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Appendix E: Weighting
With regard to the Member States (MS) which will code the causes and the circumstances only for a national sampleof accidents at work, a weighting procedure has been proposed to the Task Force during the meeting on 14/02/2001.
It has been proposed to use also this procedure for reporting levels < 100% or to solve some issues about the coverage of the data or the type of accidents covered, etc. . When various situations are cumulated (reporting level
< 100% + sample + etc.), the MS should provide for each case (accident) in the dataonly 1 weight cumulating all the effects. For MS for which no weighting is necessary, all weights will be = 1 in the datafile. It will be also the same for all fatal accidents of all MS.
Consequently a new variable “weight” would be introduced in Phase III on a compulsory basis (the default value being 1). This proposal was adopted by the ESAW Working Group during its meeting on 17/10/2001. The detailed methodology will be discussed with Member States and the Working Group. It could be based on the following proposals :
i. Situation :in Phase 3 some Member States (MS) will not encode all accidents > 3 days' absence but only a national sample of such accidents (either providing phase 1 and 2 data only on the sample or for all accidents).
Problem : Eurostat needs to extrapolate the results from the sample to all accidents > 3 days' absence for these MS.
Solution :Post-stratification method as done, for ex., in the Labour Force Survey methodology.
ii. Definition of control variables for the post-stratification : ü Economic activity (NACE 1- or 2-digit)
ü Sex ü Age group
ü Others ? (but, e.g., ISCO & employment status are not covered by all MS in ESAW).
iii. Example with 2 control variables I & J - Definition of weights and extrapolation to the whole population of accidents :
ü Nij the number of cases with values of control variables I = ‘i’ & J = ‘j’ in the whole population of accidents at work > 3 days’ absence in the MS during the reference year;
ü nij the number of cases with values of control variables I = ‘i’ & J = ‘j’ in the sample of accidents at work > 3 days’ absence codified for phase 3 variables;
ü Weight of each case in the sample with values of control variables I = ‘i’ & J = ‘j’ :
Wij = 1 / Pij = Nij / nij formula 1;
ü nijk the number of cases with values of control variables I = ‘i’ & J = ‘j’ in the sample, having the value k for the phase 3 variable K (ex. Contact);
ü Calculation of the number Nijk of accidents at work > 3 days’ absence with values of control variables I = ‘i’ &
J = ‘j’, having the value k for the phase 3 variable K in the whole population of accidents at work > 3 days’
absence occurred in the MS during the reference year :
Nijk = nijk X Wij (= nijk X Nij / nij) formula 2;
APPENDIXE: WEIGHTING
ü Calculation of the number Nk of accidents at work > 3 days’ absence having the value ‘k’ for the phase 3 variable K in the whole population of accidents at work > 3 days’ absence occurred in the MS during the reference year :
Nk = Σij Nijk = Σij nijk X Wij (= Σij nijk X Nij / nij) formula 3;
ü Calculation of the total number N of accidents at work > 3 days’ absence occurred in the MS during the reference year :
N = Σk Nk = Σijk Nijk = Σijk nijk X Wij formula 4 (= Σijk nijk X Nij / nij = Σij [Nij / nij] XΣk nijk = Σij [Nij / nij] X nij = Σij Nij).
iv. Extension of the use of weights to MS that register only partly the non-fatal accidents at work :
ü Some MS do not register 100% of the accidents at work > 3 days’ absence; these MS provide Eurostat with evaluations of their national reporting levels, breakdown mainly according to the economic activity branches -NACE sections 1 letter – (also partly by occupation - ISCO 1-digit -, employment status or size of enterprise );
this information is provided levels at 1-digit level via the evaluation questionnaire filled by the MS for each reference year’s ESAW data.
ü If I, J & K are the 3 variables NACE, ISCO and employment status (size of enterprise not used up to date);
ü The calculation done by Eurostat to estimate the numbers of accidents > 3 days’ absence occurred in these MS is based on the following formulas, according to the ESAW methodology agreed with the MS :
Ri the reporting level for people with value ‘i’ of the variable I (for ex., I = NACE, i = A agriculture, in UK in 1998, Ri = 28% = 0.28 , etc.);
Rj and Rk similarly the reporting levels for people with value ‘j’ and ‘k’ of variables J and K respectively;
Rij, Rik, Rjk, Rijk the crossed reporting level when available (ex. I = NACE & i = A agriculture etc., J = occupation & j = 6 skilled agricultural and fishery workers etc., K = employment status & k = 1 self-employed etc.);
nijk the number of reported cases with values I = ‘i’, J = ‘j’ & K = ‘k’;
Nijk the total number of accidents at work > 3 days’ absence with values I = ‘i’, J = ‘j’ & K = ‘k’ occurred in the MS during the reference year;
(respectively ni & nij and Ni & Nij when reporting levels are only available according to 1 or 2 variables, I or I & J);
N the total number of accidents at work > 3 days’ absence occurred in the MS during the reference year;
Nijk = nijk / Rijk (respectively Ni = ni / Ri, Nij = nij / Rij) N = Σijk Nijk = Σijk nijk / Rijk;
ü If we define for these MS the weights :
Wijk = 1 / Rijk similarly Wi, Wj, Wk, Wij & Wjk
(for example in UK for NACE A = agriculture in 1998, Wi = 1 / 28% = 1 / 0.28 = 3.571429);
then :
Nijk = nijk X Wijk
N = Σijk Nijk = Σijk nijk X Wijk formula 5 for 3 reporting levels’ variables;
respectively when reporting levels are only available according to 1 or 2 variables (I or I & J) in the MS :
APPENDIXE: WEIGHTING
203 1 variable I :
Nijk = nijk X Wi
N = Σijk Nijk = Σijk nijk X Wi formula 5 for 1 reporting levels’ variable (= Σi Wi Σjk nijk = Σi ni X Wi = Σi Ni) ;
2 variables I & J : Nijk = nijk X Wij
N = Σijk Nijk = Σijk nijk X Wij formula 5 for 2 reporting levels’ variables (= Σij Wij Σk nijk = Σij nij X Wij = Σij Nij) ;
formula 5 for 2 reporting levels’ variables = formula 4 Þ same method.
Consequently the “problem” of MS that register only partly the non-fatal accidents at work (> 3 days’ absence) could be managed with the same methodology as for the use of samples, defining in that case the weights as the inverses of the reporting levels.
ü This would provide MS with a more flexible case-by-case management of the reporting levels : possibility to use crossed reporting levels and then crossed weights according not only to NACE sections but also to ISCO, employment status, size of the local unit or any other variable;
ü For MS reporting 100% of the accidents at work > 3 days’ absence, all weights Wijk = Wij = Wi = 1, i.e., they should fill the weight variable imputing always the value 1; however, this method would also provide more flexibility for these MS as they would be able to consider weights≠1 for very specific cases if necessary;
ü Nevertheless, the meta-data provided via the evaluation questionnaire, should be maintained as they allow a general description of the reporting of accidents at work in Europe;
v. Broader extension of the weights to all MS :
ü Some MS can face specific situations; for example some countries, at least in a first time, had/have to include 0-3 days' absence accidents in ESAW data as they were/are not able to distinguish between > or≤3 days' absence; however, they could be able to evaluate the share S (ex. S = 80% = 0,8) of the accidents > 3 days’ absence in the total of all accidents at work in their country (or Sij if the share depends on variables I &
J as in points iii & iv above); in that case a weight could also be used in ESAW data for these MS, “Wij” = “Sij”
or “S” (= 0,8 in the example) with the same formulas and calculations as above;
ü Finally, we can imagine that in future, for ex. with the enlargement and new MS, new similar situations could occur.
In conclusion, various situations that can be solved by weighting procedures are now involved in ESAW; it would be difficult to use different methods depending on the case, maintaining the reporting levels procedure for some MS, using weights for others implementing samples, etc.; additionally “crossed”-situations could occur, with MS cumulating more than one situation of this type, and it would be very difficult to control these “crossed”-situations with different “corrections” of the data at the same time (reporting levels + weights, etc.); on the opposite it would be very simple to cover all these situations in only 1 weight for each accident > 3 days’ absence.
vi. Conclusion : compulsory variable “weight” in ESAW phase 3 methodology
It is proposed to include a weight for each case of accident at work in all ESAW Phase III datafiles submitted by the MS. The weights will be≠ 1 when using samples for the Phase III codification, when reporting levels < 100% or to solve some issues about coverage or type of accidents, etc. .
When various situations are cumulated (reporting level < 100% + sample + etc.), the MS should provide for each case (accident) in the dataonly 1 weight cumulating all the effects. For MS for which no weighting is necessary, all weights will be = 1 in the datafile. It will be also the same for all fatal accidents of all MS.
Consequently the new variable “weight” will be acompulsory variable (the default value being 1).