33 French laboratories took part in the experiments, together with 24 laboratories from other European countries. Four of the French laboratories were chosen randomly and included with the laboratories from the other countries to give a "European" experiment involving 28 laboratories. The data from the 33 French laboratories were treated as a separate "French" experiment.
The laboratories were given numerical codes that were used in all the cross-testing experiments in the first year of the programme. For the purposes of this report they have also been assigned letter-codes (because single-character codes are needed in the histograms and Mandel plots).
Samples of three materials were prepared and distributed by Partner 1. A report is available describing their preparation (Delalande, 1994). The same three materials were used throughout the four-year programme for all the cross-testing experiments that involve tests of mechanical properties of aggregates.
The samples were prepared, for each level of the experiments, as if they were laboratory samples all taken from one bulk sample, and the participants were required to prepare and test duplicate test portions from each sample. Hence the measures of repeatability and reproducibility given by the experiments are consistent with the definitions of r1 and R1 used in the programme.
Where a participant reported only a single test result for an aggregate, the missing result is shown as "---" in the data tables. Single test results have been included in the analysis, but they do not allow repeatability to be checked.
The Los Angeles test method requires test results to be rounded to the nearest whole number. However, for the purpose of the cross-testing experiment, it was asked that the test results should be reported to the nearest 0.1. This was to prevent rounding of the data affecting the assessment of the repeatability and reproducibility of the test method.
Unfortunately, data are not available rounded to 0.1 for several French laboratories. This can be seen in the histogram of ranges to have had a detrimental effect on their repeatability, particularly for Level 1. Also, if all the French data had been reported to 0.1, the value of Sr1 for the French experiment at Level 1 would have been closer to that for the European experiment, and the functional relationships would have been more similar.
Laboratory averages are used to calculate the reproducibility of the test method, and to assess laboratory biasses.
Between-test-portion ranges are used to calculate the repeatability of the test method, and to assess the repeatability of tests from individual laboratories.
The averages and ranges are shown in the histograms, and standardised values of these averages and ranges are shown in the Mandel plots.
The averages and ranges are also used to test for stragglers and outliers. Where these have been found, they are indicated using a single question mark (?) to indicate a straggler, and a double question mark (??) to indicate an outlier.
The Mandel plots are used to identify laboratories that give rise to large laboratory biasses, or large between-test-portion ranges, in more than one level of an experiment. Thus, for example, if a laboratory uses a Los Angeles machine that does not comply with the requirements of the test method, or uses a worn 1.60 mm test sieve, or does not follow the washing then sieving procedure correctly, then they can be expected to obtain laboratory biasses for all three levels that are in the same direction and large compared with those of the other laboratories. Likewise, if their staff have little experience with the method, or do not follow the method carefully, then they can be expected to obtain between-test-portion ranges that are unusually large. The horizontal broken lines in the Mandel plots show the critical values of the "h" and "k" statistics at the 5 per cent and 1 per cent significant levels, taken from the revised ISO standard on precision (ISO, 1994).
It will be of interest to compare the precision of the Los Angeles test with that of other tests of mechanical properties of aggregates. The repeatability and reproducibility standard deviations, or limits, for different test methods cannot be compared directly because they relate to different scales of measurement. Sensitivity ratios are dimensionless, so they do not suffer from this disadvantage, and they may be used to compare the precision of different tests. The formula used to calculate them is given in a separate file. It will be seen that they involve the average results for the materials used in the cross-testing experiments, so it is essential that different test methods are assessed using the same materials.