Elementary Statistics (1+1)

3.1.12 Size of sample

An important decision has to be taken in adopting a sampling technique is about the size of the sample. Size of sample means the number of unit to be sampled from the population for investigation. Different opinions have been expressed by experts on this point. For example, some have suggested that the sample size should be 5% of the size of population while others are of the opinion that sample size should be at least 10%. However, these views are of little use in practice because no hard and fast rule can be laid down that sample size should be 5%, 10% or 25% of the universe size. It may be pointed out that mere size alone does not ensure representativeness. A smaller sample but well selected sample is small it may not represent the universe and the inference drawn about the population may be misleading. On the other hand, if the size of sample is very large, it may be too burdensome financially, require a lot of time and may have serious problems of managing it. Hence the sample size should neither be too small nor too large. It should be ‘optimum’. Optimum size, according to Parten, is one that fulfils the requirements of efficiency representativeness, reliability and flexibility.

The following factors should be considered while deciding the sample size:

(i) The size of the universe—the large the size of the universe, the bigger should be the sample size.

(ii) The resource available – If the resources available are vast a larger sample size could be taken. However, in most cases resources constitute a big constraint on sample size.

(iii) The degree of accuracy or precision desired—The greater the degree of accuracy desired the larger should be sample size. However, it does not necessarily mean that bigger samples always ensure greater accuracy. If a sample is selected by experts by following scientific method, it may ensure better results even when it is small compared to a situation in which a large sample size is selected by inexperienced people.

(iv) Homogeneity or Heterogeneity of the Universe—if the universe consists of homogenous units a small sample serve the purpose but if the universe consists of heterogenous units a large sample may be inevitable.

(v) nature of study—For an intensive and continuous study a small sample may be suitable. But for studies which are not likely to be repeated and are quite extensive in nature, it may be necessary to take a larger sample size.

(vi)Method of sampling adopted—the size of sample is also influenced by the type of sampling plan adopted. For example, if the sample is a simple random sample it may necessitate a bigger sample size. However, in a properly drawn stratified sampling plan, even a small sample may give better results.

(vii) Nature of respondents—Where it is expected a large number of respondents will not co-operate and send back the questionnaires, a large sample should be selected.

The above factors have to be properly weighted before arriving at the sample size. However, the selection of optimum sample size is not that simple as it might seem to be. If the sample is used which is larger than necessary, resources are wasted, if the sample is smaller than required the objective of the analysis may not be achieved.

If, for example, p= 0.5 and q = 0.5, _p = 0.005, then n shall be determined as follows:

n= = 10,000.