Calculating the Sample Size

The sample size, in this case, refers to the number of children to be included in the survey.

Step 1: Base Sample-size Calculation

The appropriate sample size for a population-based survey is determined largely by three factors: (i) the estimated prevalence of the variable of interest chronic malnutrition in this instance, (ii) the desired level of confidence and (iii) the acceptable margin of error.

For a survey design based on a simple random sample, the sample size required can be calculated according to the following formula.

Formula:

n=

txp(1-p)

m

Description:

n= required sample sizet =confidence level at 95% (standard value of 1.96)p =estimated prevalence of malnutrition in the project aream =margin of error at 5% (standard value of 0.05)

Example

In the Al Haouz project in Morocco, it has been estimated that roughly 30% (0.3) of the children in the project area suffer from chronic malnutrition. This figure has been taken from national statistics on malnutrition in rural areas. Use of the standard values listed above provides the following calculation.

Calculation:

n=

1.96 x .3(1-.3)

.05

n=

3.8416 x .21

.0025

n=

.8068

.0025

n=

322.72 ~323

Step 2: Design Effect

The anthropometric survey is designed as a cluster sample (a representative selection of villages), not a simple random sample. To correct for the difference in design, the sample size is multiplied by the design effect (D).

The design effect is generally assumed to be2for nutrition surveys using cluster-sampling methodology.

Example

nxD= 323 x 2 =646

Step 3: Contingency

The sample is further increased by 5% to account for contingencies such as non-response or recording error.

Example

n+ 5% = 646 x 1.05 = 678.3 678

Step 4: Distribution of Observations

Finally, the calculation result is rounded up to the closest number that matches well with the number of clusters (30 villages) to be surveyed.

Thirty is the standard number of clusters established by the WHO Expanded Programme of Immunization (EPI Cluster Surveys). There is no statistically necessary reason to maintain exactly 30 clusters, and the number can be adjusted if there is a compelling motive for doing so.

Example

Final Sample Size:N = 690 children

The final sample size (N) is then divided by the number of clusters (30) to determine the number of observations per cluster.

Example

N no. clusters = 690 30 =23 children per village

General Rule: Standardized Sample Sizes for Nutrition Surveys

The following table provides the recommended sample size for various estimated levels of malnutrition, incorporating standard values for confidence level and margin of error. The final sample size includes the contingency percentage and is rounded to match well with a 30-cluster survey.

P

(est. % malnutrition)

n

(base sample size)

n x D

(n x design effect)

N

(final sample size)

0.2(20%)

246

492

540

0.25(25%)

288

576

600

0.3(30%)

323

646

690

0.35(35%)

350

700

720

0.4(40%)

369

738

750

0.45(45%)

380

760

780

0.5(50%)

384

768

810

Note:If it is not possible to find an estimated prevalence of malnutrition for the project area, the recommended action is to set the sample size at 810.

When in doubt, set the sample size at 810.

References

FAO. 1990.Conducting small-scale nutrition surveys: A field manual, Rome.

Magnani, Robert. 1997.Sampling guide. IMPACT Food Security and Nutrition Monitoring Project, Arlington, Va.

UNICEF. 1995.Monitoring progress toward the goals of the World Food Summit for Children: A practical handbook for multiple indicator surveys.New York.