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1. Introduction

To sample is to collect part of the elements of a set. The elements will be the sampling units, part of the elements will form the sample and the full set is the population. Why is sampling important? Sampling is important because most of the time it is impossible, difficult or expensive to observe all the elements of a population. If the samples are selected with an adequate criterion, it is possible to measure the precision of the conclusions or inferences about that population.

In fisheries research, the objective of sampling the fisheries is to obtain data from the stocks and their exploitation, to analyse the characteristics of the resources, the effects of exploitation on the abundance of these resources and to determine appropriate fishing levels to obtain the best possible catches at present and during future years.

In the sampling process it is convenient to distinguish between population, sample and sampling. Figure 1.1 illustrates the three different “worlds” of the whole sampling process and the relationships among them.

The first “world” of the sampling process is the population. The population “world” is entirely or partly unknown. Its elements can be of various types but they should be well-defined (e.g.the boats of one fleet, sardines landed in a fishing harbour in one day, etc.).

The second “world” of the sampling process is the sample. The sample “world” is completely known (in this aspect the sample is totally different from the population). It is from the sample data that the characteristics of the population will be estimated and, for this purpose, the selection of the sample has to be made with a well-defined criterion.

The third “world” is the sampling “world”. The sampling “world” is the set of all samples with the same size that could be selected with the same criterion from the population. It is from the properties of the sampling “world”, and based on the values of the characteristic of interest in the sample selected, that statistical inference can be carried out with pre-defined precision.

FIGURE 1.1
The three worlds of the sampling process

Figure 1.1

Population parameters summarize or characterize the distribution of the population values. The corresponding values in the sample are called statistics. Statistical inference is based on the distribution of a given statistic in the sampling. Sampling distributions are also characterized by parameters. It should be noted that often parameters of the population, statistics of the sample and parameters of the sampling distribution share the same name, e.g. the population mean, the sample mean and the sampling mean. However, practitioners should be aware that each of these represents a different quantity with different properties, and the “world” they refer to should always be made explicit.

The sampling “world” of a statistic is formed by calculating the values of this statistic in all possible samples that could be selected from that population, with the same pre-defined criterion. Sampling distributions are probability distributions. The actual sampling distribution of its values is unknown, but often the expected theoretical distribution, and its main properties, can be derived from the knowledge of the sampling process and of the statistic being considered. Sample statistics that are used in the process of estimation of population parameters are called estimators. The sampling distribution of an estimator is the basis for all statistical inference from the sample to the population regarding this estimator. Namely, it is based on these probability distributions of the estimators in the sampling that the precision of the estimation can be evaluated.

There are several different methods for selecting a sample. The most usual are simple random sampling, stratified random sampling and cluster sampling. In fisheries research, multistage sampling, a combination of several of the basic methods, is also commonly used.

In simple random sampling each possible sample has the same probability of being selected. There are two ways of selecting a simple random sample, with or without replacement of the sampling units selected. Simple random sampling is not frequently used in fisheries research, except as part of more complex methods.

In stratified random sampling the whole population is divided into sub-populations, called strata. A sample is selected using a random design within each stratum. Stratified sampling is usually applied to biological sampling of the landings and in scientific surveys.

In cluster sampling the population is also partitioned into groups, which are designated clusters. Each cluster contains one or more elements, but it is the clusters and not the elements that are the sampling units. Cluster sampling has been used in fisheries to estimate landings per trip from data of artisanal fisheries with many landing sites (beaches) and a small number of vessels operating from each site (beach).

Multistage sampling is a combination of the various methods previously mentioned. At each stage, there is a random selection of the sampling units, which can be elements or clusters. Two-stage sampling and a particular case of three-stage sampling are discussed in this manual.

In systematic sampling all the elements of the population are grouped into classes of the same size. The first element to be sampled is chosen randomly from one class. The remaining sampling units occupy the same relative position in each class. For instance, if the third element of the first class were selected then all the third elements of the other classes would also be chosen. In this method, all classes have one element sampled, and therefore, the size of the sample is equal to the number of classes. This method is not discussed further in this manual.

Fisheries research is most often concerned with the estimation of population mean and totals. The estimation of the proportion of the population that shares some characteristic of interest, e.g the proportion of vessels in a small-scale fishery that make more than two trips per day, is also a common task in fisheries research. The sampling distribution and properties of several estimators, mainly of the estimators of population means and totals, and sometimes of proportions, are discussed in the next chapters of this technical paper.


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