# Statistics and Graphs

### Definitions

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.

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

## Distribution

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 This has been replaced by a histogram which gives an idea of the actual distribution of results:

### Results grouped by 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

Z-value

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.

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.

## 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.

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

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