The UNIVARIATE Procedure
Example 3.19 Adding a Normal Curve to a Histogram
This example is a continuation of Example 3.14. 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 select Histogram ParameterEstimates GoodnessOfFit FitQuantiles Bins;
proc univariate data=Trans;
histogram Thick / normal(percents=20 40 60 80 midpercents)
odstitle = title;
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 3.19.2. It also requests a summary of the fitted distribution, which is shown in Output 3.19.1. 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 6 for the secondary options that can be specified with after the NORMAL primary option.
Output 3.19.1: 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 |
Output 3.19.2: Histogram Superimposed with Normal Curve
The histogram of the variable Thick with a superimposed normal curve is shown in Output 3.19.2.
The estimated parameters for the normal curve (
and 
) are shown in Output 3.19.1. 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 3.19.1. Because the p-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.