsFormulas for Fitted Continuous DistributionsGoodness-of-Fit TestsKernel Density EstimatesConstruction of Quantile-Quantile and Probability PlotsInterpretation of Quantile-Quantile and Probability PlotsDistributions for Probability and Q-Q PlotsEstimating Shape Parameters Using Q-Q PlotsEstimating Location and Scale Parameters Using Q-Q PlotsEstimating Percentiles Using Q-Q PlotsInput Data SetsOUT= Output Data Set in the OUTPUT StatementOUTHISTOGRAM= Output Data SetOUTKERNEL= Output Data SetOUTTABLE= Output Data SetTables for Summary StatisticsODS Table NamesODS Tables for Fitted DistributionsODS GraphicsComputational Resources
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ExamplesComputing Descriptive Statistics for Multiple VariablesCalculating ModesIdentifying Extreme Observations and Extreme ValuesCreating a Frequency TableCreating Plots for Line Printer OutputAnalyzing a Data Set With a FREQ VariableSaving Summary Statistics in an OUT= Output Data SetSaving Percentiles in an Output Data SetComputing Confidence Limits for the Mean, Standard Deviation, and VarianceComputing Confidence Limits for Quantiles and PercentilesComputing Robust EstimatesTesting for LocationPerforming a Sign Test Using Paired DataCreating a HistogramCreating a One-Way Comparative HistogramCreating a Two-Way Comparative HistogramAdding Insets with Descriptive StatisticsBinning a HistogramAdding a Normal Curve to a HistogramAdding Fitted Normal Curves to a Comparative HistogramFitting a Beta CurveFitting Lognormal, Weibull, and Gamma CurvesComputing Kernel Density EstimatesFitting a Three-Parameter Lognormal CurveAnnotating a Folded Normal CurveCreating Lognormal Probability PlotsCreating a Histogram to Display Lognormal FitCreating a Normal Quantile PlotAdding a Distribution Reference LineInterpreting a Normal Quantile PlotEstimating Three Parameters from Lognormal Quantile PlotsEstimating Percentiles from Lognormal Quantile PlotsEstimating Parameters from Lognormal Quantile PlotsComparing Weibull Quantile PlotsCreating a Cumulative Distribution PlotCreating a P-P Plot
- References
WEIGHT variable ;
The WEIGHT statement specifies numeric weights for analysis variables in the statistical calculations. The UNIVARIATE procedure
uses the values 
of the WEIGHT variable to modify the computation of a number of summary statistics by assuming that the variance of the 
th value 
of the analysis variable is equal to 
, where 
is an unknown parameter. The values of the WEIGHT variable do not have to be integers and are typically positive. By default,
observations with nonpositive or missing values of the WEIGHT variable are handled as follows:[1]
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If the value is zero, the observation is counted in the total number of observations.
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If the value is negative, it is converted to zero, and the observation is counted in the total number of observations.
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If the value is missing, the observation is excluded from the analysis.
To exclude observations that contain negative and zero weights from the analysis, use EXCLNPWGT. Note that most SAS/STAT procedures,
such as PROC GLM, exclude negative and zero weights by default. The weight variable does not change how the procedure determines
the range, mode, extreme values, extreme observations, or number of missing values. When you specify a WEIGHT statement, the
procedure also computes a weighted standard error and a weighted version of Student’s 
test. The Student’s test is the only test of location that PROC UNIVARIATE computes when you weight the analysis variables.
When you specify a WEIGHT variable, the procedure uses its values, , to compute weighted versions of the statistics[2] provided in the Moments table. For example, the procedure computes a weighted mean 
and a weighted variance 
as
![\[ \overline{x}_{w} = \frac{ \sum _{i} w_{i}x_{i} }{ \sum _{i} w_{i} } \]](images/procstat_univariate0150.png){kind=small}
and
![\[ s_{w}^{2} = \frac{ 1 }{ d } \sum _{i} w_{i} ( x_{i} - \overline{x}_{w} )^{2} \]](images/procstat_univariate0151.png){kind=small}
where is the th variable value. The divisor 
is controlled by the VARDEF= option in the PROC UNIVARIATE statement.
The WEIGHT statement does not affect the determination of the mode, extreme values, extreme observations, or the number of
missing values of the analysis variables. However, the weights are used to compute weighted percentiles.[3] The WEIGHT variable has no effect on graphical displays produced with the plot statements.
The CIPCTLDF, CIPCTLNORMAL, LOCCOUNT, NORMAL, ROBUSTSCALE, TRIMMED=, and WINSORIZED= options are not available with the WEIGHT statement.
To compute weighted skewness or kurtosis, use VARDEF=DF or VARDEF=N in the PROC statement.
You cannot specify the HISTOGRAM, PROBPLOT, or QQPLOT statements with the WEIGHT statement.
When you use the WEIGHT statement, consider which value of the VARDEF= option is appropriate. See VARDEF= and the calculation of weighted statistics for more information.
[1] In SAS 6.12 and earlier releases, observations were used in the analysis if and only if the WEIGHT variable value was greater than zero.
[2] In SAS 6.12 and earlier releases, weighted skewness and kurtosis were not computed.
[3] In SAS 6.12 and earlier releases, the weights did not affect the computation of percentiles and the procedure did not exclude the observations with missing weights from the count of observations.