SPECIFYING SAMPLE MASSES FOR GRAVIMETRIC TESTING PROCEDURES
ABSTRACT Gravimetric testing procedures often do not specify sample masses; frequently only minimum sample masses are required. If variations in sample mass occur, then the standard n-weighted sample mean is a nonoptimal estimate of the population mean, and the standard (n-l)-weighted sample variance, S2, is a biased estimate of the population variance. The standard statistical assumption that observations are identically distributed random variables is violated. Different methods of specifying sample mass result in different probability distributions for sample mass. It is shown that when a minimum sample mass is specified, the distribution of sample masses can follow a gamma distribution. When a sample mass is specified along with an allowable deviation, a number of distributions are possible including uniform and normal distributions. Theoretical expressions for the bias of S2 are derived for the gamma distribution and uniform distribution. These expressions are used to demonstrate the magnitude of errors that can occur in the estimation of variance. It is recommended that gravimetric testing procedures should specify a standard sample mass target in conjunction with allowable deviations from that designated value.