Sampling and Samples

In estimating the accuracy of a sample (sampling error), or selecting a sample to meet a required level of accuracy, there are two critical variables; the size of the sample and the measure being taken which for simplicity we shall take as a single percentage e.g. the percentage aware of a brand. A common mistake about sample size is to assume that accuracy is determined by the proportion of a population included in a sample (e.g. 10% of a population). Assuming a large population, this is not the case and what matters is the absolute size of the sample regardless of the size of the population – a sample of 500 drawn from a population of one million will be as accurate as a sample of 500 from a population of five million (assuming both are truly random samples of the respective populations).

The relationship between sampling error, a percentage measure and a sample size can be expressed as a formula.

e = z√(p%(100-p%))
?????????????? √ s

Where:
e = sampling error (the proportion of error we are prepared to accept)
s = the sample size
z = the number relating to the degree of confidence you wish to have in the result
p = an estimate of the proportion of people falling into the group in which you are interested in the population
By applying the formula it can be calculated, for example, that from a sample of 500 respondents (s), a measure of 20% aware of a brand (p), will have a sample error of +/-3.5% at the 95% confidence level.

e = 1.96√(20(80))
??????????? √ 500

This means, therefore, that based on a sample of 500 we can be 95% sure that the true measure (e.g. of brand awareness) among the whole population from which the sample was drawn will be within +/-3.5% of 20% i.e. between 16.5% and 23.5%.