European Journal of Scientific Research - EuroJournals

European Journal of Scientific Research
ISSN 1450-216X Vol.14 No.3 (2006), pp. 319-325
© EuroJournals Publishing, Inc. 2006
http://www.eurojournals.com/ejsr.htm
Determination of Sample Size
Nadia Saeed
Department of Statistics, GC University (GCU)
Lahore (Pakistan)
E-mail: nadia_gcu@yahoo.com
Muhammad Khalid Pervaiz
Chairperson, Department of Statistics
GC University (GCU), Lahore (Pakistan)
E-mail: drkhalidpervaiz@hotmail.com
Muhammad Qaiser Shahbaz
Department of Statistics, GC University (GCU)
Lahore (Pakistan)
E-mail: drshahbaz@gcu.edu.pk
Abstract
The sample size determination is one of the most frequent problems in the
discipline of Statistics. Although standard formulae are available for determining sample
size in many situations, yet specific methodology is lacking. The purpose of the paper is to
highlight the factors involved in determining a desirable sample size for a research project.
The paper offers the brief review of determining the sample size under varying situations.
Some new formulae are also developed with special reference of cost function and degree
of affordable error.
Key Words: Sample size, error, clinical trials, power analysis and cost function.
1. Introduction
The size of the sample is not only an essential element in every statistical procedure but it is also an
item of great economic importance. In a sample survey, a statistician must determine the sample size.
Statistical studies (surveys, experiments, observational studies, etc.) are always better when they are
carefully planned. Good planning has many aspects. The study must be of adequate size, relative to the
goals of the study. Sample size is important for economic 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 (Mace, 1964; Kraemer & Thiemann, 1987; Cohen, 1988; Desu &
Raghavarao, 1990; Lipsey, 1990; Shuster, 1990; and Odeh & Fox, 1991).
The points to be considered while selecting a sample size are:
i) Parameter: The population parameters to be estimated like mean the difference between
means or proportion.
ii) Variance: The samples are taken to form estimates of some characteristics of interest, like
determination of mean in simple random sampling, stratified random sampling and cluster
sampling. Most of the work has been done to determine the sample size based on precision to