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4. GENERAL SAMPLING CONSIDERATIONS
4.1 CENSUS COSTS AND OBJECTIVES OF SAMPLING
4.2 ACCURACY AND PRECISION IN SAMPLING
4.3 ACCURACY AS A FUNCTION OF SAMPLE SIZE
4.4 A PRIORI ACCURACY INDICATORS
4.5 SAFE SAMPLE SIZE FOR LANDINGS AND EFFORT
4.6 VARIABILITY INDICATORS
4.7 STRATIFICATION AND ITS IMPACT ON SURVEY COST
4.8 THE PROBLEM OF BIASED ESTIMATES
4.9 NEED FOR REPRESENTATIVE SAMPLES
4.10 THE “BOAT” AND “GEAR” APPROACHES
Choosing to undertake sample-based surveys is based primarily on the recognition that complete enumeration through census-based surveys imposes huge costs that are both unsustainable and unnecessary if the nature and methods of statistical sampling are properly considered. Such considerations include understanding of:
the reasons for and objectives of sampling.
the relationship between accuracy and precision.
the reliability of estimates with varying sample size.
the determination of safe sample sizes for surveys.
the variability of data.
the nature of stratification and its impact on survey cost.
the risks posed by biased estimates.
the differences between “boat” and “gear” statistical approaches.
Census-based techniques are generally impractical in small-scale fisheries due to the large number of fishing operations that would have to be monitored over a reference period. The following example outlines the logistics problems and costs involved in census-based surveys.
4.1 CENSUS COSTS AND OBJECTIVES OF SAMPLING
Assume a fishery of moderate size comprising 1,000 fishing canoes, each fishing 24 times during a month on a one-day-per-trip basis. This would mean that:
1) There would be about 24,000 landings during the month and all landings would have to be recorded, each with its complete set of basic fishery data (species composition, weight, etc) (Note that there will be no need for a separate survey for fishing effort, since all trips will be recorded.)
2) Assuming that a single recording of a landing would take a minimum of ten minutes (experience shows that this is the case in many data collection systems), a minimum of 240,000 minutes (4,000 work hours) will be needed.
3) If a data collector works 8 hours per day for 25 days in a month, then collection of data would require 4,000/8 × 25 = 20 data collectors just to monitor this relatively small fishery. This assumes that such a level of data collection is feasible and that landings and hence fisher availability is spread evenly over the day.
4) In addition to the costs of data collectors there would also be the costs of a) supervision, b) data editing, checking and inputting for 24,000 landings per month, and c) computer data storage for 12 x 24,000 = 288,000 landings per year.
On the other hand a well-defined sampling scheme would most likely need only one or two recorders for data collection and only a fraction of the computer storage and processing resources, due to the much lower volume of incoming data.
Thus there are three objectives of a sampling programme:
to examine representative sub-sets of the data with the purpose of producing estimates of parameters, such as CPUE, prices, etc, that are as close as possible to the “true’ values that would be obtained through complete enumeration.
to reduce operational costs.
to reduce analytical and computing requirements.
4.2 ACCURACY AND PRECISION IN SAMPLING
In sampling procedures accuracy and precision are two different statistical indicators and it is perhaps worth clarifying their meaning at this point, as frequent reference will be made to these two terms in the coming sections.
4.2.1 Sampling Accuracy
Sampling accuracy is usually expressed as a relative index in percentage form (i.e. between 0 and 100%) and indicates the closeness of a sample-based parameter estimator to the true data population value.
When expressed as a relative index, sampling accuracy is independent of the variability of the data population, i.e. data population parameters of high variability can still be estimated with good accuracy.
When sample size increases and samples are representative, sampling accuracy also increases. Its rate of growth, very sharp in the region of small samples, becomes slower beyond a certain sample size.
4.2.2 Sampling Precision
Sampling precision is related to the variability of the samples used. It is measured, in reverse sense, by the coefficient of variation (CV), a relative index of variability that utilizes the sample variance and the sample mean.
