# Quantitative and Qualitative Research 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 stratum.

"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 C_{f} and the variable cost per sampling unit, C_{u}.

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 we have:

from which we find that the required sample size