The size of a sample influences the cost of a study, as well as the usefulness of the results. A sample that is too small can exclude information. One too large is costly and cumbersome.
Often, researchers need to know the smallest sample that can be taken and yet still have estimates that are accurate.
Decision-makers first agree to the amount of error they will tolerate from the results. This is called the margin of error (E).
Along with margin of error, researchers also assign a critical value (C.V.) that is based upon the probability for extreme values in the population.
These two factors are combined with knowledge about the population's standard deviation (sigma) to reach a recommmended sample size.
n= [(C.V. * sigma) / E]^2
In order to apply the Central Limit Theorem, the common rule of thumb is a minimum sample size of 30. However, if the population is bell-shaped, it can be smaller.
