European Journal of Scientific Research - EuroJournals

Determination of Sample Size 320
minimize the variance. (Greenland, 1988; Samuels, 1992; Buderer, 1996; Satten & Kupper,
1990; Streiner, 1994 and Beal, 1989).
iii) Issues and Prior Information: If the process has been studied before, then the prior
information can be used to reduce sample sizes. This can be done by using prior mean and
variance estimates and by stratifying the population to reduce variation within groups. Increase
in sample size may reduce the sampling error but may cause increase in non-sampling error.
iv) Clinical Trials: At the planning stage of a clinical trial a key question is "How many patients
do we need?” This requires a sample size that ensures sufficient statistical power to detect a
clinically relevant improvement. Sample size must be planned carefully to ensure that the
research time, patient effort & support and costs invested in any clinical trial are not wasted.
v) Power Analysis: power analysis and sample size estimation is an important aspect of
experimental design, because without these calculations, sample size may be too high or too
low. If sample size is too low, the experiment will lack the precision to provide reliable answers
to the questions it is investigating. If sample size is too large, time and resources will be wasted,
often for minimal gain.
vi) Cost: The cost of sampling issue helps to determine how precise the estimate should be. When
choosing sample sizes, it is required to select risk values (affordable error). If the decisions
made from the sampling activity are very valuable, then these will have low risk values and
hence larger sample sizes. So some cost functions in different situations have been discussed.
Choosing the sample size is a problem faced by anyone doing a survey of any type. ‘What
sample size do I need?’ is one of the most frequently asked questions to the statisticians. The response
always starts “It depends on...” The sample size must depend on what you want to know about and
how well you want to know about it. In order to make rational sample size choices, both the quantities
to be estimated and the precision required must be specified.
Sample-size planning is very important and almost always difficult. It requires care in eliciting
scientific objectives and in obtaining suitable quantitative information prior to the study. Successful
resolution of the sample-size problem requires the close and honest collaboration of statisticians and
subject-matter experts (Russell, 2001).
Sample-size problems are context-dependent. For example, how important it is to increase the
sample size to account for such uncertainty depends on practical and ethical criteria. Moreover, sample
size is not always the main issue; it is only one aspect of the quality of a study design (Russell, 2001).
The objective of the paper is to mention available literature relevant to the determination of
sample size under various situations and to develop new formulae with reference to cost and affordable
error.
2. Sample size Estimation
In this Section a review of above mentioned points is given with reference to estimating parameters,
right variance, issues of interest, clinical trials, effect size, and power analysis.
2.1. Parameters
Chochran (1977) had given the simplest case for determination of sample size is concerned with
infinite normal population with known variance. Desu and Raghavarao (1990) had provided brief
review on sample size methodology. Further more the paired sample approach is employed by Dupont,
(1988); Parker & Bregman, (1986); Nam, (1992); Lu & Bean, (1995); Lachenbruch, (1992); Lachin,
(1992); Royston, (1993); Nam, (1997). A brief review has been given in literature to determine the
sample size for the tests of proportions by Chochran, 1977; Casagrande, Pike & Smith, 1978; Feigl,
1978; Haseman, 1978; Fleiss, 1981; Lemeshow, Hosmer & Klar, 1988; O’Neill, 1984; Thomas, 1992;
Whitehead, 1993 and Gordon & Watson, 1996 for infinite population.