Elementary Statistics (1+1)

3.1.10.3 Systematic sampling

A systematic sample if formed by selecting one unit at random and then selecting additional units at evenly spaced intervals until the sample has been formed. This method is popularly used in those cases where a complete list of the population from which sample is to be drawn is available. The list may be prepared in alphabetical, geographical, numerical or some other order. The items are serially numbered. The first item is selected at random generally by following the Lottery method. Subsequent items are selected by taking every kth item from the list where ‘k’ refers to the sampling interval or sampling ratio, i.e., the ratio of population size to the size of the sample. Symbolically:

where k= Sampling interval, N=Universe size, and n=Sample size.

While calculating k, it is possible that we get a fraction value. In such case, we should use approximation procedure, i.e., if the fraction is less than 0.5, it should be omitted and if it is more than 0.5 should be taken as 1. If it is exactly 0.5 it should be omitted if the number is even and should be taken as 1, if the number is odd. This is based on the principle that the number after approximation should preferably be even. For example if the number of students is respectively 1020, 1150 and 1100 and we want to take a sample of 200, k shall be:

Illustration 2. In a class there are 96 students with Roll Nos. from 1 to 96. It is desired to take sample of 10 students. Use the systematic sampling method to determine the sample.

Solution

From 1 to 96 Roll Nos. the first student between 1 and k, i.e., 1 and 10, will be selected at random and then we will go on taking even kth student. Suppose the first student comes out to be 4^th in the enrolement. The sample would then consist of the following Roll No.

4,14,24,34,44,54,64,74,84,94

Systematic sampling is relatively a simple technique and may be more efficient statistically than simple random sampling, provided the lists are arranged wholly at random. However, it is rarely that this requirement is fulfilled. The nearest approach to randomness is provided by alphabetical lists such as are found in telephone directory although even these may have certain non-random characteristics.

Merits . The systematic sampling design is simple and convenient to adopt. The time and work involved in sampling by this method are relatively less. The results obtained are also found to be generally satisfactory, provided care is taken to see that there are no periodic features associated with the sampling interval. If populations are sufficiently large, systematic sampling can often be expected to yield results similar to those obtained by proportional stratified sampling.

Limitations . The main limitation of the method is that it becomes less representative if we are dealing with populations having “hidden periodicities”. Also if the population is ordered in a systematic way with respect to the characteristics the investigator is interested in, then it is possible that only certain types of items will be included in the population, or at least more of certain types than others. For instance, in a study of workers’ wages the list may be such that every tenth worker on the list gets wages above Rs. 750 per month.