After collecting the data, blank results and "unpaired" results are removed from
the dataset. Unpaired results are characterized by a blank result for either sample
X (the odd numbered sample) or sample Y (the even numbered sample). The new "paired"
dataset is then subjected to a two-step routine to remove "invalid" and "outlier"
values. First, the range of the inner 75% of the "paired" dataset is increased by
a factor of 4.11 to establish upper and lower limits. Any test results beyond these
limits are categorized as "extremely unusual" and removed as "invalid". Then, the
new dataset is refined by again determining the range of the inner 75% and increasing
that new range by a factor of 2.35 to establish revised upper and lower limits.
Any test results beyond the revised upper and lower limits are categorized as "unusual"
and removed as "outliers." The remaining dataset is the "core" dataset used to determine
statistics in the analysis process.

For a more detailed description, see NCHRP Document 71.

The following statistics are determined using the "core" dataset (see above):

Laboratory's Within-Laboratory Value = [(Yi - Xi) - (Yavg - Xavg)] / √2,

where, Xi and Yi = the laboratory's test results for sample X and sample Y, and

Xavg and Yavg = the average values for sample X and sample Y.

- Average
- Standard Deviation (1s)
- Coefficient of Variation (1s%)
- Difference Two-Sigma Limit (d2s)
- Difference Two-Sigma Limit in percent (d2s%)

Laboratory's Within-Laboratory Value = [(Yi - Xi) - (Yavg - Xavg)] / √2,

where, Xi and Yi = the laboratory's test results for sample X and sample Y, and

Xavg and Yavg = the average values for sample X and sample Y.

Each laboratory is rated with two values:

Z-Score = (Laboratory Test Result - Average Value) / (Standard Deviation)

The laboratory Rating calculation is based on the absolute value of the Z-Score
(or number of standard deviations from the average). The following describes the
laboratory Rating system:

A negative sign on a Z-Score or Rating indicates that the laboratory's result was below the average, while a positive Z-Score or Rating indicates that the laboratory's result was above the average.

- Laboratory Rating (on a scale of 0 to 5)
- Z-Score

Z-Score = (Laboratory Test Result - Average Value) / (Standard Deviation)

- If Z-Score <= 1 Then Rating = 5
- If Z-Score > 1 And <= 1.5 Then Rating = 4
- If Z-Score > 1.5 And <= 2 Then Rating = 3
- If Z-Score > 2 And <= 2.5 Then Rating = 2
- If Z-Score > 2.5 And <= 3 Then Rating = 1
- If Z-Score > 3 Then Rating = 0

A negative sign on a Z-Score or Rating indicates that the laboratory's result was below the average, while a positive Z-Score or Rating indicates that the laboratory's result was above the average.