Sampling Methods

The following are typical, but by no means the only, methods used for sampling. Though there is wide variation among the methods used to suit the circumstances, there are some principles to which all sampling methods should conform to render the sam­ple worthy of statistical analysis. The sample should be representa­tive of the population, which is likely to happen if the elements of the sample are collected from the population at random. Only with these conditions, can there be a probabilistic relation between an inference drawn from the sample and a corresponding infer­ence likely from the population.

1. Simple Random Sampling

Let us say there is a set of fifty elements in a population, which comprises all the students in a class, in which there are boys and girls, good and mediocre students, coming from well-to-do and poor families. If fifteen students are to be selected for an experi­ment using a new method of teaching Spanish proposed to be better than the present method, the method of sampling is fairly simple:

1. Write the name of each student on a sheet of paper, using fifty identical sheets, and fold the sheets in an identical way and put those in a hat.
2. Get an “outsider,” say, a student from another class, and ask him or her to pick one folded sheet from the hat.
3. Keep it aside; do not replace it. This one student selected, whoever it is, had no greater chance of being selected than anyone else.

4. Shake well to mix the remaining forty-nine sheets of folded paper; ask the outsider to pick another folded sheet.
5. Keep this sheet with the one already selected. This one who is selected also had only as much chance of being selected as anyone else.
6. Repeat the steps (2) through (4) until the subset— the collection of folded sheets of paper picked as above—has fifteen elements.
7. Open the sheets, and read out the names of those who are in the subset. These are the students who form the sample of fifteen selected from the popu­lation of fifty.

The advantage of this method is that no special preparation, except writing the names of fifty students, one on each sheet, and folding those was required; it is direct and quick. The disadvan­tage arises if, instead of fifty students in a class, five thousand stu­dents in the entire school district form the population, and instead of the subset of fifteen, we need to have a subset of five hundred. The work then becomes tedious and time-consuming. Also, this method is suitable only when all the elements of the population are known, that is, when the population is finite.

2. Cluster Sampling

If, for instance, the above-mentioned experiment is to be done with all the ninth graders of the public schools in Massachusetts, the experimenter in this case is quite likely not to know how many ninth graders there are in the state, and in that sense, he or she is dealing with an infinite population. Further, the expense of involving the ninth graders of all the schools of the state is pro­hibitively high, even if the time required can be afforded. In such cases the geographical area of Massachusetts is partitioned (on a map) into smaller regions. Numbering each region and using these numbers as population, a subset of smaller number of regions is randomly selected. Each region in the subset is then, in turn, partitioned into several subregions, and a subset is randomly selected from these subregions. This process may be continued until a reasonably small number of sub-sub-sub . . . regions is selected. Then, the random selection of students is made from each such sub-sub-sub . . . region, and the collected pool of the students so selected forms the sample.

3. Stratified Sampling

Simple random sampling and even cluster sampling are suitable when the population is homogeneous, like all the students being in ninth grade, when no distinction within that category is called for. Say, instead, the sample required is from the popu­lation of all students of a large high school having three thou­sand students, and the experiment is to find how popular the proposed uniform dress code is compared to the existing no dress code. If the investigator gets to know that there are one thousand freshmen, seven hundred sophomores, seven hundred juniors, and six hundred seniors in the school, and if he decides to have a sample of close to one hundred students, he should plan to select (1,000 + 3,000) x 100 = 33 freshmen. On the same basis, twenty-three sophomores, twenty-three juniors, and twenty seniors should be selected. Further, if he gets to know that the girls’ opinion is considerably different from that of boys, he may be required to stratify on the basis of gender as well. If there are three hundred fifty girls and two hundred fifty boys among seniors, he would select (350 + 600) x 20 = 12 girls, thus 8 boys from the senior class. This final phase of the sampling can be done either by simple random sampling or by using a random digits table as described earlier in this chapter. All those so selected, boys and girls, from other grades as well, collectively form the required sample. Evidently, in this method, the population is “stratified” into segments so as to give, consciously, proportionate representation to the obvious variety that exists within the population.

4. Systematic Sampling

This method is popular among industrial quality control experts, having for their populations discrete products issued from assem­bly lines or automatic machines. Depending on the production rate, the cost of each product, and the level of stringency of qual­ity assurance, it may be decided, for instance, that for every twenty-five products issued by the assembly line, one product should be picked to form an element of the sample; thus the twenty-fifth, fiftieth, seventy-fifth, and so on, products, collected together, form the subset serving as the sample. For a production schedule of one thousand products in a required period, there will be a sample of forty elements.

5. Multistage Sampling

Where large-scale sampling is involved, such as the job rating of the U.S. president or predicting the outcome of a national elec­tion, it is fairly common to use more than one of the above meth­ods in any sequence at different stages, as is found convenient, in the process of collecting a specific sample; this is referred to as multistage sampling.

Source: Srinagesh K (2005), The Principles of Experimental Research, Butterworth-Heinemann; 1st edition.