CoverFAO FISHERIES TECHNICAL PAPER   434
Sampling methods applied to fisheries science: a manual

by
Emygdio Landerset Cadima
Consultant
Lisbon, Portugal

Ana Maria Caramelo
Fishery Resources Officer
FAO Fisheries Department
Rome, Italy

Manuel Afonso-Dias
and Pedro Conte de Barros
Professors
University of Algarve
Faro, Portugal

Merete O. Tandstad
and Juan Ignacio de Leiva-Moreno
Fishery Resources Officers
FAO Fisheries Department
Rome, Italy

FOOD AND AGRICULTURE ORGANIZATION OF THE UNITED NATIONS
Rome © FAO 2005

CONTENTS


Cover:
Illustration representing port sampling site. Emanuela D'Antoni.

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ISBN 92-5-105397-9

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Contents

Preparation of this document

Abstract

1.   INTRODUCTION

2.   THE THREE WORLDS OF SAMPLING

2.1   The population world

2.2   The sample world

2.3   The sampling world

3.   SIMPLE RANDOM SAMPLING

3.1   Introduction

3.2   The population world

3.3   The sample world

3.4   The sampling world

3.4.1   Selection of the sample

3.4.2   Estimator of the population mean y

3.4.3   Estimator of the total value of the population

3.4.4   Estimators of proportions

3.4.5   Estimator of several proportions of the population

4.   STRATIFIED RANDOM SAMPLING

4.1   Introduction

4.2   The population

4.2.1   Stratrumh

4.2.2   All strata

4.3   The sample

4.3.1   Stratrumh

4.3.2   All strata

4.4   The sampling world

4.4.1   Stratrumh

4.4.2   All strata

4.5   Allocation of the sample among the strata

4.5.1   Proportional allocation

4.5.2   Optimum allocation

4.5.3   Optimum allocation with variable cost

4.6   Comments

5.   CLUSTER SAMPLING

5.1   Introduction

5.2   The population

5.3   The sample

5.4   The sampling world

5.4.1   Selection with equal probabilities

5.4.2   Selection with unequal probabilities

6.   TWO-STAGE SAMPLING

6.1   Introduction

6.2   The population

6.3   The sample

6.4   The sampling world

6.4.1   First selection by simple random sampling, without replacement, and second selection by simple random sampling, without replacement

6.4.2   First selection with unequal probabilities, with replacement, and second selection with equal probabilities, with replacement

7.   BIOLOGICAL SAMPLING AT LANDING PORTS FOR ONE RESOURCE

7.1   Introduction

7.2   Objectives

7.3   Example of a sampling scheme for the annual length composition of the landings

7.4   Final comments

8.   EXERCISES

8.1   Exercise 1

8.2   Exercise 2

8.3   Exercise 3

8.4   Exercise 4

8.5   Exercise 5

8.6   Exercise 6

8.7   Exercise 7

9.   SOLUTIONS

BIBLIOGRAPHY

Tables

2.1   Distribution of total length measurements

3.1   Main population parameters of interest to fisheries research

3.2   Some sample statistics more frequently used in fisheries research

5.1   Summary of population parameters of most interest in fisheries research

5.2   Most common sample statistics in cluster sampling

5.3   Original data and calculation of “boat selection numbers”

6.1   Main population parameters of interest to fisheries research in two-stage sampling design

6.2   Main sample statistics of interest to fisheries research in two-stage sampling design

7.1   Summary of a sampling scheme for estimating the length composition of landings

7.2   Frequency table for fish length - fish from buckets

7.3   Length composition by box after raising frequencies

7.4   Length composition by landing

7.5   Length composition of the landings sampled

7.6   Sum of the length composition of landings

7.7   Length composition for the total landings of trawlers in Port A on January 1

8.1   Numbers of vessels according to the type of boat and gear used

8.2   All possible samples of 3 landings that could have been taken from the 10 landings that actually took place in that week

8.3   Number of vessels by power classes of a purse seiner fleet

8.4   Total landings of sardines and coefficient of variation by vessel power classes

8.5   Characteristics of the survey area

8.6   Number of vessels of each province, by landing place

8.7   Sample data

8.8   Sample data

8.9   Sample data

8.10   Sample data

Figures

1.1   The three worlds of the sampling process

2.1   Histogram of relative frequencies of total lengths

2.2   Histogram of the cumulative absolute frequencies of total lengths

2.3   Density function of the standard normal distribution

2.4   Distribution function of the standard normal variable, Z

4.1   A stratified sampling scheme for a shrimp fishing ground

7.1   Multi-stage sampling scheme for length composition of the landings of Sardinella aurita made by trawlers in Port “A” during January

7.2   Scheme of the procedure to obtain the length composition for the landings of Sardinella aurita made by trawlers in Port “A” during January