sapmle design 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=    t² x p(1-p)
    
m²
Description:
n = required sample size
t = confidence level at 95% (standard value of 1.96)
p = estimated prevalence of malnutrition in the project area
m = 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=    1.96² x .3(1-.3)
    
.05²
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 be 2 for nutrition surveys using cluster-sampling methodology.
Example
n x D = 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.