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Malaysian Journal of Medical Sciences
School of Medical Sciences, Universiti Sains Malaysia
ISSN: 1394-195X
Vol. 10, Num. 2, 2003, pp. 84-86
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Malaysian Journal of Medical Sciences, Vol. 10, No. 2, July 2003, pp. 84-86
Determination of sample size
Nyi Nyi Naing
Unit of Biostatisitcs and Research Methodology, School
of Medical Sciences, Universiti Sains Malaysia, Health Campus, 16150 Kubang
Kerian, Kelantan, Malaysia
Correspondence : Dr. Nyi Nyi Naing MBBS, DTM & H MSc(CTM) MPH MMedStats
FRSS, Unit of Biostatisitcs and Research Methodology, School of Medical Sciences,
Universiti Sains Malaysia, Health Campus, 16150 Kubang Kerian, Kelantan, Malaysia Submitted-15.11.2001,
Revised-13.5.2003,
Accepted-7.6.2003
Code Number: mj03027
There is a particular importance of determining a basic
minimum required `n' size of the sample to recognize a particular measurement
of a particular population. This article has highlighted the determination
of an appropriate size to estimate population parameters.
Key words : determonation, sample size,
population parameters
INTRODUCTION
As scientific merit and ethical issue go hand-in-hand, the
awareness of determination of minimum required sample size and application
of appropriate sampling methods are extremely important in achieving scientifically
and statistically sound results.
Statistical analysis is based on the key idea that observation
on a sample of subjects is made and then draws inferences about the population
from which the sample is drawn. If the study sample is not representative of
the population, it will well mislead and statistical procedure cannot help.
However, even a well-designed study can give only an idea of the answer sought
because of random variation in the sample. Thus results from a single sample
are subject to statistical uncertainty which is strongly related to the size
of the sample. Quality or strength of statistical inference depends
largely on the size of the sample selected (1).
In this regard, there are some concerns about determining
adequate sample size for studies where particular parameters of populations
are estimated. In these studies, the common parameters are either to estimate
a `mean' or `proportion' of a parameter of a population concerned. Common examples
are the estimation of mean body weight of children under five in a population,
the estimation of mean blood sugar level of adults aged more than thirty in
a population, the estimation of proportion of
smokers in a population and the estimation of prevalence
of disease `X' in a population.
Appropriate inclusion and exclusion criteria are also important
to obtain participants who have particular characteristics which are under
research interest. The other area, which cannot be simply ignored, is testing
validity and reliability of measurement tools before actual data collection.
A pilot study or a pretest is required to test the validity and reliability
of measurement tools. In addition, there are a number of potential biases which
can be avoided while designing study and during planning of data collection.
The following is the brief guide to approach how to determine
a sample size in this kind of studies. It is based on whether a parameter is
a `mean' or a `proportion' (2,3,4).
The quantity z representing the width of the confidence interval
(precision) is given by Δ.
For a 95% confidence interval :
Some information about the varience of the
observations (σ2) is required before
sample size can be calculated. It can be obtained from previous
studies in literature or from a pilot study if there
was no similar studies conducted before.
Example
We want to estimate the mean systolic blood
pressure of Malaysian females. The standard
deviation is around 20 mmHg and we wish to
estimate the true mean to within 5mmHg with 95%
confidence. What is the required sample size ?
Answer
We are given σ = 20, Δ = 5 and z= 1.96.
The minimum sample size required is round
up to 62 women.
If 20% drop-out is assumed, 62+12 = 74 women
needed to be sampled.
If the parameter is a proportion
Sample size
- p is expected propotion of individuals in the sample
with the charecteristic of interect at the 100 (1-σ)%
confidence interval.
- The quantity representing
the width
of the confidence interval is given by Δ.
To determine the sample size required to
estimate the proportion with the desired level of
precision, some idea is required beforehand about
the possible magnitude of the proportion. It can be
obtained from previous studies in literature or from
a pilot study if there was no similar study conducted
before.
Example
To estimate the proportion of Malaysian males who smoke, what
sample size is required to achieve a 95% confidence interval of width ±5%
(that is to be within 5% of the true value)? A study some years ago found that
approximately 30% were smokers.
Answer
The sample of 323 men is required at analysis stage. If 75%
response rate is assumed, 323+81= 404 men need to be sampled.
DISCUSSION
These studies have been conducted in many parts of the world.
There were some studies which have been done with a very minimum number of
samples. The statistical importance of required sample size, to be earmarked
as a standard value for a particular population, was rarely emphasized though
values have been recognized as references for ages. Health personnel need to
be aware of the fact that central to the planning of any such study is the
decision on how large a sample to select from the population under study. This
article has tried to discuss to a certain extent about important issue of sample
size in these studies. However, there are definitely some more facts to be
addressed in this particular area of health sciences.
REFERENCES
- Gardner MJ, Altman DG. Statistics with confidence - confidence
intervals and statistical guidelines. 1989: 1-13.
- Dobson AJ. Calculating sample size. Trans. Menzies Foundation,
1984; 7: 75-9.
- Lemeshow S, Hosmer DW, Klar J, Lwanga SK.
Adequacy of sample size in health studies. World
Health Organization. 1990: 1-4.
- Lwanga SK, Lemeshow S. Sample size determination
in health studies, A practical manual. World Health
Organization. 1991: 1-3.
Copyright 2003 - Malaysian Journal of Medical Science
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