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# Sample size determination

This question was posted the Assessment and Surveillance forum area and has 3 replies.

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### Mark Myatt

Frequent user

18 Aug 2017, 08:01

Assuming a simple random sample or a simple systematic sample from a large population the sample size required to estimate a proportion with a 95% CI of a give width:

```    n = (p * (1 - p)) / (e / 1.96)^2
```

where p is the proportion being estimated (0.45 in your case) and e is the require half-width of the 95% CI. If we table p = 0.45 (45%) and e = +/- 0.05 (5%) then:

```    n = (p * (1 - p)) / (e / 1.96)^2
n = (0.45 * (1 - 0.45)) / (0.05 / 1.96)^2
n = 380
```

Most practical samples that we use will have two or more stages. Anything that differs from a simple ramdom sample will have a design effect. I wonder what you mean by an "entire district" sample. Such a sample is the aim of cluster surveys like SMART. An "entire district" sample might use a spatially stratified sample. This will tend to give low design effects and it may be OK to ignore design effects. A smart type survey may have large design effects. Design effects can be small if you have many small clusters and prevalence that is pretty constant wherever you go then design effects will likely not be very large.

Unless you have a simple ramdom sample then I think you should (1) specify a design effect and (2) analyse the data in a way that takes into account the sample design. For the design effect, a safe design effect would be 1.5 or 2.0 (SMART people can advise). for a design effect of 1.t we have:

```    n = DEFF * ((p * (1 - p)) / (e / 1.96)^2)
n = 1.5 * ((0.45 * (1 - 0.45)) / (0.05 / 1.96)^2)
n = 570
```

ENA for SMART can analyse data from a simple random sample and from a two stage PPS cluster sample. For other designs you can use SUDAAN, STATA, R, SPSS, EpiInfo, &c.

I hope this is of some use.

### Kennedy Musumba

SMART Program Manager

Normal user

18 Aug 2017, 12:00

Hello Theo,

The Design Effect (DEFF) is a measure of homogeneity of the indicator of interest (Stunting in your case) in a target population. The DEFF factor is meant to compensate for notable variations among clusters/villages and only applicable when doing Cluster Sampling.

If simple or systematic random sampling method is applied in your survey, the DEFF will be 1 and this shouldn’t be a worry in your sample size determination.

Further details are available in the Sampling for SMART guide available in Complementary Tools and Resources - Download Handouts

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