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The MEANS Procedure |
Computation of Moment Statistics |
PROC MEANS uses single-pass algorithms to compute the moment statistics (such as mean, variance, skewness, and kurtosis). See Keywords and Formulas for the statistical formulas.
The computational details for confidence limits, hypothesis test statistics, and quantile statistics follow.
Confidence Limits |
With the keywords CLM, LCLM, and UCLM, you can compute confidence limits for the mean. A confidence limit is a range, constructed around the value of a sample statistic, that contains the corresponding true population value with given probability (ALPHA=) in repeated sampling.
A two-sided
% confidence interval for the mean has upper and lower limits
A one-sided
% confidence interval is computed as
A two-sided
% confidence interval for the standard deviation has lower
and upper limits
A
% confidence interval for the variance has upper and lower
limits that are equal to the squares of the corresponding upper and lower
limits for the standard deviation.
If you use the WEIGHT statement or WEIGHT= in a VAR
statement and the default value of VARDEF=, which is DF, the
% confidence interval for the weighted mean has upper and
lower limits
Student's t Test |
PROC MEANS calculates the t statistic as
When you use the WEIGHT statement or WEIGHT= in a VAR statement and the default value of VARDEF=, which is DF, the Student's t statistic is calculated as
Quantiles |
The options QMETHOD=, QNTLDEF=, and QMARKERS= determine how PROC MEANS calculates quantiles. QNTLDEF= deals with the mathematical definition of a quantile. See Quantile and Related Statistics. QMETHOD= deals with the mechanics of how PROC MEANS handles the input data. The two methods are
If data set A has 100 unique values for a numeric variable X and data set B has 1000 unique values for numeric variable X, then QMETHOD=OS for data set B will take 10 times as much memory as it does for data set A. If QMETHOD=P2, then both data sets A and B will require the same memory space to generate quantiles.The QMETHOD=P2 technique is based on the piecewise-parabolic (P²) algorithm invented by Jain and Chlamtac (1985). P² is a one-pass algorithm to determine quantiles for a large data set. It requires a fixed amount of memory for each variable for each level within the type. However, using simulation studies, reliable estimations of some quantiles (P1, P5, P95, P99) cannot be possible for some data sets such as data sets with heavily tailed or skewed distributions.
If the number of observations is less than the QMARKERS= value, then QMETHOD=P2 produces the same results as QMETHOD=OS when QNTLDEF=5. To compute weighted quantiles, you must use QMETHOD=OS.
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Copyright © 2010 by SAS Institute Inc., Cary, NC, USA. All rights reserved.