National Water Quality Laboratory

Technical Memorandum 2005.01

**Statistical Definition Summary**

**Bias** -- The measure of the difference between the average of a set
of measurements and the true value.

**Coefficient of Variance (Coef. Var.)** -- Measure of the relative
variability of the data specified. It is the standard deviation divided
by the mean.

**Confidence Level (95 or 99 percent)** -- Reports a range of
concentrations within which a particular parameter would likely occur if
samples were taken repeatedly from the sample distribution.

**Count** -- The number of concentrations minus the number of cases that
have missing concentrations.

**F-pseudosigma** -- Measurement of variance. Interquartile range
divided by 1.349.

**F-test** -- This test shows whether the variance of one group is
smaller, larger, or equal to the variance of the other group.

**Interquartile Range (IQR)** -- The interquartile range is calculated
by subtracting the 25th % value from the 75th % value. It is the range
of concentrations containing the central 50% of the data. The IQR is
based around the median.

**LT--MDL**-- Long-Term Method Detection Level -- A detection level
derived by determining the standard deviation of a minimum of 24 method
detection limit spike sample measurements over an extended period.
LT--MDL data are collected on a continuous basis to assess year -to-year
variations in the LT--MDL. The LT--MDL controls false positive error.
The chances of falsely reporting a concentration at or greater than the
LT--MDL, for a sample that did not contain analyte, is predicted to be
less than or equal to 1 percent.

**Mann-Whitney Test** --This tests the hypothesis that the medians of
the two groups are the same. This test deals with the ranked
concentrations, so outliers do not influence it.

**Maximum** -- Identified largest value in the data.

**Mean** -- The sum of all of the concentrations divided by the number
of concentrations.

**Median** -- The middle value of all concentrations, when all
concentrations are listed in numeric order.

**MRL** -- Minimum reporting level -- Smallest measured concentration of
a constituent that may be reliably reported by using a given analytical
method.

**Minimum** -- Identified smallest value in data.

**P10** -- The data value that 10% of the observations are less than.

**P25** -- The data value that 25% of the observations are less than.

**p-value** -- A reporting convention that is used to report on the
chance of or the hypothesis from certain statistical tests. A p-value
close to 1 means the chance of or the hypothesis is true and the data,
with respect to the specific test, are the same. A p-value close to 0
means the chance of or the hypothesis is not true and the data, with
respect to the specific test, are not the same. For the 95th percentile
confidence interval criteria, a p-value of \> 0.05 means the data are
statistically similar. A p-value \< 0.05 means the data are
statistically different.

**Precision** -- The measurement of the degree of concentration of
measurements about their mean.

**Range** -- The difference between the maximum and minimum
concentrations.

**RELIQ** -- Interquartile range of recovery divided by the median. Used
to assess variability.

**Standard Deviation (Std Dev)** -- Measurement of the spread about the
mean. It is the square root of the differences between each data value
and the mean, divided by one less than the number of concentrations. It
is the square root of the variance.

**Standard Error (Std Error)** -- Measurement of the standard error of
the mean. Computed by taking the standard deviation and dividing it by
the square root of the number of concentrations.

**t-test** -- This test compares the means of the two groups and
determines the likelihood of the observed differences occurring by
chance.

**Variance** -- Measurement of the spread about the mean. It is
calculated by taking the square of the differences between each data
value and the mean, and then dividing by one less than the number of
concentrations. It is the square of the standard deviation.

**Uncited References**

Abacus Concepts, Inc., 1996, StatView reference manual: Berkley, Calif.,
USA.

Miller, J.C., and Miller, L.N., 1993, Statistics for analytical
chemists, 3rd ed.: Ellis Horwood Limited, Chichester, West Sussex,
England.

Ott, W.R., 1995, Environmental statistics and data analysis: CRC Press,
Inc., Boca Raton, Fla., USA.

Montgomery, D.C., 1991, Introduction to statistical quality control, 2nd
ed.: John Wiley & Sons, USA.