11.1 Introduction
11.2 Deck sampling methods
In chapter 10 we discussed the sampling aspect of trawling surveys for total biomass estimates. The next information required is the species composition of the catch. Deck sampling serves this purpose (composition of the catch).
The catch rarely consists of one species and if it is taken with a bottom trawl it may contain a large variety of fish. Because of the mechanical segregation of the gear fish on deck tend to be segregated by size (largest at the outer edges or top of the pile, smallest at the bottom). Large fish are kept separately and completely enumerated (census approach). Deck sampling is conducted for estimating qualitative and quantitative characteristics of the smallest fish.^{1}
^{1} Through deck sampling estimates are also be calculated of the length composition of the catch.
11.2.1 Direct sampling for proportions
11.2.2 Cluster sampling for proportions
11.2.3 Multistage sampling for proportions
The sampling methods used for species composition can be grouped under the following headings.^{2}
SM1: Direct sampling for proportionsEstimates can be calculated either by taking the specimen as the survey unit, in such a case proportions will be calculated on the basis of number of fish, or by introducing the meaning of the “statistical unit” which is defined as equal to 1 kg of fish, in this case proportions will be calculated on the basis of weight of fish. For our estimates below the latter unit of measurement was taken into account.
SM2: Cluster sampling for proportions
SM3: Multistage sampling for proportions^{2} For small catches the method of complete enumeration (census approach) is employed.
11.2.1.1 More than one haul
Suppose the population (threedimensional pile of smallest fish on deck) consists of _{h}M statistical units (kg, h: stands for a given haul) and a simple random sample of _{h}m statistical units is selected from the population without replacement.^{3}(SWR)
^{3} In practice one selection procedure used is defined by, mixing, dividing and random choice. This is because of the mechanical segregation of the gear, the population of fish on deck is not in random order; see Bazigos, G.P. (1973): Deck Sampling, UNDP/SF/MLW.16, 39 p.If the number of statistical units falling in the i^{th} speciesdomain in the population is _{h}M_{i} and _{h}m_{i} in the sample, an estimate of the proportion of statistical units in the population failing in the i^{th} speciesdomain is denoted by _{h}p_{i}, so that
(1) _{h}p_{i} = _{h}m_{i}/_{h}m
The estimated variance of p is given (SWR) by,
(2) , where _{h}q_{i} = 1  _{h}p_{i}
If _{h}M is large relative to _{h}m, and this is the case in practice, formula (2) is simplified as follows
(2a)
In calculating confidence limits it is worthwhile to amend the above formula by inserting a correction for continuity. Specifically, the calculated confidence limits for a given probability level are
(3)
(4)
If more than one haul has been conducted in a given area, e.g., space/depth domain, the sample data should be tested for homogeneity (X^{2}test) before pooling together.
For calculation purposes a general contingency table containing rrows (species or species groups, i = 1, 2,..., r) and ccolumns (number of sample tows, h = 1, 2,..., c) is used. The X  value is estimated^{4} by
where
_{h}m_{i}: number of statistical units (kg) in the h^{th} haul of species i^{th}The estimated X^{2} value is compared with the tabulated . The hypothesis is valid if X^{2} < ; the hypothesis is discredited if X^{2} > .
=: probability that a statistical unit will be a member of the i^{th} row
: probability that a statistical unit will be a member of the h^{th} column^{4} See Bazigos, G.P. (1974) Applied fishery statistics. FAO Fish.Tech.Pap., (135):164 p.
Example
The table below provides the obtained sample data of a deck sampling conducted in a survey area for estimating the species composition of the survey stocks. The sample data are expressed in statistical units (kg). Estimate the confidence limits for the population proportions (a = 5%).
Groups of species(i) 
Empirical values 
Theoretical values 

Hauls (h, kg) 
Marginal totals 
Hauls (h, kg) 
Marginal totals 

1 
2 
3 
1 
2 
3 

GS  1 
34 
23 
15 
72 
30.00 
24.00 
18.00 
72 
 2 
8 
6 
5 
19 
7.92 
6.33 
4.75 
19 
 3 
1 
2 
3 
6 
2.50 
2.00 
1.50 
6 
 4 
3 
4 
4 
11 
4.58 
3.67 
2.75 
11 
 5 
4 
5 
3 
12 
5.00 
4.00 
3.00 
12 
Marginal totals 
50 
40 
30 
120 
50.00 
40.00 
30.00 
120 
Groups of species 
(h^{m’}ih^{m’}i)/h^{m’}i 
Testing hypothesis of homogeneity 

1 
2 
3 

GS  1 
0.53 
0.04 
0.50 
1: degrees of freedom: (r1) × (c1) = 8 2: 3: Hypothesis of homogeneity valid: 
 2 
0.01 
0.02 
0.01 

 3 
0.90 
0 
1.50 

 4 
0.55 
0.03 
0.57 

 5 
0.20 
0.20 
0.20 


2.19 
0.29 
2.78 

b) Pooling samples together  Estimated population proportions
Groups of species 
Statist. units (kg) 
p_{i} 



GS  1 
72 
0.60 
0.0020 
0.0447 
7.45 
 2 
19 
0.16 
0.0011 
0.0332 
20.75 
 3 
6 
0.05 
0.0004 
0.0200 
40.00 
 4 
11 
0.09 
0.0007 
0.0265 
29.44 
 5 
12 
0.10 
0.0008 
0.0283 
28.30 

120 
100.00 



Group of species  1:
etc.
Again, sampling for species composition can be carried out if the fish catch is transferred from the deck into containers and a simple random sample of containers is selected for a complete enumeration. In such a case, each sample container can be regarded as a cluster of individuals (statistical units), and the individuals in a cluster cannot automatically be regarded as random samples from the survey population. In this situation, the observed proportions will vary from one cluster to another more than would be expected as a result of random sampling of individuals.
If is the observed proportion of the i^{th} speciesdomain in the j^{th} sample container, the proportion in the population may be estimated^{5} by
(5)
where
n: number of sample containers (j = 1, 2, 3..., n)^{5} A second estimator is
, _{h}M_{j} = number of statistical sample container
The estimated variance of is,
(6)
Where
(7) : variance between clusters
f_{1}: is the sampling fraction of clusters (, where, N total number of containers in the population)For the estimation of confidence limits for population proportions, etc. see section 11.2.1.
In some cases an exact determination of proportions for selected fish containers may not be practical. Instead a Sample of fish (statistical units) is selected (secondstage sample) from each sample container (firststage sample), and proportions h^{p}ijk calculated from these samples, where,
: is the observed proportion of the i^{th} speciesdomain in the k^{th} secondstage sample selected from the j^{th} sample container (firststage sample).An estimate of the proportion in the population may be calculated by
The estimated variance of will now involve both the variance between clusters and the variance within clusters,
where
,
and
,
where
For the estimation of confidence limits for population proportions, etc. see section 11.2.1.