|Resources > Sampling Plan
1. How big should a sample be?
It is frequently a matter of concern as to the size of a sample
drawn, and the notion is that if the sample size is not "large
enough", the sampling results are likely to be inaccurate.
"It is sometimes presumed that a sample should be based
on some agreed percentage of the population from which it is taken.
The view that there is a constant percentage, often thought to
be around 10 per cent, which can be applied when sampling populations
of all kinds and sizes is quite wrong". (Ref. Chisnall,
Peter M., Marketing Research, Maidenhead, UK, McGraw-Hill, 1986)
The size of a sample depends upon the basic characteristics of
the population. If there is complete homogeneity, a sample size
of 1 would be sufficient, while a larger sample is obviously required
where the required characteristics display wide heterogeneity.
One of the ways of dealing with heterogeneity is to break the
population into sub-groups or strata, which display homogeneity
among the sample units. This is known as stratified (random) sampling,
which is statistically more efficient than simple random sampling.
However, strictly speaking, we need a sample frame such as a list
of all students in a college from which to draw a sample. Where
we are sampling from a very much larger population, as in say,
a city, ideally we require the voters list for each ward from
which to randomly select a given sample, subject to certain characteristics
such as age, income etc., which might be set as "quotas".
It is also necessary to ensure that the smallest sub-group or
stratum should contain "sufficient" sampling units so
that accurate and reliable estimates can be found of the population
"Samples in the US range from 1500 to 2000 for national
surveys, unless minority sub-sampling is involved when larger
samples would be used. In the UK, national surveys of housewives´
buying habits are frequently about 2000, and this figure is also
relevant for Europe". (ibid)"
The error of the sample is inversely proportional to the square
root of the sample size. This means that although a sample of
8000 is four times as large as a sample of 2000, it can only be
twice as accurate, since the square root of 4 is 2.
The important fact to remember is that a sample size is a balancing
act between precision (or reliability) and cost of the survey.
Daniel and Terrel have suggested a formula for calculation of
sample size when we have a fixed budget for a sample study. (See
Daniel, Wayne W., and Terrel, James C., BUSINESS STATISTICS for
Management and Economics, Boston, USA, 1992 Houghton Mifflin)
The budget represents the total cost C for a sampling study,
which can be broken into two parts - the fixed cost Cf
and the variable cost per sampling unit, Cu.
The sample size n is given by the formula:
Let us assume that the budget available for a sample survey is
Rs.800,000; the cost per questionnaire charged by the Market Research
firm is Rs.150, and the fixed costs associated with the study
(mainly supervision and management costs) are Rs.1,50,000. Then
from which we find that the required sample size