Elementary Statistics (1+1)

3.1.14.1.3 Method of Reducing Sampling Errors

Once the absence of bias has been ensured, attention should be given to the random sampling errors. Such errors must be reduced to the minimum so as to attain the desired accuracy.

Apart from reducing errors of bias, the simplest way of increasing the accuracy of a sample is to increase its size. The sampling error usually decreases with increase in sample size (number of units selected in the sample) and in fact in many situations the decrease is inversely proportional to the square root of the sample size as can be seen from the diagram below.

From this diagram it is clear that though the reduction in sampling error is substantial for initial increases in sample size, it becomes marginal after a certain stage. In other words, considerably greater effort is needed after a certain stage to decrease the sampling error than in the initial instances. Hence after that stage sizeable reduction in cost can be achieved by lowering even slightly the precision required. From this point of view, there is a strong case for resorting to a sample survey to provide estimates within permissible margins of error instead of a complete enumeration survey, as in the latter the effort and the cost needed will be substantially higher due to the attempt to reduce the sampling error to zero.

As regards non-sampling errors they are likely to be more in case of complete enumeration survey than in case of a sample survey, since it is possible to reduce the non-sampling errors to a greater extent by using better organization and suitably trained personnel at the field and tabulation stages. The behavior of the non-sampling errors with increase in sample size is likely to increase with increase in sample size. In many situations, it is quite possible that the non-sampling error in a complete enumeration survey is greater than both the sampling and non-sampling errors taken together in a sample survey, and naturally in such situations the latter is to be preferred to the former.