Sample size calculation for comparing two surveys
In some situations two sequential cross-sectional surveys are planned; frequently the
first cross-sectional survey is to establish a pre-intervention baseline estimate, and then
after a period of time (usually 1-5 years), a second cross-sectional survey (“follow-up”
survey) is performed to assess the estimated impact of interventions. This approach to
sample size calculation requires a number of assumptions and preferences for certain
values. In the calculations below it is assumed that the sample size in each survey will
be the same.
Estimates and preferences are needed for:
p1
The estimated proportion with disease or intervention at baseline survey
p2
The estimated proportion with disease or intervention at follow-up survey
DEFF
The estimated design effect - here it is assumed the DEFF will be the
same for both surveys
α
Level of significance (“alpha”), usually .05 or 5% (corresponds with 95%
confidence interval)
1- β
Power, usually .8 (80%) or .9 (90%)
The formula is:
Z α/2
n  DEFF 
2pq - Z 1 β p1q1  p2 q2
2
(p1  p 2 )2
where
p
p1  p 2
and q  1  p when sample sizes are to be equal
2
q1 = 1 – p1
q2 = 1 – p2
Z/2 is the Z-value for the level of significance
Z1- is the Z-value for the Power
The most common Z-values for the level of significance and Power are provided in
Tables 1 and 2, respectively.
(Gorstein J, Sullivan KM, Parvanta I, Begin F. Indicators and methods for cross-sectional
surveys of vitamin and mineral status of populations. Micronutrient Initiative (Ottawa)
and Centers for Disease Control and Prevention (Atlanta), May 2007, pg 31).
Table 1 Two-sided Z-values ( Z α/2 ) for various significance levels
Significance level (α)
.01
.05
.10
2-sided Z-value
2.576
1.960
1.645
Table 2 One-sided Z-values (Z1-) for various Power (1- β) levels
β value
Power (1- β)
1-sided Z-value
.01
.99
-2.326
.05
.95
-1.645
.10
.90
-1.282
.20
.80
-0.842
Example: A country is going to begin fortifying flour with iron and estimate the baseline
prevalence of anemia to be 50% in women of childbearing age. They estimate that iron
fortification of flour will lower the prevalence in this group to 40%.
Example:
p1 = .50, q1 = .50
p2 = .40, q2 = .60
α = .05, therefore Zα/2 = 1.96
β = .20, therefore Z1β = -.842
DEFF = 2
Need to calculate p . For equal sample sizes:
p
.50  .40
 .45 , q  1  .45  .55
2
1.96
n  2
2(.45)(.55 ) - (-.842) (.50)(.50)  (.40)(.60)
(.50  .40 ) 2
2  2  3.876  776
.01
The sample size would be 776 individuals in for each cross-sectional survey, i.e., 776 for
the baseline survey and 776 in the follow-up survey.