BetaResearch.com - BetaWaves

SEPTEMBER 1997

Determining Sample Size

THE OUTSIDE ENVELOPE

When planning a sample to determine percentage values, a prepared table, such as shown below, is useful, both in determining the required size of sample and in appraising the reliability of a completed sample. It must be emphasized that use of the formula of the standard error of a percentage and the following table both assume that a sample is being taken from a population which is homogeneous throughout with respect to frequency of occurrence of the phenomena being sampled.

For example, this assumes that, in a city like Chicago, the percentage of automobile owners expecting to have a six cylinder engine in their next car would be uniform in all sections of the city. If this assumption is, in fact, not justified, and it generally is not, then adequate-sized samples must be taken from each section of the city, and these samples must then be weighted with appropriate population and other market measures to prepare a weighted average that then would truly be representative of the entire city.

SIZES OF SAMPLE REQUIRED FOR CERTAIN
MAXIMUM PERCENTAGES OF ERROR
Frequency of Occurrence

There is 95 percent certainty that, with a sample of the sizes indicated above and when the frequency of occurrence is that shown in the vertical columns, the maximum percentage points of sampling error will be no greater than those given in the column at the left. This assumes a random sample. *Based on methods first described by T.H. Brown, The Use of Statistical Techniques in Certain Problems of Market Research, Harvard University, Graduate School of Business Administration, Business Research Studies.

Examination of this table reveals certain important aspects of sample size to measure sample percentages, as follows:

In order to obtain greater reliability, or a lower standard error, the sample size must be increased at a more rapid rate than the gain in reliability. In the column "20% or 80%" frequency of occurrence, on the horizontal line for ą2% confidence limits, will be found the figure of 1,537 which had been computed for the 6-cylinder motor example. If the reliability were to be doubled, this would be reduction of the probable error 1%. Moving up to that column we find that four times as great a sample, 6,147, is required.

As the frequency of occurrence approaches 50 percent, the required size of sample increases. If our sample had been the proportion of automobile owners who expect to have power steering on their next car, and if this were expected to be around 40 percent (or 60 percent), the size of sample would have to be 2,305, not 1,537, for the same degree of reliability. Since the highest size requirement is at 50 percent occurrence, one should conservatively estimate that frequency when lacking any basis of guessing the likely frequency.

Conversely, as the frequency of occurrence moves away from 50 percent, the needed sample size diminishes. If we sought to determine the proportion of new car buyers who expect their next car to be air conditioned and expect the result to be in the vicinity of 10 percent, such a result would call for only 864 in the sample (again on the basis of 2 percentage points of probable error). On a relative basis, it will be recognized, 10 ą 2 percent is a greater relative fluctuation from the mean value than is 20 ą 2 percent. To have the same relative deviation would call for only a 10 ą 1 percent, and therefore a larger example, than would 20 ą 2 percent.