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 Multi-stage sampling for proportions
The sampling methods used for species composition can be grouped under the following headings.2
SM-1: 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.
SM-2: Cluster sampling for proportions
SM-3: Multi-stage sampling for proportions2 For small catches the method of complete enumeration (census approach) is employed.
11.2.1.1 More than one haul
Suppose the population (three-dimensional pile of smallest fish on deck) consists of hM statistical units (kg, h: stands for a given haul) and a simple random sample of hm 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 ith species-domain in the population is hMi and hmi in the sample, an estimate of the proportion of statistical units in the population failing in the ith species-domain is denoted by hpi, so that
(1) hpi = hmi/hm
The estimated variance of p is given (SWR) by,
(2) 
,
where hqi = 1 - hpi
If hM is large relative to hm, 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 (X2-test) before pooling together.
For calculation purposes a general contingency table containing r-rows (species or species groups, i = 1, 2,..., r) and c-columns (number of sample tows, h = 1, 2,..., c) is used. The X - value is estimated4 by
where
hmi: number of statistical units (kg) in the hth haul of species ithThe estimated X2 value is compared with the tabulated=: probability that a statistical unit will be a member of the ith row
: probability that a statistical unit will be a member of the hth column
4 See Bazigos, G.P. (1974) Applied fishery statistics. FAO Fish.Tech.Pap., (135):164 p.
. The hypothesis
is valid if X2 <
; the hypothesis is
discredited if X2 >
.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 |
(hm’i-hm’i)/hm’i |
Testing hypothesis of homogeneity |
||
|
1 |
2 |
3 |
||
|
GS - 1 |
0.53 |
0.04 |
0.50 |
1: degrees of freedom: (r-1) × (c-1) = 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) |
pi |
|
|
|
|
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 ith species-domain in the jth
sample container, the proportion in the population may be estimated5
by
(5)
where
n: number of sample containers (j = 1, 2, 3..., n)5 A second estimator is
,
hMj = number of statistical sample container
The estimated variance of
is,
(6)
Where
(7) 
:
variance between clusters
f1: is the sampling fraction of clusters (For the estimation of confidence limits for population proportions, etc. see section 11.2.1., where, N total number of containers in the population)
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 (second-stage sample) from each sample container (first-stage sample), and proportions hpijk calculated from these samples, where,
An estimate of the proportion in the population may be calculated by: is the observed proportion of the ith species-domain in the kth second-stage sample selected from the jth sample container (first-stage sample).
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.
