This document discusses calculating sample sizes for cross-sectional studies measuring prevalence. It explains that the outcome being measured in a cross-sectional study is prevalence of a disease/risk factor. It recommends doing a literature review to estimate prevalence and determining the absolute precision required, usually between 3 to 5 percentage points. It provides the formula for calculating sample size and an example calculating a sample size for a study measuring obesity prevalence. It also discusses calculating sample sizes when the population is known and alternatives when prior information is not available.

1. © Dr Azmi Mohd Tamil, 2012
Calculate Your Own
Sample Size – Part 3
Cross-Sectional Study –
Measuring Prevalence
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2. © Dr Azmi Mohd Tamil, 2012
Cross-Sectional
What is the outcome being measured?
 Is it the prevalence of disease/risk
factor?
 In the specific objective, it is stated that the
study is conducted to determine the
prevalence of the disease/risk factor.
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3. © Dr Azmi Mohd Tamil, 2012
Prevalence in
Cross-Sectional
Do a literature review to estimate the
prevalence being studied.
Determine the absolute precision required i.e.
5 percentage points (usually between 3 to 5).
Calculate using (Kish L. 1965)
n = (Z1-α)2(P(1-P)/D2)
or refer to a table in S.K. Lwanga, S.
Lemeshaw 1991, Sample Size Determination
in Health Studies, pg 25
Or use StatCalc from EpiInfo6.
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4. © Dr Azmi Mohd Tamil, 2012
Example – To determine
Prevalence of Obesity
Confidence interval = 1 - α = 95%;
Z1-α = Z0.95 = 1.96
(from normal distribution table).
Prevalence = P = 20%
Absolute precision required = 5 percentage
points,
(therefore if the calculated prevalence of the
study is 20%, then the true value of the
prevalence lies between 15-25%).
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5. © Dr Azmi Mohd Tamil, 2012
Calculate Manually
n = (Z1-α)2(P(1-P)/D2) where
Z1-α = Z0.95 = 1.96 (from normal distribution
table. This value of 1.96 is standard for
CI of 95%).
P = 20% = 0.2 in this example
D = 5% = 0.05 in this example
n = 1.962 x (0.2(1-0.2)/0.052) = 245.84
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6. © Dr Azmi Mohd Tamil, 2012
Refer to Table
Refer to the table in S.K. Lwanga, S.
Lemeshaw 1991, Sample Size
Determination in Health Studies pg 25.
With a Prevalence (P) of 20%, precision
of 0.05, the table indicates that the
sample size required is 246.
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7. © Dr Azmi Mohd Tamil, 2012
Prevalence = 20%
precision = 0.05
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8. © Dr Azmi Mohd Tamil, 2012
Alternative to table
http://www.palmx.org/samplesize/Calc_Samplesize.xls
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9. Or use StatCalc (Step 1)
© Dr Azmi Mohd Tamil, 2012
P = 20% = 0.2 in this example
D = 5% = 0.05 therefore the true value of the prevalence lies between 15-
25%. So worse acceptable result is either 15% or 25%
Press F4 to calculate.
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10. StatCalc (Step 2)
© Dr Azmi Mohd Tamil, 2012
Using 95% confidence level, the sample size required
is 246, the same value as manual calculation & the
table.
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11. Formula for Sample Size of
© Dr Azmi Mohd Tamil, 2012
A Prevalence Study
It is the same since all calculations uses the same formula.
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12. © Dr Azmi Mohd Tamil, 2012
If Prevalence Below 10%
or Above 90%
If the prevalence being studied is below 10%,
therefore the level of precision should be half
of the prevalence; i.e. prevalence of Diabetes
Mellitus is 6% therefore d must be set at 3%.
The same applies to prevalence of above
90%. The level of precision should be half of
the (1-prevalence); i.e. prevalence of BCG
vaccination is 96% therefore d must be set at
2%.
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13. © Dr Azmi Mohd Tamil, 2012
SS Calculation for a
Known Population
What if the required sample size is
larger than the population being
studied?
i.e. study on stress among staff at
Rembau Health Clinic. Expected rate of
stress is 50% therefore at 5% precision,
the required sample size is 384. But the
number of staff is only 30!
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14. © Dr Azmi Mohd Tamil, 2012
SS Calculation for a
Known Population
Krejcie & Morgan
 Krejcie, R.V. & Morgan, D.W. (1970). Determining sample size for
research activities. Educational & Psychological Measurement, 30,
607-610.
 S = required sample size
N = the given population size
P = prevalence
d = the degree of accuracy
X2 = 3.841 for the .95 confidence level
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15. © Dr Azmi Mohd Tamil, 2012
Table - Krejcie, R.V. &
Morgan, D.W. (1970).
Assumption of the table;
prevalence = 50%. So
need only 28 out of 30
for the study on stress,
not 384.
If population > 250,000,
sample size equal to
Kish’s formula.
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16. © Dr Azmi Mohd Tamil, 2012
Kish, L (1960) = Krejcie, R.V.
& Morgan, D.W. (1970) ?
Kish, L (1960) Krejcie, R.V. & Morgan, D.W. (1970)
n = (Z1-α)2(P(1-P)/D2)
S = n/(1+(n/population)
(Z1-α)2 = X2 = 3.841
Population = N
So we can use STATCALC
P= P
to calculate sample size for
D2 = d2 = 0.0025 (for 5%) a known population!
We usually use only 1st half of the formula!
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17. StatCalc
© Dr Azmi Mohd Tamil, 2012
Using 95% confidence level, the sample size required
is 28, the same value as in the table.
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18. © Dr Azmi Mohd Tamil, 2012
What If There Is
No Prior Information?
Instead of saying "Sample sizes are not
provided because there is no prior
information on which to base them“, do this
instead;
 Find previously published information
 Conduct small pre-study
 If a very preliminary pilot study, sample size
calculations not usually necessary
 Assume that the prevalence is 50% since that will
give you the largest required sample size.
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19. © Dr Azmi Mohd Tamil, 2012
Conclusion
You can calculate your own sample size.
Tools are available and most of them are free.
Decide what is your study design and choose
the appropriate method to calculate the
sample size.
If despite following ALL these notes
fastidiously, your proposal is still rejected by
the committee due to sample size, kindly SEE
THEM, not us.
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20. © Dr Azmi Mohd Tamil, 2012
References (incl. for StatCalc)
Fleiss JL. Statistical methods for rates and proportions. New
York: John Wiley and Sons, 1981.
Gehan EA. Clinical Trials in Cancer Research. Environmental
Health Perspectives Vol. 32, pp. 3148, 1979.
Jones SR, Carley S & Harrison M. An introduction to power and
sample size estimation. Emergency Medical Journal
2003;20;453-458. 2003
Kish L. Survey sampling. John Wiley & Sons, N.Y., 1965.
Krejcie, R.V. & Morgan, D.W. (1970). Determining sample size
for research activities. Educational & Psychological
Measurement, 30, 607-610.
Snedecor GW, Cochran WG. 1989. Statistical Methods. 8th Ed.
Ames: Iowa State Press.
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21. © Dr Azmi Mohd Tamil, 2012
References (PS2)
Dupont WD, Plummer WD, Jr: Power and Sample Size Calculations: A Review
and Computer Program. Controlled Clinical Trials 11:116-128, 1990
Dupont WD, Plummer WD, Jr: Power and Sample Size Calculations for Studies
Involving Linear Regression. Controlled Clinical Trials 19:589-601, 1998
Schoenfeld DA, Richter JR: Nomograms for calculating the number of patients
needed for a clinical trial with survival as an endpoint. Biometrics 38:163-170,
1982
Pearson ES, Hartley HO: Biometrika Tables for Statisticians Vol. I 3rd Ed.
Cambridge: Cambridge University Press, 1970
Schlesselman JJ: Case-Control Studies: Design, Conduct, Analysis. New York:
Oxford University Press, 1982
Casagrande JT, Pike MC, Smith PG: An improved approximate formula for
calculating sample sizes for comparing two binomial distributions. Biometrics
34:483-486, 1978
Dupont WD: Power calculations for matched case-control studies. Biometrics
44:1157-1168, 1988
Fleiss JL. Statistical methods for rates and proportions. New York: John Wiley
and Sons, 1981.
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22. © Dr Azmi Mohd Tamil, 2012
THANK
YOU
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