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The concept of relative standard deviation (rsd), its purpose, syntax, and differences with other statistical measures such as coefficient of variation. It also provides examples of how to use the relative standard deviation let subcommand in sas and its applications in exploratory data analysis. The document also includes a reference to a statistical methods book and an implementation date.
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RELATIVE STANDARD DEVIATION Statistics LET Subcommands
Compute the relative standard deviation of a variable.
The relative standard deviation is:
relsd = 100*(standard deviation/|mean|)
Some analysts prefer to call this the percent relative standard deviation and to call the relative standard deviation the value that is obtained without multiplying by 100. If this is your preference, simply use the LET command to divide by 100.
Note that this statistic differs in a minor way from the commonly used coefficient of variation. The coefficient of variation divides by the mean rather than the absolute value of the mean. If the mean is negative, the coefficient of variation will be negative while the relative standard deviation (as defined here) will always be positive. In addition, some sources define the coefficient of variation as a fraction rather than a percent. To calculate the traditional coefficient of variation, use the COEFFICIENT OF VARIATION LET subcommand.
LET
Versions prior to 94/2 divide by the mean rather than the absolute value of the mean. The 94/12 version implements the COEFFICIENT OF VARIATION command as a distinct command. The COEFFICIENT OF VARIATION command divides by the mean rather than the absolute value of the mean.
None
COEFFICIENT OF VARIATION = Compute the coefficient of variation of a variable. MEAN = Compute the mean of a variable. STANDARD DEVIATION = Compute the standard deviation of a variable. RELATIVE VARIANCE = Compute the relative variance of a variable. RELATIVE STAND DEVI PLOT = Generate a relative standard deviation versus subset plot.
“Statistical Methods,” Sixth Edition, Snedecor and Cochran, The Iowa State University Press, 1967 (pp. 62-64).
Exploratory Data Analysis
Pre-1987 (definition changed 94/2)
Statistics LET Subcommands RELATIVE STANDARD DEVIATION
The computed relative standard deviation is 0.63.