Despite the assumption made in most university statistics courses, in marketing research we are not always dealing with an infinite population.  Take business-to-business research as an example.  You might be most interested in the 20% of customers who provide 80% of sales.

Where we have populations that are small (i.e. N is finite), valid statistical analysis can still be carried out by applying the ‘finite population correction’ factor (fpc).  The purpose of the ‘fpc’ adjustment is to correct for a bias that is introduced when sampling without replacement from a finite population.  The larger the sample relative to the population, the greater the adjustment made.  The ‘fpc’ is applied by being multiplied by the variance measure and when relevant, reduces this variance.

In sample size calculations, the fpc factor is employed by being incorporated into the formula for ‘n’.  But first, let’s have a look at the fpc factor itself:

So, where it is not really relevant (ie. N is large, say 10,000 and assume n=100):

In this case then, when the variance is multiplied by the fpc factor of 1, it remains unchanged.  This means that the sample size will not change either.

However, when the population is small, say 300, then the fpc factor becomes:

Here, it is useful as the ‘fpc’ is less than 1, so when multiplied through the sample size formula, the ‘fpc’ will always result in a smaller required sample size.  That is, when sampling from small populations, the fpc factor enables the same levels of precision and reliability to be achieved, but with smaller sample sizes.  This of course, translates to cost reductions.  It is important to note, that in order to apply the fpc factor, the size of the population must also be known.

One example of where finite populations are common is in pharmaceutical marketing research; for example Oncology Specialists.  This segment comprises not only a small population of Specialists, in this case N=47, but for various reasons, these Specialists are also difficult to get access to.  Consequently, it would be impossible to achieve the sample required by a standard sample size calculation (i.e. for 95% level of confidence, 5% precision and standard deviation of 2 on an 11-point Likert scale, the required sample size would be n=126!)

However, by using the fpc adjusted sample size formula, the required sample size drops to only 35!  Yet despite this marked decrease in sample size, estimates and inferences drawn from this sample, are still statistically valid and reliable.

In marketing research, particularly business-to-business, small populations are not uncommon.  Fortunately however, statistically valid samples can still be drawn and inferences made by using the correct formula – that is, the fpc adjusted sample size formula.