Data are evaluated using nonparametric statistics as described by Hoaglin and others (1983). This statistical approach is a resistant statistic because outliers have less influence on the median, than on the mean in traditional parametric statistics. Analytical data for each analyte are presented in tabular and graphical forms in the links above. Tabulated data for each analyte include the laboratory identification number; reported values; analytical method; most probable value (MPV); number of reported analyses, excluding less than values, (n); data range; the F-pseudosigma; and the Z-value. The Z-value is equivalent to the Z-score of traditional statistics. The F-pseudosigma approximates the standard deviation of traditional statistics when the data has a Gaussian distribution.

The median value, calculated from the reported results, is the MPV. The F-pseudosigma is calculated by dividing the fourth-spread (analogous to interquartile range) by 1.349; therefore the smaller the F-pseudosigma the more precise the determinations. The 1.349 value is derived from the number of standard deviations that encompasses 50% of the data. Statistical tables show that 25% of the area under a normal curve lies 0.6745 from the mean, so 50% lies 1.349 . The MPV and F-pseudosigma are replaced with the term "inadequate data" when the overall number of analyses is less than seven or the calculated F-pseudosigma is greater than the MPV. However, if an analyte has at least five analyses by a given method, the median and F-pseudosigma are reported in the block of data listed for each method. Based on an assessment of analyte data (Keith Long, Branch of Quality Systems, verbal comm., 1998), when the F-pseudosigma is less than 5 percent of the MPV, the rating criterion is set to 5 percent of the MPV. When applicable, the rating criterion is shown in the tables.

**LABORATORY PERFORMANCE RATINGS**

Laboratory performance ratings are listed in a link above. For each SRS, averages of all the analyte ratings and the number of rated analyses are given for each participating laboratory. The actual reported values by all the laboratories were used to calculate the statistical results and performance ratings presented above. Laboratory determination of each analyte is rated on a scale 4 to 0, based on the absolute Z-value.

Absolute Z-value |
Rating |

0.00 - 0.50 | 4 (Excellent) |

0.51 - 1.00 | 3 (Good) |

1.01 - 1.50 | 2 (Satisfactory) |

1.51 - 2.00 | 1 (Marginal) |

greater than 2.00 | 0 (Unsatisfactory) |

NR (Not Rated) |

Laboratories reporting less-than values are not performance rated unless their less-than value is less than the MPV (known as false negative) and has a Z-value greater than 2. In this case, the laboratory would receive a rating of 0 for that analyte.

Ratings are based on the relative performance of laboratories on specific samples and should be reviewed and evaluated on a case-by-case basis for each laboratory considering such factors as methods used and data needs of specific USGS projects using the laboratory data.