Sample size calculation for comparing two surveys

Дата канвертавання28.04.2016
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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:


and when sample sizes are to be equal

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 () for various significance levels

Significance level (α)

2-sided Z-value







Table 2 One-sided Z-values (Z1-) for various Power (1- β) levels

β value

Power (1- β)

1-sided Z-value













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%.

p1 = .50, q1 = .50

p2 = .40, q2 = .60

α = .05, therefore = 1.96

β = .20, therefore = -.842

DEFF = 2

Need to calculate . For equal sample sizes:


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.

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