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
This example is a continuation of Example 4.14. The following statements fit a normal distribution to the thickness measurements in the Trans data set and superimpose the fitted density curve on the histogram:
title 'Analysis of Plating Thickness';
ods graphics off;
ods select ParameterEstimates GoodnessOfFit FitQuantiles Bins MyPlot;
proc univariate data=Trans;
histogram Thick / normal(percents=20 40 60 80 midpercents)
name='MyPlot';
inset n normal(ksdpval) / pos = ne format = 6.3;
run;
The ODS SELECT statement restricts the output to the “ParameterEstimates,” “GoodnessOfFit,” “FitQuantiles,” and “Bins” tables; see the section ODS Table Names. The NORMAL option specifies that the normal curve be displayed on the histogram shown in Output 4.19.2. It also requests a summary of the fitted distribution, which is shown in Output 4.19.1. goodness-of-fit tests, parameter estimates, and quantiles of the fitted distribution. (If you specify the NORMALTEST option in the PROC UNIVARIATE statement, the Shapiro-Wilk test for normality is included in the tables of statistical output.)
Two secondary options are specified in parentheses after the NORMAL primary option. The PERCENTS= option specifies quantiles, which are to be displayed in the “FitQuantiles” table. The MIDPERCENTS option requests a table that lists the midpoints, the observed percentage of observations, and the estimated percentage of the population in each interval (estimated from the fitted normal distribution). See Table 4.6 for the secondary options that can be specified with after the NORMAL primary option.
Output 4.19.1: Summary of Fitted Normal Distribution
| Analysis of Plating Thickness |
| Parameters for Normal Distribution | ||
|---|---|---|
| Parameter | Symbol | Estimate |
| Mean | Mu | 3.49533 |
| Std Dev | Sigma | 0.032117 |
| Goodness-of-Fit Tests for Normal Distribution | ||||
|---|---|---|---|---|
| Test | Statistic | p Value | ||
| Kolmogorov-Smirnov | D | 0.05563823 | Pr > D | >0.150 |
| Cramer-von Mises | W-Sq | 0.04307548 | Pr > W-Sq | >0.250 |
| Anderson-Darling | A-Sq | 0.27840748 | Pr > A-Sq | >0.250 |
| Histogram Bin Percents for Normal Distribution |
||
|---|---|---|
| Bin Midpoint |
Percent | |
| Observed | Estimated | |
| 3.43 | 3.000 | 3.296 |
| 3.45 | 9.000 | 9.319 |
| 3.47 | 23.000 | 18.091 |
| 3.49 | 19.000 | 24.124 |
| 3.51 | 24.000 | 22.099 |
| 3.53 | 15.000 | 13.907 |
| 3.55 | 3.000 | 6.011 |
| 3.57 | 4.000 | 1.784 |
| Quantiles for Normal Distribution | ||
|---|---|---|
| Percent | Quantile | |
| Observed | Estimated | |
| 20.0 | 3.46700 | 3.46830 |
| 40.0 | 3.48350 | 3.48719 |
| 60.0 | 3.50450 | 3.50347 |
| 80.0 | 3.52250 | 3.52236 |
The histogram of the variable Thick with a superimposed normal curve is shown in Output 4.19.2.
The estimated parameters for the normal curve (
and 
) are shown in Output 4.19.1. By default, the parameters are estimated unless you specify values with the MU= and SIGMA= secondary options after the NORMAL
primary option. The results of three goodness-of-fit tests based on the empirical distribution function (EDF) are displayed
in Output 4.19.1. Because the 
-values are all greater than 0.15, the hypothesis of normality is not rejected.
A sample program for this example, uniex08.sas, is available in the SAS Sample Library for Base SAS software.