The UNIVARIATE Procedure
- Overview
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Getting Started
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Syntax
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Details
Missing Values Rounding Descriptive Statistics Calculating the Mode Calculating Percentiles Tests for Location Confidence Limits for Parameters of the Normal Distribution Robust Estimators Creating Line Printer Plots Creating High-Resolution Graphics Using the CLASS Statement to Create Comparative Plots Positioning Insets Formulas for Fitted Continuous Distributions Goodness-of-Fit Tests Kernel Density Estimates Construction of Quantile-Quantile and Probability Plots Interpretation of Quantile-Quantile and Probability Plots Distributions for Probability and Q-Q Plots Estimating Shape Parameters Using Q-Q Plots Estimating Location and Scale Parameters Using Q-Q Plots Estimating Percentiles Using Q-Q Plots Input Data Sets OUT= Output Data Set in the OUTPUT Statement OUTHISTOGRAM= Output Data Set OUTKERNEL= Output Data Set OUTTABLE= Output Data Set Tables for Summary Statistics ODS Table Names ODS Tables for Fitted Distributions ODS Graphics Computational Resources
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Examples
Computing Descriptive Statistics for Multiple Variables Calculating Modes Identifying Extreme Observations and Extreme Values Creating a Frequency Table Creating Plots for Line Printer Output Analyzing a Data Set With a FREQ Variable Saving Summary Statistics in an OUT= Output Data Set Saving Percentiles in an Output Data Set Computing Confidence Limits for the Mean, Standard Deviation, and Variance Computing Confidence Limits for Quantiles and Percentiles Computing Robust Estimates Testing for Location Performing a Sign Test Using Paired Data Creating a Histogram Creating a One-Way Comparative Histogram Creating a Two-Way Comparative Histogram Adding Insets with Descriptive Statistics Binning a Histogram Adding a Normal Curve to a Histogram Adding Fitted Normal Curves to a Comparative Histogram Fitting a Beta Curve Fitting Lognormal, Weibull, and Gamma Curves Computing Kernel Density Estimates Fitting a Three-Parameter Lognormal Curve Annotating a Folded Normal Curve Creating Lognormal Probability Plots Creating a Histogram to Display Lognormal Fit Creating a Normal Quantile Plot Adding a Distribution Reference Line Interpreting a Normal Quantile Plot Estimating Three Parameters from Lognormal Quantile Plots Estimating Percentiles from Lognormal Quantile Plots Estimating Parameters from Lognormal Quantile Plots Comparing Weibull Quantile Plots Creating a Cumulative Distribution Plot Creating a P-P Plot
- References
| Modeling a Data Distribution |
In addition to summarizing a data distribution as in the preceding example, you can use PROC UNIVARIATE to statistically model a distribution based on a random sample of data. The following statements create a data set named Aircraft that contains the measurements of a position deviation for a sample of 30 aircraft components.
data Aircraft; input Deviation @@; label Deviation = 'Position Deviation'; datalines; -.00653 0.00141 -.00702 -.00734 -.00649 -.00601 -.00631 -.00148 -.00731 -.00764 -.00275 -.00497 -.00741 -.00673 -.00573 -.00629 -.00671 -.00246 -.00222 -.00807 -.00621 -.00785 -.00544 -.00511 -.00138 -.00609 0.00038 -.00758 -.00731 -.00455 ;
An initial question in the analysis is whether the measurement distribution is normal. The following statements request a table of moments, the tests for normality, and a normal probability plot, which are shown in Figure 4.5 and Figure 4.6:
title 'Position Deviation Analysis';
ods graphics on;
ods select Moments TestsForNormality ProbPlot;
proc univariate data=Aircraft normaltest;
var Deviation;
probplot Deviation / normal (mu=est sigma=est)
square;
label Deviation = 'Position Deviation';
inset mean std / format=6.4;
run;
When ODS Graphics is enabled, the procedure produces ODS Graphics output rather than traditional graphics. (See the section Alternatives for Producing Graphics for information about traditional graphics and ODS Graphics.) The INSET statement displays the sample mean and standard deviation on the probability plot.
| Position Deviation Analysis |
| Moments | |||
|---|---|---|---|
| N | 30 | Sum Weights | 30 |
| Mean | -0.0053067 | Sum Observations | -0.1592 |
| Std Deviation | 0.00254362 | Variance | 6.47002E-6 |
| Skewness | 1.2562507 | Kurtosis | 0.69790426 |
| Uncorrected SS | 0.00103245 | Corrected SS | 0.00018763 |
| Coeff Variation | -47.932613 | Std Error Mean | 0.0004644 |
| Tests for Normality | ||||
|---|---|---|---|---|
| Test | Statistic | p Value | ||
| Shapiro-Wilk | W | 0.845364 | Pr < W | 0.0005 |
| Kolmogorov-Smirnov | D | 0.208921 | Pr > D | <0.0100 |
| Cramer-von Mises | W-Sq | 0.329274 | Pr > W-Sq | <0.0050 |
| Anderson-Darling | A-Sq | 1.784881 | Pr > A-Sq | <0.0050 |
All four goodness-of-fit tests in Figure 4.5 reject the hypothesis that the measurements are normally distributed.
Figure 4.6 shows a normal probability plot for the measurements. A linear pattern of points following the diagonal reference line would indicate that the measurements are normally distributed. Instead, the curved point pattern suggests that a skewed distribution, such as the lognormal, is more appropriate than the normal distribution.
A lognormal distribution for Deviation is fitted in Example 4.26.
A sample program for this example, univar2.sas, is available in the SAS Sample Library for Base SAS software.
