This document discusses sample size determination and calculation. It defines sample size as the subset of a population chosen for a study to make inferences about the total population. The key factors in determining sample size are the desired level of accuracy, allowing for appropriate analysis, and validity of significance tests. The document provides formulas and methods for calculating sample size for different study designs and populations, including using formulas, readymade tables, nomograms, and computer software. Accurately determining sample size is essential for research.

1. Greetings to you all

2. Determination of Sample Size

3. What is Sample Size ?
 This is the Sub population to be studied in order to make an
inference to a reference population ( A broader population to which
the findings from a study are to be generalized ).
 In census , the sample size is equal to the population size .
However , in research , because of time constraint and budget , a
representative sample are normally used .
 The larger the sample size the more accurate the findings from a
study .

5. What is Sample Size Determination ?
• Sample size determination is the mathematical estimation of the
number of subjects/units to be included in a study .
• When a representative sample is taken from a population , the
findings are generalized to the population
• Optimum sample size determination is required for the following
reasons :
 To provide the desired level of accuracy
 To allow for appropriate analysis
 To allow validity of significance test

6. How Large Sample Do I Need ?
• If a sample size is too small :
 Even a well conducted study may fail to answer its research question
 It may fail to detect important effect or association
 It may associate the effect imprecisely
• Conevrsely if the sample size is too large :
 The study will be difficult and costly
 Time constraint
 Loss of accuracy

7. Ways to Calculate Sample Size
There are four procedures that could be used for calculating sample
size :
1. Use of formulae
2. Ready made table
3. Nomograms
4. Computer software

8. Use of Formulae For Sample Size Calculation
• There are many formulae for calculating sample size in different
situations for different study designs.
• The appropriate sample size for population based study is determined
by 3 factors –
 The estimated prevalence of the variable of interest
 The desired level of confidence
 The acceptable margin of error

9. • To calculate the minimum sample size required for accuracy , in
estimating promotions , following decisions must be taken :
• Decide on a reasonable estimate of key proportions (P) to be
measured in the study
• Decide on the degree of accuracy(D) that is desired in the study , 1%-
5% or .01-.05 .
• Decide on the confidence level(Z) you want to use . Usually 95%
• Determine the size(N) of the population that the sample is supposed
to represent
• Decide on the minimum differences you would expect to find
statistical significance .

10. • For population >10,000.
n=Z2pq/d2
n= desired sample size(when the population>10,000)
Z=standard normal deviate; usually set at 1.96(or a~2), which
correspond to 95% confidence level.
p=proportion in the target population estimated to have a particular
characteristics. If there is no reasonable estimate, use 50%(i.e 0.5)
q=1-p(proportion in the target population not having the particular
characteristics)
d= degree of accuracy required, usually set at 0.05 level( occasionally
at 2.0)28

11. • If study population is < 10,000
nf=n/1+(n)/(N)
nf= desired sample size, when study population <10,000
n= desired sample size, when the study population > 10,000
N= estimate of the population size
Example, if n were found to be 400 and if the population size were
estimated at 1000, then nf will be calculated as follows
nf= 400/1+400/1000
nf= 400/1.4
nf=28630

12. Sample Size Formula For Comparison Of Groups
• If we wish to test difference(d) between two sub-samples regarding a
proportion & can assume an equal number of cases(n1=n2=n’) in two
sub- samples, the formula for n’ is
n’=2z2pq/d2
E.g suppose we want to compare an experimental group against a
control group with regards to women using contraception. If we expect
p to be 40 & wish to conclude that an observed difference of 0.10 or
more is significant at the 0.05 level, the sample size will be:
n’= 2(1.96)2(0.4)(0.6)/0.12
=184
Thus, 184 experimental subject & another 184 control subjects are
required.

13. Use Of Readymade Table For Sample Size Calculation
• How large a sample of patients should be followed up if an
investigator wishes to estimate the incidence rate of a disease to
within 10% of it’s true value with 95% confidence?
• The table show that for e=0.10 & confidence level of 95%, a sample
size of 385 would be needed.
• This table can be used to calculate the sample size making the
desired changes in the relative precision & confidence level .e.g if the
level of confidence is reduce to 90%, then the sample size would be
271.
• Such table that give ready made sample sizes are available for
different designs & situation

15. Use Of Nomogram For Sample Size Calculation
• For use of nomogram to calculate the sample size, one needs
to specify the study(group 1) & the control group(group 2). It
could be arbitrary or based on study design; the nomogram
will work either way.
• The researcher should then decide the effect size that is
clinically important to detect. This should be expressed in
terms of % change in the response rate compared with that
of the control group

16. USE OF COMPUTER SOFTWARE FOR SAMPLE
SIZE CALCULATION & POWER ANALYSIS
The following software can be used for calculating sample size & power :
• Epi-info
• nQuerry
• Power & precision
• Sample
• STATA
• SPSS

17. Finally -
Sample size determination is one of the most essential
component of every research/study.
• The larger the sample size, the higher the degree accuracy,
but this is limit by the availability of resources.
• It can be determined using formulae, readymade table,
nomogram or computer software