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 Basic Summary PlotsAnalyzing 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
Example 4.11 Computing Robust Estimates
This example illustrates how you can use the UNIVARIATE procedure to compute robust estimates of location and scale. The following
statements compute these estimates for the variable Systolic in the data set BPressure, which was introduced in Example 4.1:
title 'Robust Estimates for Blood Pressure Data';
ods select TrimmedMeans WinsorizedMeans RobustScale;
proc univariate data=BPressure trimmed=1 .1
winsorized=.1 robustscale;
var Systolic;
run;
The ODS SELECT statement restricts the output to the "TrimmedMeans," "WinsorizedMeans," and "RobustScale" tables; see the
section ODS Table Names. The TRIMMED= option computes two trimmed means, the first after removing one observation and the second after removing 10%
of the observations. If the value of TRIMMED= is greater than or equal to one, it is interpreted as the number of observations
to be trimmed. The WINSORIZED= option computes a Winsorized mean that replaces three observations from the tails with the
next closest observations. (Three observations are replaced because , and three is the smallest integer greater than 2.2.) The trimmed and Winsorized means for Systolic are displayed in Output 4.11.1.
Output 4.11.1: Computation of Trimmed and Winsorized Means
| Robust Estimates for Blood Pressure Data |
| Trimmed Means | ||||||||
|---|---|---|---|---|---|---|---|---|
| Percent Trimmed in Tail |
Number Trimmed in Tail |
Trimmed Mean |
Std Error Trimmed Mean |
95% Confidence Limits | DF | t for H0: Mu0=0.00 |
Pr > |t| | |
| 4.55 | 1 | 120.3500 | 2.573536 | 114.9635 | 125.7365 | 19 | 46.76446 | <.0001 |
| 13.64 | 3 | 120.3125 | 2.395387 | 115.2069 | 125.4181 | 15 | 50.22675 | <.0001 |
Output 4.11.1 shows the trimmed mean for Systolic is 120.35 after one observation has been trimmed, and 120.31 after 3 observations are trimmed. The Winsorized mean for Systolic is 120.64. For details on trimmed and Winsorized means, see the section Robust Estimators. The trimmed means can be compared with the means shown in Output 4.1.1 (from Example 4.1), which displays the mean for Systolic as 121.273.
The ROBUSTSCALE option requests a table, displayed in Output 4.11.2, which includes the interquartile range, Gini’s mean difference, the median absolute deviation about the median, , and .
Output 4.11.2 shows the robust estimates of scale for Systolic. For instance, the interquartile range is 13. The estimates of range from 9.54 to 13.32. See the section Robust Estimators.
A sample program for this example, uniex01.sas, is available in the SAS Sample Library for Base SAS software.
Output 4.11.2: Computation of Robust Estimates of Scale