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Statistics and Graphs

ISO 13528 - Statistical methods for use in proficiency testing by interlaboratory comparisons - is applied


Lab Bias = Lab Result - Mean
% Difference = (Lab Bias / Mean) x 100
Z-value = Lab Bias / Standard Deviation

Notes to this version

In some of the graph legends below, Average is sometimes used for Mean.

Bika Interlab Proficiency Testing LIMS Select Period and Graph

Graphs were generated with random data, they'll be a more meaningful with the real data.


For the results of a particular analysis on a sample, Interlab 1 used a bell curve with individual results. This has been replaced by a histogram which gives an idea of the actual distribution of results:

Bika Interlab Proficiency Testing LIMS Z-value Distribution 

Results grouped by method

Bika Interlab Proficiency Testing LIMS Results per Method

Individual Tests

Regarding laboratory statistics for specific analyses, Interlab 1 graphs Z-score vs time for the previous 12 months. Similar graphs will now be available showing

Lab Bias
Percentage difference

and will be available for previous years as well. Some examples below.
There are also cumulative graphs, which makes it easier to monitor overall bias in cases where results are sometimes above and sometimes below the mean.

Bika Interlab Proficiency Testing LIMS Cumulative Bias

Another view plots results for one year and 'errors' against the mean values. This allows a lab to see, for example, that their Z-score for an analysis tends to increase at higher concentrations.

Bika Interlab Proficiency Testing LIMS % Difference vs Average

Test overview

There are also a few graphs for each type of analysis, e.g. alcohol or density.

The first is a 'participation' graph showing how many labs do the analysis, and how many of them use each available method.

Bika Interlab Proficiency Testing LIMS Participation per Method

Another shows standard deviation vs time, which should give an idea of whether the overall accuracy of the participating labs is improving.

Bika Interlab Proficiency Testing LIMS Robust Standard Deviation

Finally, there are graphs comparing the accuracy of the various methods used, for example:

Bika Interlab Proficiency Testing LIMS Absolute Deviation as % of Average