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# 4.1.2. Sampling error

Sampling error is the error that occurs because a sample is taken instead of examining the whole population (Lohr, 2010). A survey allows estimation of characteristics of variables (typically a population mean, sum, or proportion) concerning a whole population, on the basis of a sample. Such an estimate is inevitably not the exact value of the population quantity. The only way to obtain the exact value is to calculate it from the whole population, but this is rarely possible.

If the sample has been randomly selected from the population, this error can be quantified by calculating the standard error (standard deviation) of the estimate. This is an estimate of the variation of the estimator used between different samples of the same size selected from the same population. When a non-random sample is used, there is no appropriate analytical form for the standard error (see any elementary textbook on survey sampling, e.g.  Schaeffer et al., 1990) and therefore the results of any such calculation should be viewed with caution.

This variation from sample to sample is usually presented by quoting a confidence interval for the estimate obtained from the sample. A confidence interval can only be reported if the sample is representative for the population of interest. An example of the calculation is given in Box 2.

 Box 2.  Example of confidence interval. The overall proportion of colonies lost from those at risk is estimated as 19.5%, with a standard error (s.e.) of 1.5%. The corresponding 95% confidence interval is obtained in the usual way as the estimate +/- 1.96 (s.e.) giving 19.5% +/- 1.96 (1.5)%, which yields 16.6% to 22.4%. This means that in about 95% of cases when such a calculation is made, using a sample of the same size from the same population, the interval quoted will contain the true value of the overall proportion of colonies lost. This calculation assumes that the sample estimate is approximately normally distributed.

The sampling error can be reduced by increasing the size of the sample. It is possible to calculate the optimum size of the sample for a satisfactory estimate at a given cost, depending on the chosen confidence level or required precision or margin of error. Having some approximate knowledge of the population quantities is needed for such a calculation of the sample size (see section 9.).