Sample Size Calculator: Two Proportions Cross-Sectional

Descriptive Prevalence Study

Data Input: (Help) (Example)

Input	Results
α
β	NKelsey
P0	NFleiss
P1	NFleiss-cc
r

Note:

Variables	Descriptions
α	Probability of type I error
β	Probability of type II error
P0	Proportion of disease population 1
P1	Proportion of disease population 2
r	Ratio of population 2 to population 1
NKelsey	Sample size for population 1 using Kelsey formula
NFleiss	Sample size for population 1 using Fleiss formula
NFleiss-cc	Sample size for population 1 using Fleiss with continunity correction formula

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Application: This section illistrates how to determine the minimum sample size for a two proportion cross sectional study.

Procedure:

1. Enter

a)    Value of α, the two-sided confidence level

b)    Value of β, the type II error (1-power)

c)    Proportion for disease in population 1

d)    Proportion for disease in population 2

e)    The ratio of diseased in population 2 to population 1

2. Click the button “Calculate” to obtain

a)    various sample size

3. Click the button “Reset” for a new calculation

Formulae:

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Variable Notations:

α             The probability of type I error (significance level) is the probability of rejecting the true null hypothesis

β             The probability of type II error (1 - power of the test) is the probability of failing to reject the false null hypothesis.

P₀ The proportion of disease in population 1

P₁ The proportion of disease in population 2

r               The ratio of population 2 to population 1 (r population 2 to 1 population 1)

N_Kelsey Required sample size for the population 1 group using Kelsey formula

N_Fleiss Required sample size for the population 1 using Fleiss formula

N_Fleiss-cc Required sample size for the population 1 group using Fleiss formula with continunity correction

Example

Example 1: A researcher is doing a cross-sectional study on the smoking prevalence among male and female university students. Assume a two-sided significance level of 95%, a power of 80%, two equal groups, and the expected prevalence of smoking among female university students to be 35% and among males to be 50%. What is the desired sample size?

α = 0.05

β = 0.2

P₀ = 0.35

P₁=0.50

r=1

N_Kelsey = (1.960+0.842)²*0.4*0.6*2 / (0.35-0.5)²= 171

Therefore, using Kelsey's formula 171 male and 171 female are required for the cross-sectional study.

N_Fleiss = [1.96 sqrt(2*0.425*0.575)+0.842*sqrt(0.35*0.65+0.5*0.5)]²/(0.35-0.5)²=170

Therefore, using Fleiss's formula 170 male and 170 female are required.

Example 2: 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%. What is the desired sample size?

α = 0.05

β = 0.2

P₀ = 0.50

P₁=0.40

r=1

N_Kelsey = (1.960+0.842)²*0.45*0.55*2 / (0.50-0.40)²= 389

Therefore, using Kelsey's formula 778 subjects are required for the cross-sectional study.

N_Fleiss = [1.96 sqrt(2*0.45*0.55)+0.842*sqrt(0.4*0.6+0.5*0.5)]²/(0.5-0.4)²=388

Therefore, using Fleiss's formula 776 subjects are required for the cross-sectional study.

Reference:

Lemeshow, S., Hosmer Jr., D.W., Klar, J.,and Lwanga S.K. Adequacy of Sample Size in Health Studies. WHO, 1990. Print.

Kelsey J.L., Whittemore A.S., Evans A.S.,and Thompson W.D. Methods in Observational Epidemiology 2nd EditionOxford University Press, 1996. Print.

Fleiss, J.L. Statistical Methods for Rates and Proportions. 2nd Ed. NewYork: John Wiley, 1981. Print.

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

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