# Inter-laboratory proficiency testing in Excel

This tutorial will help you set up and interpret an inter-laboratory proficiency test in Excel using the XLSTAT software.

## What is inter-laboratory proficiency testing?

**Proficiency Testing**, also called **interlaboratory comparison**, compares the measurements made by several laboratories. This process aims at evaluating and monitoring laboratoriesâ€™ performance and is an essential part of quality assurance activities for testing laboratories.

XLSTAT allows for a highly automated analysis of the laboratory data and can yield a series of general and robust statistics. It is useful to interpret the results and define to what extent the proficiency standards are met.

This tool is based on the ISO-13528 standard. It was first developed using the 2015 edition. As some errors have been detected in the 2015 version of the document (see here for further details), XLSTAT gives you the possibility to run the analysis with or without the errors.

## Dataset

The data provides the results obtained by testing two similar proficiency test items for antibody concentrations. The data are numbers of units in thousands per litre of sample, where a unit is defined by the concentration of an international reference material.

Rows represent the laboratories and columns the concentrations of antibodies for two allergens.

*Source: Statistical methods for use in proficiency testing by interlaboratory comparison.*

## Setting up an inter-laboratory proficiency test in XLSTAT

Once XLSTAT is open, select the XLSTAT / **Laboratory data analysis** / **Inter-laboratory proficiency testing** feature.

The **inter-laboratory proficiency testing** dialog box appears.

In the **General** tab, select the measuring results collected for each item (laboratories in this case) and choose the **Item/Tests** table format as rows correspond to laboratories and columns to measurements.

In the **Options** tab, choose whether you want to use the mean or the median as the location statistic. If you want XLSTAT to exclude the errors in the computation of the Qn statistic (read our article for more details), deactivate the ISO-13528-2015 errors option.

Select the **scale statistic** (range or the standard deviation) to be estimated by the robust using the algorithm S. For the algorithm A, you have the option to use the range, the standard deviation using the Grubbs approach to remove outliers, the nIQR, Qn or Q as the scale statistic.

The choice of the algorithm is usually taken by the proficiency testing provider and depends on various factors such as the number of participants and the amount of outliers in the measurements.

If the median absolute deviation (MAD) is zero, then you may replace it with the median of the absolute differences with the mean. It is also possible to update the robust estimate s* (scale) at each iteration of the algorithm.

## Results of an inter-laboratory proficiency test in XLSTAT

In this example, there are multiple laboratories and two tests (measurements) so XLSTAT displays a list of summary statistics for each of them, including **robust statistics** such as the median, scaled median absolute deviation (MAD), and normalized IQR (nIQR). The latter ones are simple estimators.

The Qn and Q methods for estimating standard deviation are particularly useful for situations where a large proportion (>20 %) of results can be inconsistent (estimator with high breakdown), or where data cannot be reliably reviewed by experts.

The same statistics are then computed across all items.

The next output provides the estimates from **advanced algorithms** described in ISO-13528 (Algorithm A, Algorithm S, Q/Hampel), some of them being very resistant to outliers. Algorithm A and the Q/Hampel method are used to obtain robust estimators of location and standard deviation. Algorithm S is used to estimate the scale estimator from standard deviations or ranges.

Algorithm A is an alternative mean and standard deviation estimator for near-normal data and is most useful where the expected proportion of outliers is below 20 %. More details about the advantages of each method are given in the ISO-13528 standard document.

Last, a **homoscedasticity plot** is displayed to compare the location and scale estimates of the different laboratories. The greater the spread on the vertical axis is, the less valid is the assumption of constant variance across individuals. Confidence lines (90%, 95%, 99%) are displayed to identify laboratories that show values that are potential outliers like labs 5, 23 and 8.

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