Using balanced sampling in creel surveys
Section 3. A creel survey for striped bass in the Gaspé Peninsula

The Gaspé Peninsula is on the Canadian East Coast in the Province of Québec. In 2015 a creel survey for striped bass was conducted in this peninsula as recreational striped bass fishing had just been reintroduced after a long moratorium.

The study area, presented in Figure 3.1, is scattered over more than 250 kms, on the Gaspé Peninsula coast. The survey is carried out by a single wildlife agent; it is not possible for him to visit two distant sites on the same day. For that reason, neighboring sites are grouped into three sectors as shown in Figure 3.1. We consider the survey for the 33 holidays. The survey variable is the fishing effort, in number of hours of fishing. As some sites attract more fishermen than others, the number of visits to site l MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaWGSbaaaa@3276@ of sector i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaWGPbaaaa@3273@ has to be proportional to its importance x i l MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaWG4bWaaSbaaSqaaiaadMgacaWGSb aabeaaaaa@348D@ as given in Table 3.1. In addition, for the purpose of the survey, a day is divided into three periods (AM, PM, EV), where EV stands for evening, and six subperiods (AM1, AM2, PM1, PM2, and EV1, EV2). For instance AM1 goes from 8:00 to 10:00 while AM2 is from 10:00 to 12:00. A working day contains two periods and four subperiods. For instance if the agent works AM and PM, then he has a free evening. Thus during a working day he is able to visit four sites, two per working period.

The survey population on a day consists of 54 quadruplets, ( sector × period × subperiod × site ) , MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaabohacaqGLbGaae4yai aabshacaqGVbGaaeOCaiaaysW7caqGxdGaaGjbVlaabchacaqGLbGa aeOCaiaabMgacaqGVbGaaeizaiaaysW7caqGxdGaaGjbVlaabohaca qG1bGaaeOyaiaabchacaqGLbGaaeOCaiaabMgacaqGVbGaaeizaiaa ysW7caqGxdGaaGjbVlaabohacaqGPbGaaeiDaiaabwgaaiaawIcaca GLPaaacaGGSaaaaa@587A@ 4 of which are sampled. To denote population units the following indices are useful:

  1. h = 1, , H = 33 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaWGObGaaGypaiaaigdacaaISaGaeS OjGSKaaGilaiaadIeacaaI9aGaaG4maiaaiodaaaa@3990@ represents the days;
  2. i = 1,2,3 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaWGPbGaaGypaiaaigdacaaISaGaaG OmaiaaiYcacaaIZaaaaa@36DA@ stands for the sectors in Figure 3.1;
  3. j = 1,2,3 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaWGQbGaaGypaiaaigdacaaISaGaaG OmaiaaiYcacaaIZaaaaa@36DB@ denotes a period within a day;
  4. k = 1,2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaWGRbGaaGypaiaaigdacaaISaGaaG Omaaaa@3569@ represents the subperiods within a period;
  5. l = 1,2,3 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaWGSbGaaGypaiaaigdacaaISaGaaG OmaiaaiYcacaaIZaaaaa@36DD@ represents the sites, see Figure 3.1, within a sector.

The goal is to estimate the fishing effort for combination of subperiod (6 levels) and site (9 levels). We want to plan a survey with a predetermined sample size for the 54 cells of the cross-classified table. The basic selection probabilities are

π h i j k l = 2 x i l 3 x , ( 3.1 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacqaHapaCdaWgaaWcbaGaamiAaiaadM gacaWGQbGaam4AaiaadYgaaeqaaOGaaGypamaalaaabaGaaGOmaiaa dIhadaWgaaWcbaGaamyAaiaadYgaaeqaaaGcbaGaaG4maiaadIhada WgaaWcbaGaeyOiGCRaeyOiGClabeaaaaGccaaISaGaaGzbVlaaywW7 caaMf8UaaGzbVlaaywW7caGGOaGaaG4maiaac6cacaaIXaGaaiykaa aa@4DC0@

where replacing i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaWGPbaaaa@3273@ or l MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaWGSbaaaa@3276@ by MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacqGHIaYTaaa@330A@ means that a summation is taken on the corresponding index. Observe that the sum of π h i j k l MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacqaHapaCdaWgaaWcbaGaamiAaiaadM gacaWGQbGaam4AaiaadYgaaeqaaaaa@3819@ over the indices ( i , j , k , l ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaaIOaGaamyAaiaaiYcacaWGQbGaaG ilaiaadUgacaaISaGaamiBaiaaiMcaaaa@38CA@ is equal to 4, the number of units visited by the wildlife technician on a single day.

At a first glance, the sample could possibly be drawn in a single stage using selection probabilities (3.1) by balancing on the 54 site by subperiod indicator variables. This is not feasible because of operational constraints. The first one is that on a single day the technician visits sites from the same sector to limit the traveling between sites. The second constraint is that on a working day the technician is off duty for the two subperiods of the same period. In order to meet these operational constraints we propose, in the next section, a design having three levels of sampling where sectors are selected at level 1, periods are selected at level 2 and sites are selected at level 3.

Figure 3.1 of article 54954 issue 2018002

Description for Figure 3.1

Geographical map showing the nine sites to be surveyed for striped bass. The map is divided in three sectors: East, Centre and West. There are three surveyed sites in each sector. In the East sector, there are Boom Défense, E. St-Jean and Barachois. In the Centre sector, there are Ste-T. de Gaspé, Chandler and Malbaie. In the West sector, there are Bonaventure, P. Henderson and C. Carleton.

Table 3.1
Average and expected number of visits to each site
Table summary
This table displays the results of Average and expected number of visits to each site. The information is grouped by Sector (appearing as row headers), Site and (équation) (appearing as column headers).
Sector Site x i l MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeqabeqadiWa ceGabeqabeqabeqadeaakeaacaWG4bWaaSbaaSqaaiaadMgacaWGSb aabeaaaaa@36BA@ E ( n i l ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeqabeqadiWa ceGabeqabeqabeqadeaakeaacaWGfbWaaeWaaeaacaWGUbWaaSbaaS qaaiaadMgacaWGSbaabeaaaOGaayjkaiaawMcaaaaa@390D@ n ¯ i l MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeqabeqadiWa ceGabeqabeqabeqadeaakeaaceWGUbGbaebadaWgaaWcbaGaamyAai aadYgaaeqaaaaa@36C8@ Sd n i l MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeqabeqadiWa ceGabeqabeqabeqadeaakeaacaqGtbGaaeizamaaBaaaleaacaWGUb WaaSbaaWqaaiaadMgacaWGSbaabeaaaSqabaaaaa@38A5@
East ( i = 1 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadMgacaaI9aGaaGymaa GaayjkaiaawMcaaaaa@37A1@ Boom Défense ( l = 1 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadYgacqGH9aqpcaaIXa aacaGLOaGaayzkaaaaaa@37E3@ 2 20.308 20.286 0.850
E. St-Jean ( l = 2 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadYgacqGH9aqpcaaIXa aacaGLOaGaayzkaaaaaa@37E3@ 1 10.154 10.153 0.621
Barachois ( l = 3 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadYgacqGH9aqpcaaIXa aacaGLOaGaayzkaaaaaa@37E3@ 2 20.308 20.296 0.881
Centre ( i = 2 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadMgacaaI9aGaaGymaa GaayjkaiaawMcaaaaa@37A1@ Ste-T. de Gaspé ( l = 4 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadYgacqGH9aqpcaaIXa aacaGLOaGaayzkaaaaaa@37E3@ 1 10.154 10.176 0.865
Malbaie ( l = 5 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadYgacqGH9aqpcaaIXa aacaGLOaGaayzkaaaaaa@37E3@ 1 10.154 10.155 0.880
Chandler ( l = 6 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadYgacqGH9aqpcaaIXa aacaGLOaGaayzkaaaaaa@37E3@ 1 10.154 10.162 0.881
West ( i = 3 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadMgacaaI9aGaaGymaa GaayjkaiaawMcaaaaa@37A1@ Bonaventure ( l = 7 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadYgacqGH9aqpcaaIXa aacaGLOaGaayzkaaaaaa@37E3@ 2 20.308 20.311 1.004
P. Henderson ( l = 8 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadYgacqGH9aqpcaaIXa aacaGLOaGaayzkaaaaaa@37E3@ 1 10.154 10.153 0.681
C. Carleton ( l = 9 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadYgacqGH9aqpcaaIXa aacaGLOaGaayzkaaaaaa@37E3@ 2 20.308 20.309 1.016

3.1  A balanced multi-stage design for creel survey

This section describes the three stages of the survey that ensures that the operational constraints presented in the previous section are met. It also gives, for each stage, the balancing variables.

The first stage is stratified by day; for each day a single sector is drawn with selection probabilities x i / x . MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaWcgaqaaiaadIhadaWgaaWcbaGaam yAaiabgkci3cqabaaakeaacaWG4bWaaSbaaSqaaiabgkci3kabgkci 3cqabaaaaOGaaiOlaaaa@3A30@ At level two, for each sector selected at level 1, two periods are selected out of 3 using simple random sampling (i.e., with selection probabilities 2/3). At level three, a sector*period is stratified by subperiod and one site is selected for each subperiod, the selection probabilities are x i l / x i . MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaWcgaqaaiaadIhadaWgaaWcbaGaam yAaiaadYgaaeqaaaGcbaGaamiEamaaBaaaleaacaWGPbGaeyOiGCla beaaaaGccaGGUaaaaa@3905@ In summary the selection probabilities at the three levels are

π h i ( 1 ) = x i x , π j | i ( 2 ) = 2 3 , π l | i j k ( 3 ) = x i l x i . MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacqaHapaCdaqhaaWcbaGaamiAaiaadM gaaeaadaqadaqaaiaaigdaaiaawIcacaGLPaaaaaGccaaI9aWaaSaa aeaacaWG4bWaaSbaaSqaaiaadMgacqGHIaYTaeqaaaGcbaGaamiEam aaBaaaleaacqGHIaYTcqGHIaYTaeqaaaaakiaaiYcacaaMf8UaeqiW da3aa0baaSqaamaaeiaabaGaamOAaiaayIW7aiaawIa7aiaayIW7ca WGPbaabaWaaeWaaeaacaaIYaaacaGLOaGaayzkaaaaaOGaaGypamaa laaabaGaaGOmaaqaaiaaiodaaaGaaGilaiaaywW7cqaHapaCdaqhaa WcbaWaaqGaaeaacaWGSbGaaGjcVdGaayjcSdGaaGjcVlaadMgacaWG QbGaam4AaaqaamaabmaabaGaaG4maaGaayjkaiaawMcaaaaakiaai2 dadaWcaaqaaiaadIhadaWgaaWcbaGaamyAaiaadYgaaeqaaaGcbaGa amiEamaaBaaaleaacaWGPbGaeyOiGClabeaaaaGccaaIUaaaaa@66EE@

As expected the product π h i ( 1 ) × π j | i ( 2 ) × π l | i j k ( 3 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacqaHapaCdaqhaaWcbaGaamiAaiaadM gaaeaadaqadaqaaiaaigdaaiaawIcacaGLPaaaaaGccqGHxdaTcqaH apaCdaqhaaWcbaWaaqGaaeaacaWGQbGaaGjcVdGaayjcSdGaaGjcVl aadMgaaeaadaqadaqaaiaaikdaaiaawIcacaGLPaaaaaGccqGHxdaT cqaHapaCdaqhaaWcbaWaaqGaaeaacaWGSbGaaGjcVdGaayjcSdGaaG jcVlaadMgacaWGQbGaam4AaaqaamaabmaabaGaaG4maaGaayjkaiaa wMcaaaaaaaa@533A@ is equal to (3.1), the target selection probability.

The goal is still to get a sample with predetermined sample sizes for the 54 site by subperiod combinations. Thus balanced sampling needs to be implemented at each stage. At level 1 we need to balance on the indicator variables for the three sectors while at level 2 balancing on the 9 indicator variables for the sector by period combinations is needed. Balancing at level 3 is slightly more complicated as it involves several strata.

At level 2, 33 × 2 = 66 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaaIZaGaaG4maiabgEna0kaaikdaca aI9aGaaGOnaiaaiAdaaaa@3819@ sector*periods have been selected. Each one is stratified by subperiod so we are facing 132 strata at level 3 and one site is selected from each one. Balancing is needed with respect to the 54 site by subperiod indicator functions. This is a complex problem and the balancing constraints (2.3) involve the inverse of a large variance covariance matrix. Thus to implement a rejective algorithm in this context one would need an alternative to criterion (2.3) for accepting a sample. For now we discuss the implementation of balanced sampling for this design with the cube method. Comparisons between the cube method and rejective sampling in the context of a simplified creel survey are presented in Section 4.

Among the 132 third stage strata, the number of strata for one subperiod, say AM2, in sector i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaWGPbaaaa@3273@ is an integer close to 22 x i / x MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaWcgaqaaiaaikdacaaIYaGaamiEam aaBaaaleaacaWGPbGaeyOiGClabeaaaOqaaiaadIhadaWgaaWcbaGa eyOiGCRaeyOiGClabeaaaaaaaa@3AEC@ that depends on the stage 2 sample. This integer plays the role of i = 1 N I i ( ω ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaaeWaqaaiaadMeadaWgaaWcbaGaam yAaaqabaGcdaqadaqaaiabeM8a3bGaayjkaiaawMcaaaWcbaGaamyA aiaai2dacaaIXaaabaGaamOtaaqdcqGHris5aaaa@3C12@ in equation (2.2) for balancing the sites of sector i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaWGPbaaaa@3273@ at stage 3 while, for the l th MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaWGSbWaaWbaaSqabeaacaqG0bGaae iAaaaaaaa@3485@ site, the probability in (2.2) is π ω = x i l / x i . MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacqaHapaCdaWgaaWcbaGaeqyYdChabe aakiaai2dadaWcgaqaaiaadIhadaWgaaWcbaGaamyAaiaadYgaaeqa aaGcbaGaamiEamaaBaaaleaacaWGPbGaeyOiGClabeaaaaGccaGGUa aaaa@3D8C@ The stage 3 calibration equations for the 54 site by subperiod indicator functions can be described in a similar way. Clearly, it is not possible to meet exactly the 54 balancing equations and the cube method will give a sample that is approximately balanced.

The approximation occurs at the landing phase of the algorithm where balancing constraints are dropped in order to complete the selection of the sample, as introduced in Deville and Tillé (2004). As the stage 3 sample is highly stratified, we use the implementation of the landing phase in the function balancedstratification2 developed in Hasler and Tillé (2014), with a small correction that prevents it from stopping when the sample is already balanced at the start of the landing phase. In the matrix of balancing constraints, the site constraints were given more importance than those which make visits to each site equally distributed among subperiods at level 3. They were the last ones to be dropped at the landing phase of the cube method.

To investigate how a failure to meet all balancing equations impacted the sample design, we generated B = 10,000 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaWGcbGaaGypaiaabgdacaqGWaGaae ilaiaabcdacaqGWaGaaeimaaaa@3742@ random replications of the balanced sample. The number of visits n i l MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaWGUbWaaSbaaSqaaiaadMgacaWGSb aabeaaaaa@3483@ to site ( i , l ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadMgacaaISaGaamiBaa GaayjkaiaawMcaaaaa@35A3@ was noted. Table 3.1 compares the average n ¯ i l MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaaceWGUbGbaebadaWgaaWcbaGaamyAai aadYgaaeqaaaaa@349B@ of n i l MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaWGUbWaaSbaaSqaaiaadMgacaWGSb aabeaaaaa@3483@ over the Monte Carlo replications,

n ¯ i l = 1 B b = 1 B n i l ( r ) , MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaaceWGUbGbaebadaWgaaWcbaGaamyAai aadYgaaeqaaOGaaGypamaalaaabaGaaGymaaqaaiaadkeaaaWaaabC aeaacaWGUbWaa0baaSqaaiaadMgacaWGSbaabaWaaeWaaeaacaWGYb aacaGLOaGaayzkaaaaaaqaaiaadkgacaaI9aGaaGymaaqaaiaadkea a0GaeyyeIuoakiaacYcaaaa@429D@

to its expectation, E ( n i l ) . MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaWGfbWaaeWaaeaacaWGUbWaaSbaaS qaaiaadMgacaWGSbaabeaaaOGaayjkaiaawMcaaiaac6caaaa@3792@ For all practical purposes, the two are equal and a failure to meet some balancing equations has no impact on the site selection probabilities. Table 3.1 also reports the standard deviations

Sd n i l = { 1 B 1 b = 1 B ( n i l ( b ) n ¯ i l ) 2 } 1 / 2 . ( 3.2 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaqGtbGaaeizamaaBaaaleaacaWGUb WaaSbaaWqaaiaadMgacaWGSbaabeaaaSqabaGccaaI9aWaaiWaaeaa daWcaaqaaiaaigdaaeaacaWGcbGaeyOeI0IaaGymaaaadaaeWbqaam aabmaabaGaamOBamaaDaaaleaacaWGPbGaamiBaaqaamaabmaabaGa amOyaaGaayjkaiaawMcaaaaakiabgkHiTiqad6gagaqeamaaBaaale aacaWGPbGaamiBaaqabaaakiaawIcacaGLPaaadaahaaWcbeqaaiaa ikdaaaaabaGaamOyaiaai2dacaaIXaaabaGaamOqaaqdcqGHris5aa GccaGL7bGaayzFaaWaaWbaaSqabeaadaWcgaqaaiaaigdaaeaacaaI YaaaaaaakiaaygW7caaIUaGaaGzbVlaaywW7caaMf8UaaGzbVlaayw W7caGGOaGaaG4maiaac6cacaaIYaGaaiykaaaa@5D6C@

Most of the standard deviations are less than 1 in Table 3.1. Thus the absolute differences between target and realized sample sizes are less than or equal to 2 for most Monte Carlo samples.

Table 3.2 gives the expected number of visits in the 6 subperiods; they are all equal to 22, up to two decimal points, with standard deviations less than 0.2. Thus the period and subperiod constraints are met. Table 3.3 gives a realized sample for the first five days of the creel survey. It shows a harmonious permutation of sectors at level 1, periods at level 2, and sites at level 3 through the days because of the way in which the sample design was constructed. Given a balanced sample produced by the cube algorithm, an arbitrary permutation of the days gives an alternative balanced sample. Indeed the sampling design is invariant to a relabeling of the days. For instance, with the sample of Table 3.3 the technician has to travel from the western to the eastern sector between days 4 and 5. To avoid this long trip one could interchange days 1 and 5: the first two days would then be spent in the eastern sector and between days 4 and 5 the technician would travel from the western to the central sector. The alternative and the original samples have the same estimated totals for the calibration variables.

Table 3.2
Average and expected number of visits at each subperiod
Table summary
This table displays the results of Average and expected number of visits at each subperiod. The information is grouped by Period (appearing as row headers), Subperiod and (équation) (appearing as column headers).
Period Subperiod E ( n j k ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeqabeqadiWa ceGabeqabeqabeqadeaakeaacaWGfbWaaeWaaeaacaWGUbWaaSbaaS qaaiaadQgacaWGRbaabeaaaOGaayjkaiaawMcaaaaa@390D@ n ¯ j k MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeqabeqadiWa ceGabeqabeqabeqadeaakeaaceWGUbGbaebadaWgaaWcbaGaamOAai aadUgaaeqaaaaa@36C8@ Sd n j k MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeqabeqadiWa ceGabeqabeqabeqadeaakeaacaqGtbGaaeizamaaBaaaleaacaWGUb WaaSbaaWqaaiaadQgacaWGRbaabeaaaSqabaaaaa@38A5@
Morning ( j = 1 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadQgacaaI9aGaaGymaa GaayjkaiaawMcaaaaa@37A2@ 8h00-10h00 ( k = 1 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadUgacaaI9aGaaGymaa GaayjkaiaawMcaaaaa@37A3@ 22 22.000 0.000
10h00-12h00 ( k = 2 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadUgacaaI9aGaaGymaa GaayjkaiaawMcaaaaa@37A3@ 22 22.000 0.000
Afternoon ( j = 2 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadQgacaaI9aGaaGymaa GaayjkaiaawMcaaaaa@37A2@ 12h00-15h00 ( k = 3 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadUgacaaI9aGaaGymaa GaayjkaiaawMcaaaaa@37A3@ 22 21.999 0.184
15h00-18h00 ( k = 4 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadUgacaaI9aGaaGymaa GaayjkaiaawMcaaaaa@37A3@ 22 21.999 0.184
Evening ( j = 3 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadQgacaaI9aGaaGymaa GaayjkaiaawMcaaaaa@37A2@ 18h00-20h30 ( k = 5 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadUgacaaI9aGaaGymaa GaayjkaiaawMcaaaaa@37A3@ 22 22.001 0.184
20h30-23h00 ( k = 6 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadUgacaaI9aGaaGymaa GaayjkaiaawMcaaaaa@37A3@ 22 22.001 0.184
Table 3.3
Units selected in a balanced sample for the first five days
Table summary
This table displays the results of Units selected in a balanced sample for the first five days. The information is grouped by H (appearing as row headers), Sector, Period, Subperiod and Site (appearing as column headers).
H Sector Period Subperiod Site
1 Centre ( i = 2 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadMgacaaI9aGaaGOmaa GaayjkaiaawMcaaaaa@37A2@ Afternoon ( j = 2 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadQgacaaI9aGaaGOmaa GaayjkaiaawMcaaaaa@37A3@ 12h-15h ( k = 3 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadUgacaaI9aGaaG4maa GaayjkaiaawMcaaaaa@37A5@ Chandler ( l = 6 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadYgacaaI9aGaaGOnaa GaayjkaiaawMcaaaaa@37A9@
15h-18h ( k = 4 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadUgacaaI9aGaaG4maa GaayjkaiaawMcaaaaa@37A5@ Malbaie ( l = 5 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadYgacaaI9aGaaGOnaa GaayjkaiaawMcaaaaa@37A9@
Evening ( j = 3 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadQgacaaI9aGaaGOmaa GaayjkaiaawMcaaaaa@37A3@ 18h-20h30 ( k = 5 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadUgacaaI9aGaaG4maa GaayjkaiaawMcaaaaa@37A5@ Chandler ( l = 6 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadYgacaaI9aGaaGOnaa GaayjkaiaawMcaaaaa@37A9@
20h30-23h ( k = 6 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadUgacaaI9aGaaG4maa GaayjkaiaawMcaaaaa@37A5@ Ste-T. de Gaspé ( l = 4 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadYgacaaI9aGaaGOnaa GaayjkaiaawMcaaaaa@37A9@
2 East ( i = 1 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadMgacaaI9aGaaGOmaa GaayjkaiaawMcaaaaa@37A2@ Morning ( j = 1 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadQgacaaI9aGaaGOmaa GaayjkaiaawMcaaaaa@37A3@ 8h-10h ( k = 1 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadUgacaaI9aGaaG4maa GaayjkaiaawMcaaaaa@37A5@ E. St-Jean ( l = 2 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadYgacaaI9aGaaGOnaa GaayjkaiaawMcaaaaa@37A9@
10h-12h ( k = 2 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadUgacaaI9aGaaG4maa GaayjkaiaawMcaaaaa@37A5@ Boom Défense ( l = 1 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadYgacaaI9aGaaGOnaa GaayjkaiaawMcaaaaa@37A9@
Evening ( j = 3 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadQgacaaI9aGaaGOmaa GaayjkaiaawMcaaaaa@37A3@ 18h-20h30 ( k = 5 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadUgacaaI9aGaaG4maa GaayjkaiaawMcaaaaa@37A5@ Barachois ( l = 3 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadYgacaaI9aGaaGOnaa GaayjkaiaawMcaaaaa@37A9@
20h30-23h ( k = 6 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadUgacaaI9aGaaG4maa GaayjkaiaawMcaaaaa@37A5@ E. St-Jean ( l = 2 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadYgacaaI9aGaaGOnaa GaayjkaiaawMcaaaaa@37A9@
3 Centre ( i = 2 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadMgacaaI9aGaaGOmaa GaayjkaiaawMcaaaaa@37A2@ Morning ( j = 1 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadQgacaaI9aGaaGOmaa GaayjkaiaawMcaaaaa@37A3@ 8h-10h ( k = 1 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadUgacaaI9aGaaG4maa GaayjkaiaawMcaaaaa@37A5@ Malbaie ( l = 5 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadYgacaaI9aGaaGOnaa GaayjkaiaawMcaaaaa@37A9@
10h-12h ( k = 2 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadUgacaaI9aGaaG4maa GaayjkaiaawMcaaaaa@37A5@ Ste-T. de Gaspé ( l = 4 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadYgacaaI9aGaaGOnaa GaayjkaiaawMcaaaaa@37A9@
Afternoon ( j = 2 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadQgacaaI9aGaaGOmaa GaayjkaiaawMcaaaaa@37A3@ 12h-15h ( k = 3 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadUgacaaI9aGaaG4maa GaayjkaiaawMcaaaaa@37A5@ Malbaie ( l = 5 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadYgacaaI9aGaaGOnaa GaayjkaiaawMcaaaaa@37A9@
15h-18h ( k = 4 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadUgacaaI9aGaaG4maa GaayjkaiaawMcaaaaa@37A5@ Chandler ( l = 6 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadYgacaaI9aGaaGOnaa GaayjkaiaawMcaaaaa@37A9@
4 West ( i = 3 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadMgacaaI9aGaaGOmaa GaayjkaiaawMcaaaaa@37A2@ Morning ( j = 1 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadQgacaaI9aGaaGOmaa GaayjkaiaawMcaaaaa@37A3@ 8h-10h ( k = 1 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadUgacaaI9aGaaG4maa GaayjkaiaawMcaaaaa@37A5@ P. Henderson ( l = 8 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadYgacaaI9aGaaGOnaa GaayjkaiaawMcaaaaa@37A9@
10h-12h ( k = 2 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadUgacaaI9aGaaG4maa GaayjkaiaawMcaaaaa@37A5@ Bonaventure ( l = 7 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadYgacaaI9aGaaGOnaa GaayjkaiaawMcaaaaa@37A9@
Afternoon ( j = 2 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadQgacaaI9aGaaGOmaa GaayjkaiaawMcaaaaa@37A3@ 12h-15h ( k = 3 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadUgacaaI9aGaaG4maa GaayjkaiaawMcaaaaa@37A5@ C. Carleton ( l = 9 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadYgacaaI9aGaaGOnaa GaayjkaiaawMcaaaaa@37A9@
15h-18h ( k = 4 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadUgacaaI9aGaaG4maa GaayjkaiaawMcaaaaa@37A5@ C. Carleton ( l = 9 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadYgacaaI9aGaaGOnaa GaayjkaiaawMcaaaaa@37A9@
5 East ( i = 1 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadMgacaaI9aGaaGOmaa GaayjkaiaawMcaaaaa@37A2@ Afternoon ( j = 2 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadQgacaaI9aGaaGOmaa GaayjkaiaawMcaaaaa@37A3@ 12h-15h ( k = 3 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadUgacaaI9aGaaG4maa GaayjkaiaawMcaaaaa@37A5@ Boom Défense ( l = 1 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadYgacaaI9aGaaGOnaa GaayjkaiaawMcaaaaa@37A9@
15h-18h ( k = 4 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadUgacaaI9aGaaG4maa GaayjkaiaawMcaaaaa@37A5@ Barachois ( l = 3 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadYgacaaI9aGaaGOnaa GaayjkaiaawMcaaaaa@37A9@
Evening ( j = 3 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadQgacaaI9aGaaGOmaa GaayjkaiaawMcaaaaa@37A3@ 18h-20h30 ( k = 5 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadUgacaaI9aGaaG4maa GaayjkaiaawMcaaaaa@37A5@ Boom Défense ( l = 1 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadYgacaaI9aGaaGOnaa GaayjkaiaawMcaaaaa@37A9@
20h30-23h ( k = 6 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadUgacaaI9aGaaG4maa GaayjkaiaawMcaaaaa@37A5@ Barachois ( l = 3 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacPqpw0le9 v8qqaqFD0xXdHaVhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadYgacaaI9aGaaGOnaa GaayjkaiaawMcaaaaa@37A9@

3.2  Estimation of the fishing effort and of its variance

Once the survey is completed, the sample is a set of site × MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacqGHxdaTaaa@339C@ subperiod { ( h , i , j , k , l ) } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaGadaqaamaabmaabaGaamiAaiaaiY cacaWGPbGaaGilaiaadQgacaaISaGaam4AaiaaiYcacaWGSbaacaGL OaGaayzkaaaacaGL7bGaayzFaaaaaa@3CC2@ with sampling weights equal to the inverse of the selection probabilities given in (3.1). As the balancing equations for the 54 cells of the site by subperiod cross-classified table are not met exactly, we propose, following Deville and Tillé (2004), calibrating the survey weights on the total, H , MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaWGibGaaiilaaaa@3302@ of the indicator variables for these 54 cells. All the sampled units in cell ( i , j , k , l ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadMgacaaISaGaamOAai aaiYcacaWGRbGaaGilaiaadYgaaiaawIcacaGLPaaaaaa@38EE@ have the same weight, namely 1 / π i j k l MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaWcgaqaaiaaigdaaeaacqaHapaCda WgaaWcbaGaamyAaiaadQgacaWGRbGaamiBaaqabaaaaaaa@37FD@ where π i j k l = π h i j k l , MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacqaHapaCdaWgaaWcbaGaamyAaiaadQ gacaWGRbGaamiBaaqabaGccaaI9aGaeqiWda3aaSbaaSqaaiaadIga caWGPbGaamOAaiaadUgacaWGSbaabeaakiaacYcaaaa@3F4B@ defined in (3.1), does not depend on h . MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaWGObGaaiOlaaaa@3324@ The calibrated weight for a sampled unit in cell ( i , j , k , l ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadMgacaaISaGaamOAai aaiYcacaWGRbGaaGilaiaadYgaaiaawIcacaGLPaaaaaa@38EE@ is

w i j k l ( c ) = 1 π i j k l × H n i j k l / π i j k l = H n i j k l , MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaWG3bWaa0baaSqaaiaadMgacaWGQb Gaam4AaiaadYgaaeaadaqadaqaaiaadogaaiaawIcacaGLPaaaaaGc caaI9aWaaSaaaeaacaaIXaaabaGaeqiWda3aaSbaaSqaaiaadMgaca WGQbGaam4AaiaadYgaaeqaaaaakiabgEna0oaalaaabaGaamisaaqa amaalyaabaGaamOBamaaBaaaleaacaWGPbGaamOAaiaadUgacaWGSb aabeaaaOqaaiabec8aWnaaBaaaleaacaWGPbGaamOAaiaadUgacaWG SbaabeaaaaaaaOGaaGypamaalaaabaGaamisaaqaaiaad6gadaWgaa WcbaGaamyAaiaadQgacaWGRbGaamiBaaqabaaaaOGaaGilaaaa@550C@

where n i j k l MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaWGUbWaaSbaaSqaaiaadMgacaWGQb Gaam4AaiaadYgaaeqaaaaa@3662@ is the sample size for cell ( i , j , k , l ) ; MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadMgacaaISaGaamOAai aaiYcacaWGRbGaaGilaiaadYgaaiaawIcacaGLPaaacaGG7aaaaa@39AD@ it is the number of days for which site l MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaWGSbaaaa@3276@ of sector i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaWGPbaaaa@3273@ has been visited during subperiod k MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaWGRbaaaa@3275@ of period j . MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaWGQbGaaiOlaaaa@3326@ In general n i j k l MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaWGUbWaaSbaaSqaaiaadMgacaWGQb Gaam4AaiaadYgaaeqaaaaa@3662@ is a random variable. When the samples are perfectly balanced, (2.2) implies that n i j k l = H π i j k l ; MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaWGUbWaaSbaaSqaaiaadMgacaWGQb Gaam4AaiaadYgaaeqaaOGaaGypaiaadIeacqaHapaCdaWgaaWcbaGa amyAaiaadQgacaWGRbGaamiBaaqabaGccaGG7aaaaa@3E70@ the calibrated and basic weights are then equal. Now if y h i j k l MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaWG5bWaaSbaaSqaaiaadIgacaWGPb GaamOAaiaadUgacaWGSbaabeaaaaa@375A@ represents the fishing effort for population unit ( h , i , j , k , l ) , MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadIgacaaISaGaamyAai aaiYcacaWGQbGaaGilaiaadUgacaaISaGaamiBaaGaayjkaiaawMca aiaacYcaaaa@3B41@ the fishing effort in cell ( i , j , k , l ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadMgacaaISaGaamOAai aaiYcacaWGRbGaaGilaiaadYgaaiaawIcacaGLPaaaaaa@38EE@ is Y U i j k l = h y h i j k l . MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaWGzbWaaSbaaSqaaiaadwfacaWGPb GaamOAaiaadUgacaWGSbaabeaakiaai2dadaaeqaqaaiaadMhadaWg aaWcbaGaamiAaiaadMgacaWGQbGaam4AaiaadYgaaeqaaaqaaiaadI gaaeqaniabggHiLdGccaGGUaaaaa@414E@ Its calibrated estimator is Y ^ i j k l = H y ¯ s i j k l MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaaceWGzbGbaKaadaWgaaWcbaGaamyAai aadQgacaWGRbGaamiBaaqabaGccaaI9aGaamisaiaayIW7ceWG5bGb aebadaWgaaWcbaGaam4CaiaadMgacaWGQbGaam4AaiaadYgaaeqaaa aa@3F84@ where y ¯ s i j k l MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaaceWG5bGbaebadaWgaaWcbaGaam4Cai aadMgacaWGQbGaam4AaiaadYgaaeqaaaaa@377D@ is the average fishing effort for the n i j k l MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaWGUbWaaSbaaSqaaiaadMgacaWGQb Gaam4AaiaadYgaaeqaaaaa@3662@ units sampled for that cell of the cross classified table. An estimator for the total fishing effort is obtained by summing the cells’ estimated totals.

The evaluation of a design based variance estimator for the calibrated estimator of the total fishing effort is complex. A simple variance estimator for the estimated total for a single cell of the cross-classified table is available. The sample of days selected for cell ( i , j , k , l ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaadaqadaqaaiaadMgacaaISaGaamOAai aaiYcacaWGRbGaaGilaiaadYgaaiaawIcacaGLPaaaaaa@38EE@ is a Bernoulli sample with selection probabilities π i j k l , MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacqaHapaCdaWgaaWcbaGaamyAaiaadQ gacaWGRbGaamiBaaqabaGccaGGSaaaaa@37E6@ neglecting the balancing constraints. Thus by conditioning on the sample size, n i j k l , MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaWGUbWaaSbaaSqaaiaadMgacaWGQb Gaam4AaiaadYgaaeqaaOGaaiilaaaa@371C@ Y ^ i j k l MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaaceWGzbGbaKaadaWgaaWcbaGaamyAai aadQgacaWGRbGaamiBaaqabaaaaa@365D@ is H MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8rrps0l bbf9q8WrFfeuY=Hhbbf9y8WrFv0dc9vqFj0db9qqvqFr0dXdHiVc=b YP0xH8peuj0dYddrpe0db9Wqpepic9Lr=xfr=xfr=xmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaWGibaaaa@3252@ times the sample mean of a simple random sample. It is a design-unbiased estimator whose variance can be estimated using the formula for the variance of an estimated total in a simple random sampling design. We claim that these results are still valid when the balancing constraints are taken into account since the balanced sample design is invariant to a relabelling of the days. The estimated fishing efforts for the 54 cells of the cross-classified table are however dependent and it seems difficult to come up with a conditionally unbiased design based variance estimator for their total. A model based estimator seems to be only approach available for this total.

For the survey actually conducted in 2015, the methods used to estimate fishing effort and total catch are among those proposed in Pollock et al. (1994). It was a roving survey and the fishing effort at a sampled site was calculated as the average number of anglers on the site during the subperiod times the length, in hours, of the subperiod. Fishing efforts were estimated using calibrated weights; additional results are available in (Daigle, Crépeau, Bujold and Legault, 2015).


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