3. INTRODUCTION
■ Sample size is determination is
important in ensuring validity of the
findings in quantitative researches
■ Also, there are scientific, ethical, and
economic reasons for determining
sample size in studies
4. Scientific Reasons
■ In a trial with negative results and a
sufficient sample size, the result is
concrete
■ In a trial with negative results and
insufficient power (insufficient sample
size), may mistakenly conclude that
the treatment under study made no
difference
5. Ethical Reasons
■ An undersized study can expose
subjects to potentially harmful
treatments without the capability to
advance knowledge
■ An oversized study has the potential to
expose an unnecessarily large number
of subjects to potentially harmful
treatments
6. Economic Reasons
■ Undersized study is a waste of
resources due to its inability to yield
useful results
■ Oversized study may result in
statistically significant result with
doubtful clinical importance leading to
waste of resources
7. 7
TERMS ASSOCIATED WITH SAMPLE
SIZE AND SAMPLING
□ Study population
□ Sample population
□ Sampling
□ Precision
□ Confidence level
□ Power of the study
8. 8
Definitions of terms-1
□ Study population
■ A group of subjects to which we would
like to make inferences
□ Sample population
■ A subset of study population selected to
participate in the research when the
whole study population cannot be
reached
10. 10
Definition of terms-2
□ Sampling
A process of selecting a sample
□ Precision
A measure of how close an estimate from the
sample is to the true value of a population
parameter
□ Confidence level
The probability that an estimate of a
population parameter is within certain
specified limits of the true value
11. 11
Definition of terms-3
□ Power
The probability of detecting an association
given that an association exist
Power = 1-(type II error)
■ Normally set at least 0.8, meaning that there
is 20% chance that we will fail to detect the
real association
12. 12
SAMPLE SIZE DETERMINATION
□ Very few studies use the whole population
(Census)
□ Most studies use a subset of a population
(Sample)
□ How big should a sample be?
■ Too large or too little sample is unethical:
□ Too large: waste resources
□ Too little: Inconclusive results
NB: If you intend to use the whole population,
then you don’t need to determine a sample
13. 13
Two types of sample sizes
□ Desirable – calculated using
standard formulae
□ Feasible – not calculated, depends
on available resources (human,
time, money transport)
■ Eventual sample size – compromise
between desirable and feasible
14. 14
Desirable sample size
□ Determined by standard formulae
□ There are formulae depending on:
■ Aim of study
■ Nature of study
15. 15
Aim of the study
Study aim could be:
□ Estimating a population proportion
with specified precision
□ Hypothesis testing
16. 16
Nature of study
Nature of studies could be:
■ One sample situation
■ Two sample situation
■ Cohort
■ Case-control
■ Intervention
Each of these have different formulae
for determining sample size
17. 17
Factors to consider in determining sample
size
□ Power
□ Precision
□ Confidence level
□ Type and size of parameter being
estimated
□ Size of the population
18. Steps to calculate sample size
□ Consider the nature of the study
□ Identify major study variables/outcomes
□ Determine the type of estimate (e.g.
proportion, mean, rate, ratio)
□ Chose desirable precision of the
estimate
□ Choose desirable confidence level
□ Use appropriate formula to calculate
□ Adjust for expected response rate
18
19. Identify major study variables/outcomes
□ A study may have more than one
major variable/outcome
□ Separate sample size calculation
should be done for each important
variable/outcome & then use the
max. estimate
19
20. Adjusting for expected response rate
□ Not all subjects who are selected will
agree to participate
■ Thus, need to increase sample size to
account for non-response
■ Multiply non-response rate by the
obtained sample size, then add this
number to the sample size get the
ultimate sample
20
21. 21
Note that
□ Sample size calculation gives you the minimum
you require
□ Sample size determination formulae are
available in statistics books
□ There are computer softwares to aid calculating
sample sizes e.g. EPI info
□ It is advisable to consult a statistician if
available
