- Tables of repeatability and reproducibility values.
- Figure showing functional relations for the precision values.
- Histograms of the data from the precision experiment.
- Mandel plots of the data from the precision experiment.
- Return to PSV test Summary Page.
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Estimates of repeatability and reproducibility are given in Table 1. The standard deviations are also shown in Figure 1. These estimates have been calculated by excluding the data for Laboratory L at all three levels.

In Figure 1 it can be seen that the points representing the repeatability and reproducibility standard deviations fall close to straight lines, so that it is possible to fit functional relations to these results. However, neither the repeatability nor the reproducibility standard deviations vary very much over the three levels of the experiment, so it would be equally valid to summarise the results of the experiment by calculating average values for the repeatability and reproducibility values over the three levels.

It has been argued (J¯rck, Sym and Powell, 1994. *A study of mechanical tests of aggregates. * Green Land Reclamation Ltd Report GLR 3036/03a.) that the reproducibility standard deviation of a mechanical test, when expressed as a coefficient of variation, should be no more than about 8 %, if the test method is to be used to assess the compliance of aggregates with specifications. The results in Table 3 show that the reproducibility of the PSV test meets this criterion easily.

However, it is the practice in the UK to specify different levels of PSV according to the site category (e.g. motorway, approaches to major junctions, approaches to roundabouts, etc.) and according to amount of traffic, and the levels that are used are closely-spaced - being only 2 or 3 PSV units apart. One must question whether it is possible to distinguish between such levels correctly with a test that has a reproducibility of 5 or 6 PSV units. This can only be done if there is experience, based on regular comparative tests between laboratories (i.e. proficiency tests), that allows the individual laboratory biasses to be established.

The Mandel plots show relations between the PSV results for different levels. Even though the results have been adjusted using the control stone tests, they show evidence of correlations between the levels, indicating that some factor is (or some factors are) influencing the results, so that it should be possible to improve the reproducibility of the test.

Tables A to D, below, give analyses of variance of the data for individual specimens. Data for Laboratory L have been excluded from these calculations. The analysis of variance involves fitting a model to the data:

X_{ijkl} = A + L_{i} + T_{ij} + R_{ijk} + S_{ijkl}

- A
- represents the general average
- L
_{i} - allows for variation between laboratories (i = 1 to 18)
- T
_{ij} - allows for variation between test results within laboratories (j = 1 to 2)
- R
_{ijk} - allows for variation between runs within test results (k = 1 to 2)
- S
_{ijkl} - allows for variation between specimens within runs (l = 1 to 2)

Standard deviations may then be calculated that measure the amount of variation arising from the various terms in the model. Thus:

*the standard deviation for laboratories*- a standard deviation of laboratory averages (where a laboratory average is the average result for 8 specimens: 2 tests ( 2 runs ( 2 specimens)
*the standard deviation for test results*- a standard deviation of test averages within laboratories (where a test average is the average result for 4 specimens: 2 runs ( 2 specimens)
*the standard deviation for runs*- a standard deviation of run averages within tests (where a run average is the average result for 2 specimens)
*the standard deviation for specimens*- a standard deviation of the results for individual specimens within runs.

The critical ranges are obtained by multiplying the respective standard deviations by 2.8. Comparison of the standard deviations in the analysis of variance table for the control stone with those for the other three aggregates reveals that the control stone gives the lowest values of the standard deviations in all cases. Thus the control stone gives less variability between laboratories, between runs, between test results, and between specimens, than the other three materials.

prEN 1097-8 specifies that the between-run range for the control stone (with two test specimens per run) should not exceed 5.0 units. In Table D the critical range for the source of variation "Runs" is 2.57 units for the control stone. Because a multiplier of 2.8 has been used to derive this value, it should be exceeded in not more than one in twenty tests, so the limit of 5.0 units in the Standard should be exceeded much less frequently than this rate.

For Levels 1 to 3, the analyses of variance show that the critical ranges for between-specimen ranges or between-run ranges fall between 3.4 and 4.2 units. Hence, as a method of assessing their repeatability for measurements made on aggregates other than the control stone, laboratories could use a critical range of 4.0 units. They could check that this value is exceeded in no more than one in twenty tests by their between-specimen ranges and by their between-run ranges.

Source of variation | Sum of squares | Degrees of freedom | Mean square | Standard deviation | Critical range |
---|---|---|---|---|---|

Laboratories | 974.620 | 17 | 57.331 | 2.677 | 7.496 |

Test results | 90.098 | 18 | 5.005 | 1.119 | 3.132 |

Runs | 116.381 | 36 | 3.233 | 1.271 | 3.560 |

Specimens | 104.653 | 72 | 1.454 | 1.206 | 3.376 |

Source of variation | Sum of squares | Degrees of freedom | Mean square | Standard deviation | Critical range |
---|---|---|---|---|---|

Laboratories | 854.767 | 17 | 45.118 | 2.375 | 6.650 |

Test results | 109.621 | 18 | 6.090 | 1.234 | 3.455 |

Runs | 151.290 | 36 | 4.203 | 1.450 | 4.056 |

Specimens | 113.423 | 72 | 1.575 | 1.255 | 3.514 |

Source of variation | Sum of squares | Degrees of freedom | Mean square | Standard deviation | Critical range |
---|---|---|---|---|---|

Laboratories | 1147.628 | 17 | 67.508 | 2.905 | 8.134 |

Test results | 105.933 | 18 | 5.885 | 1.213 | 3.396 |

Runs | 111.096 | 36 | 3.086 | 1.242 | 3.478 |

Specimens | 158.700 | 72 | 2.204 | 1.485 | 4.157 |

Source of variation | Sum of squares | Degrees of freedom | Mean square | Standard deviation | Critical range |
---|---|---|---|---|---|

Laboratories | 355.378 | 17 | 20.905 | 1.617 | 4.526 |

Test results | 53.319 | 18 | 2.962 | 0.861 | 2.410 |

Runs | 60.653 | 36 | 1.685 | 0.918 | 2.570 |

Specimens | 44.676 | 72 | 0.621 | 0.788 | 2.206 |