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
| Confidence Limits for Parameters of the Normal Distribution |
The two-sided 
confidence interval for the mean has upper and lower limits
 |
where 
and 
is the 
percentile of the 
distribution with 
degrees of freedom. The one-sided upper confidence limit is computed as 
and the one-sided lower confidence limit is computed as 
. See Example 4.9.
The two-sided confidence interval for the standard deviation has lower and upper limits,
 |
respectively, where 
and 
are the and 
percentiles of the chi-square distribution with degrees of freedom. A one-sided confidence limit has lower and upper limits,
 |
respectively. The confidence interval for the variance has upper and lower limits equal to the squares of the corresponding upper and lower limits for the standard deviation. When you use the WEIGHT statement and specify VARDEF=DF in the PROC statement, the confidence interval for the weighted mean is
 |
where 
is the weighted mean, 
is the weighted standard deviation, 
is the weight for 
th observation, and 
is the percentile for the distribution with degrees of freedom.