Keywords and Formulas

Transcription

1 Page 1 of 10 Previous Page Next Page SAS Elementary Statistics Procedures Keywords and Formulas Simple Statistics The base SAS procedures use a standardized set of keywords to refer to statistics. You specy these keywords in SAS statements to request the statistics to be displayed or stored in an output data set. In the following notation, summation is over observations that contain nonmissing values of the analyzed variable and, except where shown, over nonmissing weights and frequencies of one or more: is the nonmissing value of the analyzed variable for observation i. is the frequency that is associated with statement, then i. you use a FREQ statement. If you omit the FREQ is the weight that is associated with automatically exclude the values of you use a WEIGHT statement. The base procedures By default, the base procedures treat a negative weight as it is equal to zero. However, you use the ECLNPWGT option in the statement, then the procedure also excludes those values of with nonpositive weights. Note that most SAS/STAT procedures, such as TTEST and GLM, exclude values with nonpositive weights by default. If you omit the WEIGHT statement, then for all i. is the number of nonmissing values of,. If you use the ECLNPWGT option and the WEIGHT statement, then is the number of nonmissing values with positive weights. is the mean is the variance

2 Page 2 of 10 where is the variance divisor (the VARDEF= option) that you specy in the statement. Valid values are as follows: When VARDEF= equals... N DF WEIGHT WDF The default is DF. is the standardized variable The standard keywords and formulas for each statistic follow. Some formulas use keywords to designate the corresponding statistic. The Most Common Simple Statistics Statistic MEANS and SUMMARY UNIVARIATE TABULATE REPORT CORR SQL Number of missing values Number of nonmissing values Number of observations Sum of weights Mean Sum Extreme values Minimum Maximum Range Uncorrected sum of squares Corrected sum of squares Variance Covariance

3 Page 3 of 10 Standard deviation Standard error of the mean Coefficient of variation Skewness Kurtosis Confidence Limits of the mean of the variance of quantiles Median Mode Percentiles/Deciles/Quartiles t test for mean=0 for mean= Nonparametric tests for location Tests for normality Correlation coefficients Cronbach's alpha Descriptive Statistics The keywords for descriptive statistics are CSS is the sum of squares corrected for the mean, computed as CV is the percent coefficient of variation, computed as

4 Page 4 of 10 KURTOSIS KURT is the kurtosis, which measures heaviness of tails. When VARDEF=DF, the kurtosis is computed as where is. The weighted kurtosis is computed as When VARDEF=N, the kurtosis is computed as and the weighted kurtosis is computed as where is. The formula is invariant under the transformation. When you use VARDEF=WDF or VARDEF=WEIGHT, the kurtosis is set to missing. Note: MEANS and TABULATE do not compute weighted kurtosis. MA is the maximum value of. MEAN is the arithmetic mean. MIN is the minimum value of. MODE is the most frequent value of. Note: When QMETHOD=P2, REPORT, MEANS, and TABULATE do not compute MODE. N is the number of less than one and equal to missing or (when you use the ECLNPWGT option) are excluded from the analysis and are not included in the calculation of N.

5 Page 5 of 10 NMISS is the number of values that are missing. Observations with missing or (when you use the ECLNPWGT option) are excluded from the analysis and are not included in the calculation of NMISS. NOBS is the total number of observations and is calculated as the sum of N and NMISS. However, you use the WEIGHT statement, then NOBS is calculated as the sum of N, NMISS, and the number of observations excluded because of missing or nonpositive weights. RANGE is the range and is calculated as the dference between maximum value and minimum value. SKEWNESS SKEW is skewness, which measures the tendency of the deviations to be larger in one direction than in the other. When VARDEF=DF, the skewness is computed as where is. The weighted skewness is computed as When VARDEF=N, the skewness is computed as and the weighted skewness is computed as The formula is invariant under the transformation. When you use VARDEF=WDF or VARDEF=WEIGHT, the skewness is set to missing. Note: MEANS and TABULATE do not compute weighted skewness. STDDEV STD is the standard deviation s and is computed as the square root of the variance,. STDERR STDMEAN is the standard error of the mean, computed as

6 Page 6 of 10 when VARDEF=DF, which is the default. Otherwise, STDERR is set to missing. SUM is the sum, computed as SUMWGT is the sum of the weights,, computed as USS is the uncorrected sum of squares, computed as VAR is the variance. Quantile and Related Statistics The keywords for quantiles and related statistics are MEDIAN is the middle value. P1 P5 P10 P90 P95 is the 1 st percentile. is the 5 th percentile. is the 10 th percentile. is the 90 th percentile. is the 95 th percentile.

7 Page 7 of 10 P99 Q1 Q3 is the 99 th percentile. is the lower quartile (25 th percentile). is the upper quartile (75 th percentile). QRANGE is interquartile range and is calculated as You use the QNTLDEF= option (PCTLDEF= in UNIVARIATE) to specy the method that the procedure uses to compute percentiles. Let is the smallest value, smallest value, and define as the integer part of and as the fractional part of, so that. Then Here, QNTLDEF= species the method that the procedure uses to compute the tth percentile, as shown in the table that follows. When you use the WEIGHT statement, the tth percentile is computed as where is the weight associated with is the sum of the weights. When the observations have identical weights, the weighted percentiles are the same as the unweighted percentiles with QNTLDEF=5. Methods for Computing Quantile Statistics QNTLDEF= Description Formula 1 weighted average at where

8 Page 8 of 10 2 observation numbered closest to is even is odd where i is the integer part of 3 empirical distribution function 4 weighted average aimed at where 5 empirical distribution function with averaging Hypothesis Testing Statistics The keywords for hypothesis testing statistics are T is the Student's t statistic to test the null hypothesis that the population mean is equal to calculated as By default, is equal to zero. You can use the MU0= option in the UNIVARIATE statement to specy. You must use VARDEF=DF, which is the default variance divisor, otherwise T is set to missing. By default, when you use a WEIGHT statement, the procedure counts the values with nonpositive weights in the degrees of freedom. Use the ECLNPWGT option in the statement to exclude values with nonpositive weights. Most SAS/STAT procedures, such as TTEST and GLM automatically exclude values with nonpositive weights. PROBT PRT is the two-tailed p-value for Student's t statistic, T, with probability under the null hypothesis of obtaining a more extreme value of T than is observed in this sample.

9 Page 9 of 10 Confidence Limits for the Mean The keywords for confidence limits are CLM is the two-sided confidence limit for the mean. A two-sided for the mean has upper and lower limits percent confidence interval where is, is the ( ) critical value of the Student's t statistics with by default is Unless you use VARDEF=DF, which is the default variance divisor, CLM is set to missing. LCLM is the one-sided confidence limit below the mean. The one-sided interval for the mean has the lower limit percent confidence Unless you use VARDEF=DF, which is the default variance divisor, LCLM is set to missing. UCLM is the one-sided confidence limit above the mean. The one-sided interval for the mean has the upper limit percent confidence Unless you use VARDEF=DF, which is the default variance divisor, UCLM is set to missing. Using Weights For more information on using weights and an example, see WEIGHT. Data Requirements for Summarization Procedures The following are the minimal data requirements to compute unweighted statistics and do not describe

10 Page 10 of 10 recommended sample sizes. Statistics are reported as missing VARDEF=DF (the default) and the following requirements are not met: N and NMISS are computed regardless of the number of missing or nonmissing observations. SUM, MEAN, MA, MIN, RANGE, USS, and CSS require at least one nonmissing observation. VAR, STD, STDERR, CV, T, PRT, and PROBT require at least two nonmissing observations. SKEWNESS requires at least three nonmissing observations. KURTOSIS requires at least four nonmissing observations. SKEWNESS, KURTOSIS, T, PROBT, and PRT require that STD is greater than zero. CV requires that MEAN is not equal to zero. CLM, LCLM, UCLM, STDERR, T, PRT, and PROBT require that VARDEF=DF. Previous Page Next Page Top of Page Copyright 2010 by SAS Institute Inc., Cary, NC, USA. All rights reserved.