Define the target population and sampling element.    Definitions for the target population and the sampling element are generally made together. Definition of one pretty well defines the other. With the sampling element defined, the target population becomes the aggregation of all elements or units with the characteristics defined for the sampling element. Starting the other way, a clear, specific definition of the target population also defines the elements comprising this population. Either way, however, we would need a sampling frame.

Select a sampling frame. This is a crucial step in developing a simple random sample design.   Any potential sample frame you plan to use should be carefully examined to determine to what extent it matches the target population.

Returning to the faculty example, we would need to obtain a list of the members of the faculty. This should be easy to get, but, even with the list, we still have to define our target population. Should we include only full time staff or should part time faculty be included as well? What about administrative and support staff: Should they be included or are we limiting the target population to teaching staff only? Do we include visiting faculty from other universities? Answers to these and other questions will depend on the purpose of our research. If our purpose is to investigate teaching experience, we obviously would limit the target population to only teaching faculty and exclude administrative and support staff. If we were investigating morale of all university staff members, teaching and administrative staff as well, we would want to include all staff.

Regardless of how the target population is defined, any faculty list would be checked to make sure it corresponds to the target population as we defined it.   We would want to make sure that the list is up to date, that names of all eligible members are included, that no names are listed more than once, and that no other errors occurred.   Any of these errors could invalidate of sample.

Finding a suitable, valid sampling frame is frequently difficult. In many developing countries, there is limited census data to draw on. Further, with civil unrest, wars, drought, and other problems, large population changes frequently occur, making previous census data inaccurate.   It is always a good idea, therefore, to carefully check the accuracy of any sampling frame you intend to use. Lists of residents in a village, for example, can be checked for accuracy with village elders. Names of dead persons or those who have moved away can be removed and names of new residents can be added. With these changes, a local list of residents could become a suitable sampling frame for designing a simple random sample of households in a village. Similar checking can be used to convert a questionable list of employees of a factory or other organization into a useable sampling frame. When a trustworthy sampling frame cannot be found or created, other forms of sampling should be considered.

Osman's research (1995) illustrates extreme care in testing the adequacy of a sampling frame. He wanted a random sample of farmers in a rural area of the Sudan. Available lists of households in each village could have served as the sampling frame. But he made sure the lists were accurate and up-to-date before he used them. In consultation with local leaders, Osman eliminated duplicate names, deleted households that had left the area, and added new households. As a further step, he checked the revised lists for each village against lists maintained for those eligible to receive government rations. After further revisions were made, Osman used the lists as his sampling frame. He wrote the names of each household head on a slip of paper, put the papers in a box, and drew out the number of slips he needed for his sample size. His sample was as random as possible under the conditions he had to work with.

Select the sample.   Once you are satisfied that the sampling frame represents the target population reasonably well, you can select your sample.   You can use the "box" procedure as Osman did or you can use an alternative. Instead of writing the names on slips of paper, putting them in a box, and drawing out names, you could use a safe shortcut.    The following illustration shows how this can be done using a table of random numbers.

Using a table of random numbers

There are two ways to find a table of random numbers. One way is to find a statistics textbook with a table of random numbers. Your library or instructor probably has a statistic book with a table for random numbers. The other way is to use one of the sets of random numbers that are available online free. Following are some suggestions: