Simple Random Sampling

Sampling Techniques: Simple Random Sampling

As we have already mentioned, sampling involves the selection of a portion of a population as representative of that population. To help ensure that the sample is representative, the ideal solution, seldom achieved, is to select a random sample from the target population. A random sample is one in which each individual in the defined population has an equal chance of being included. It should be noted that the use of sampling techniques can be quite complicated.

This is particularly true when these techniques are used to draw a random sample from a national population. However, sampling from a national population usually occurs only in survey research, such as public opinion polls. Samples used in experimental, causal-comparative, or correlational research are generally drawn from a much more limited accessible population, such as all the elementary school teachers in a particular school district.

The main purpose for using random sampling techniques is that random samples yield research data that can be generalized to a larger population within margins of error that can be determined statistically. Random sampling is also preferred because it permits the researcher to apply inferential statistics to the data. Inferential statistics enable the researcher to make certain inferences about population values (e.g., mean, standard deviation, correlation coefficient) on the basis of obtained sample values. If a random sample has not been drawn from a defined population, however, the logic of inferential statistics is violated and the results of inferential statistics must be interpreted with much more caution.

Simple Random Sampling In simple random sampling, all the individuals in the defined population have an equal and independent chance of being selected as a member of the sample. By "independent" is meant that the selection of one individual does not affect in any way the selection of any other individual. Various techniques can be used to derive a simple random sample. Suppose the research director of a large city school system wishes to obtain a random sampling of 100 pupils currently enrolled in the ninth grade from a population of 972 cases. First, he would obtain a copy of the district census for ninth-grade pupils and assign a number to each pupil. Then he might use a table of random numbers to draw a sample from the census list.

Generally these tables consist of long series of five-digit numbers generated randomly by a computer. On the facing page is a small portion of a typical table. To use the random numbers table, the researcher randomly selects a row or column as a starting point, then selects all the numbers that follow in that row or column. If more numbers are needed, he proceeds to the next row or column until enough numbers have been selected to make up the desired sample size. In effect the researcher may start at any random point in the table and select numbers from a column or row or diagonally if he wishes.

Suppose, in our example, the researcher selects row 1 column 5 as his starting point in the above table and selects numbers vertically. Since there are 972 cases in our illustrative city school system, it is only necessary to use the last three digits of each five-digit number. If the above table of random numbers were used, the researcher would select the 732nd pupil on the census list, the 970th pupil, the 554th pupil, and so on. He would skip the number 983 since there are only 972 cases in his population. This procedure would be followed (with a much larger table of random numbers, of course) until a sample of 100 pupils had been selected. If a small population is used, another method of selecting a simple random sample is sometimes followed. This method involves placing a slip of paper with the name or identification number of each individual in the population in a container, mixing the slips thoroughly, and then drawing the required number of names or numbers.

Simple random sampling is well illustrated by a study involving the collection of a national random sample of secondary school physics teachers. The researchers responsible for this curriculum evaluation study wished to avoid using a nonrandom sample consisting largely of "volunteer" teachers. This procedure, typical of many curriculum evaluation studies, makes it difficult to generalize the findings of the curriculum evaluation to other groups of teachers, especially nonvolunteers, who might be required to teach the new curriculum.

Whenever a research project extends over a considerable period of time, there is likely to be attrition of subjects. Not only can attrition lead to bias in the research sample (since those who leave the study may differ in important ways from those who persist), but also the reduced sample size can make it more difficult to find statistically significant differences. Thus, if the research study makes considerable demands on subjects or lasts over a long period of time, it is advisable to include more subjects in the random sample than are needed in order to provide for possible attrition. It is also important to take any steps possible to keep attrition to a minimum

The human relations procedures described can do much to reduce attrition, as can the ten steps for increasing the rate of volunteering given later in this chapter. Some attrition may reflect careless or poorly planned techniques for gathering, processing, and analyzing research data. Loss of data often occurs because the subject is not contacted by the data gatherer or the subject does not provide all the information needed for analysis. Much attrition in school research is the result of student absences on testing days or incorrectly completed measures. Prompt checking of data, careful recordkeeping, and a systematic follow-up procedure can greatly reduce this problem." Great care is required at all stages of data collection, processing, and analysis if attrition is to be reduced and valid data obtained. In summary, simple random sampling is a powerful technique for selecting a sample that representative of a larger population.

Nevertheless, it is rarely possible to study a simple random sample that is perfect. Even if a simple random sample is initially selected, some subjects probably will refuse to cooperate and others will be lost through attrition, leaving the researcher with a sample that is not truly random.