Though it is difficult t draw a clear-cut line of demarcation between large and small samples it is normally agreed amongst statisticians that a sample is to be recorded as large only if its size exceeds 30. The tests of significance used for dealing with problems samples for the reason that the assumptions that we make in case of large samples do not hold good for small samples.
The assumption made while dealing with problems relating to large samples are:-
(i) The random sampling distribution of a statistic is approximately normal. and
(ii) Values given by the samples are sufficiently close to the population value and can be used in its place for calculating the standard error of the estimate.
When conducting research, quality sampling may be characterized by the number and selection of subjects or observations. Obtaining a sample size that is appropriate in both regards is critical for many reasons. Most importantly, a large sample size is more representative of the population, limiting the influence of outliers or extreme observations. A sufficiently large sample size is also necessary to produce results among variables that are significantly different. For qualitative studies, where the goal is to “reduce the chances of discovery failure,” a large sample size broadens the range of possible data and forms a better picture for analysis.
Sample size is also important for economic and ethical reasons. “An under-sized study can be a waste of resources for not having the capability to produce useful results, while an over-sized one uses more resources than are necessary. In an experiment involving human or animal subjects, sample size is a pivotal issue for ethical reasons. An under-sized experiment exposes the subjects to potentially harmful treatments without advancing knowledge. In an over-sized experiment, an unnecessary number of subjects are exposed to a potentially harmful treatment, or are denied a potentially beneficial one.”
