F-pseudosigma = (data [Fourth-spread])/1.349

where, the Fourth-spread is analogous to the interquartile range of the data. In addition, they show that the F-pseudosigma yields an unbiased estimate of standard deviation when the data distribution is Gaussian. However, it is recognized that some of the SRWS project data sets may not have Gaussian data distributions, the regression equations will be derived from a combination of parametric and nonparametric results.

The SRWS project MPV's are used to estimate the MPV's of the Inorganic Blind Sample Project mixes based on the proportion of the SRWS used. Likewise, if deionized water is used in the preparation of a blind sample mix, then a sample concentration of zero is applied to estimate the resultant MPV based on the proportion used. The resulting MPV's are used in the Inorganic Blind Sample Project to compare with analytical results.

For each constituent, a regression equation was used to estimate the F-pseudosigma (F_s), over a continuous range of concentrations. The equations were derived by regressing the F-pseudosigma or standard deviation against the MPV using ordinary least-squares. Helsel and Hirsch (1992) provide a general model for estimation of ordinary least-squares regression,

F_s, = ß₀ + ß₁MPV_i + e_i            i = 1,2,..., n

where F_α = the ith observation of the response variable, F_s,
MPV_i = the ith observation of the explanatory variable, MPV,
ß₀ = the intercept,
ß₁ = the slope,
e_i = the random error or residual for the ith observation, and
n = the sample size.

SRWS project summary data for semi-annual round-robin sample studies conducted during the last 7 years were used to derive regression equations for each constituent. The table below presents the concentration range of SRWS samples used, the derived F_s equation, and the correlation.