Example of data analysis: Choosing the second site

By David Causeur

Goals

The main objective is to evaluate repeatability and reproducibility of European methods for grading pig carcasses.

The aim of this preliminary trial is to search for the most relevant second site for the future trials conducted in order to test for the system effect and the operator effect.

Sampling Procedure

The trial took place in a single slaughterhouse. The measurements were done by the same operator and the same equipment. The 3 thicknesses actually used for classification (a back fat thickness G2 and a back muscle thickness M2 between the 3rd and 4th last rib and a vertebral fat thickness G1 between the 3rd and 4th last vertebra) were measured on 80 carcasses chosen at random together with 5 other measurements at the sites defined as follows :

The sample is distributed as follows relative to sex:

 

Male

Female

 

Morning

20.00

27.5

47.5

Afternoon

21.25

31.25

52.5

 

41.25

58.75

100

The lean meat percentage estimated throughout the measurements of the thick nesses at the classification sites is distributed as follows:

 

Min.

1st quartile

Median

Mean

3rd quartile

Max.

Standard deviation

Est. Lean meat %

53.10

58.05

59.79

59.95

61.63

65.60

2.82

Reproducibility

Evaluation of the reproducibility is based on the statistical modelling of the relationships between measurements of the thicknesses measured at the reference classification site (X) and another site (Y). The following regression model is assumed :

Both variables are assumed to be subject to errors and these errors are supposed to have equal variances. Consequently, the coefficients of the model are estimated throughout an orthogonal fit (PCA instead of OLS). Reproducibility relies then on two criteria : 

In order to be consistent in the management of these two objectives, robust procedures have been used to estimate the parameters and of course to identify the outliers. Some discrepancies have been detected in reproducibility criteria between sexes, which can not be assigned to any controlled factor of variability ... Therefore, for each thickness, the candidate sites are classified in decreasing order of their reproducibility capabilities evaluated within sex and within period of the day. What can be said without any statistical arguments but only after an overview of the results is first that reproducibility is better for the muscle thickness than for the fat ones. Moreover, reproducibility for the measurement of the back fat thickness is better than for the vertebral one.

General comments

Concerning the measurement of G1, site 5 shows particularly great discrepancies between the morning and the afternoon measurements in the evaluation of reproducibility. It also seems that reproducibility of G1 measurement is for most sites better for females than for males. Due to a high quality of reproducibility for the G2 measurements, examination of the reproducibility criteria for this thickness is not discriminated between the candidate sites. Finally, investigating the reproducibility criteria for the M2 measurements shows high percentage of outliers and poor correlations for the most distant sites from the classification site.

Conclusion

Reproducibility is better for sites close to the classification sites. Apart from technical problems eventually occurring in experimental conditions, the nearest sites (sites 3 and 4) from the classification site can be reasonably proposed as good candidates for the future trial.