# Sample size determination and Random sampling

The actual application of the sample size formulas given in this article requires consideration of a number of related issues. These include the following:

(1) The formulas given are applicable strictly to simple random sampling only. Other commonly used sampling systems will be a larger sample size of the same precision.
(2) These formulas relate to the sample size needed for the estimation of one particular characteristics of interest. A survey is hardly ever done to obtain only one estimate. Typically, several characteristics are to be estimated and each may require different sample size. Thus, it may be necessary to compromise on the question of sample size, with some estimates being provided with less precision than is desired and others being provided with more precision than is necessary.
(3) It may be desirable to have different precision requirements for different universe segments. For instance, in chain stress it may be desirable to have results that are accurate within 10 percent, while in independent stores the accuracy might be relaxed to 15 percent.
(4) Management’s concern for the precision of the results must be realistic. Executives sometimes over estimate the precision with which estimates must be provided. Because of the influence of this factor on the sample size needed, it is critical that a realistic appraisal be made.

(5) To be useful, the sample size formulas must be based on adequate information about the universe; the more that is known of a universe, the more efficiently it can be sampled.

Practical Problems in using simple Random sampling:

Although simple random sampling serves well to introduce the basic ideas of sampling, it is not suitable for most sampling problems in marketing research. Its use is severely limited by the four factors discussed below:

Cost:

One factor limiting the use of simple random sampling is the cost because the method guarantees that every possible item in the universe has the same chance of being chosen, the actual sample selected often consists of universe items that are widely dispersed geographically. If personal interviews are used, interviewers may have to travel considerable distance, thereby increasing the costs of the field operation Thus, a simple random sample may cost more than some of the other types of probability samples, discussed. On the other hand, cost may not be a limiting factor if a mail or telephone survey is used.

Availability of a Current Listing of Universe Elements:

A second serious limitation to practical use of simple random sampling is the need for an accurate list of universe elements. It is usually difficult to obtain such a list of even a relatively fixed universe such as all grocery stores in the state of Illinois For human universe it may be impossible. This is partly the result of the large numbers and high mobility of humans. But it is also true because many universes are a small percentage of the total and are not easy to identify – for example, people who have purchased a compact disc player in the last month.

Statistical Efficiency:

A third difficulty associated with simple random sampling is that it is often statistically inefficient. One sample design is said to be statistically more efficient than another when, for the same size sample, a smaller standard error is obtained. Given some knowledge or perhaps just educated guesses about a universe, one may ordinarily improve the precision of the sample mean or percentage by imposing certain restrictions on the sampling procedure.