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After reading this article you will learn about the definition and factors influencing optimum sample for a study.
Definition of an Optimum Sample:
An optimum sample for a study may be defined as that sample which fulfills the requirements of efficiency, representativeness, reliability and flexibility. That is, the sample should be small enough to forestall unnecessary expense and large enough to help the researcher avoid sample-error beyond the limit to tolerance.
It should be large enough to yield statistically representative and significant results in all tabulations of any import but it need not be so large as to result in wastage of funds, retarding the project and achieving needlessly high precision. The sample should yield the desired estimates with the required level of reliability at a minimum cost.
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It should be remembered that in practice efficient sampling involves making the most of available resources in terms of technique and organization of statistical data and adjusting, as best as possible, to the limitations of time, funds and personnel, originally imposed on the study.
In addition, it should be possible in some instances to expand or contract the sample-size to meet unforeseen exigencies arising in the course of the study. In certain situations, reliability and efficiency may be improved by effecting the desired changes in the size of sample.
At the level of practice, these ideals can be approached but rarely realized and so one cannot be expected to choose the correct sample size.
Factors Influencing Optimum Sample:
The choice of the size of sample for a given study is affected by several factors. These factors are interrelated and vary greatly in different studies with respect to their relative importance in determining the sample size.
(1) The Nature of Population (Homogeneous-Heterogeneous):
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The size of the sample in a study will depend upon the degree of homogeneity of the population. The more homogeneous the population, fewer the cases required to yield a reliable sample of it and conversely, the more heterogeneous the population more the cases required to constitute a reliable sample of it.
The size of sample required for a satisfactory study of a heterogeneous population can be cut down by classifying the population into strata. Some of these strata will be more homogeneous and others less so. More homogeneous strata can be represented by smaller samples than the relatively heterogeneous ones.
This is so because the more homogeneous a stratum, the better can a random sample of a given size represent it, i.e., more alike will be the cases in the sample hence, less variable their mean.
(2) Complexity of Tabulation:
In making a decision about the size of the sample, one must also take into account the number of categories and classes into which the findings are to be grouped and analyzed. The greater the number of categories, the larger would be the total sample needed to yield reliable statistical measures of them.
Even though a sample may seem quite adequate for the main tabulation, the number is likely to thin down very quickly when detailed tabulations are prepared.
For example, a sample of 1,000 students might seem like an adequate number for a survey designed to ascertain the proportion of students favouring co-education. Let us say that only 25% are in favour (250 students).
If the researcher wanted to go further and know the type of students who favoured co-education, he would have to classify these respondents further, on the dimensions like, whether they had a prior experience of the coeducational institution? Which social class they come from? What kind of family background they have? What was the nature of their experience (if any) of the coeducational institution? And so on.
Proceeding thus, the researcher may finally find only 10 or 15 cases of a particular type (viz., no prior experience of co-education, middle class, orthodox family background, etc.). Such a sample can afford only a very, flimsy basis for arriving at significant and generalizable conclusions about the relationship among variables.
The size of sample chosen should be large enough to give reliable measures of the smallest important categories. When data are broken down into smaller and smaller sub-classes, the number of cases falling into various cells soon becomes so small that statistical measures computed from the cell entries are likely to be unreliable.
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Thus, intensiveness of tabulation is a factor that has importance for the decision relating to sample-size.
(3) Problems Relating to Collection of Data:
Usually, the size of the sample must be kept within the numerical limit of cases which can be secured with given funds and time. The volume of data is affected by length of the questionnaire/schedule, the number of field-workers, the dispersion or concentration of cases in a geographical area, the refusal-rate, the losses of cases, the type of sampling employed and finally, the method of data-collection.
The transportation cost involved in getting from one address to another and in callbacks (second or third call) must be considered when deciding the size of the sample. While planning the sample-size, the researcher must always anticipate that he may fall short in the collection of the number assigned for questioning.
People migrate, die, are unable to give information owing to illness, go vacationing or on business, cannot be located, refuse to answer, addresses prove wrong, and so on.
It is a good policy to plan to obtain information from every case in the sample if humanly possible. This means that considerably more time will be required than what would be required if only accessible and cooperative cases are obtained. However, it is better to have a smaller sample without bias than a large sample which is likely to be unrepresentative of the universe for reason of bias.
(4) Type of Sampling:
Generally, a smaller sample will suffice when stratification is employed. This is because the effect of stratification is to resolve the relatively heterogeneous totality into a number of individually homogeneous sub-samples. More heterogeneous the population, the greater the economy of cases possible through stratification.
In sampling known as double sampling, the researcher combines a large random sample (for the collection of a few basic items of information) with a very small controlled or stratified sample (from which detailed or complicated information is secured).
The requirement here is that the size of the random sample should be large enough to yield reliable weights for the various strata. The stratified sample itself inquires fewer cases compared to simple random sample because the sample in each stratum needs to be representative of that stratum and not of the ‘universe.’
One important factor in determining the necessary number of cases is the size of the sampling units. In fact, larger the sampling unit, the greater the number of cases which will be needed for individual tabulation.