# Representative sample

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### Anonymous 490

SMART Survey Consultant

Normal user

1 Apr 2015, 21:02

What is the smallest/least representative sample or number of children/households one can assess in a SMART survey.

### Mark Myatt

Frequent user

2 Apr 2015, 09:32

I will try to give some short answers ...

SMALLEST : The SMART survey method is derived from the much older EPI survey method for estimating vaccine coverage. EPI surveys typically use a two-stage clusters sample of 30 clusters of 7 children (i.e. the overall sample size is n = 210). This sample size was chosen to return an estimate (any level) with a 95% CI of +/- 10% or better with as survey design effect of about 2.0.

If you were only using SMART to look at an indicator such as the proportion of children meeting a minimum dietary diversity then this level of precision(i.e. +/- 10%) might be good enough. It is, however, too coarse for assessing the prevalence of small proportions such as you might expect with GAM. If (e.g.) you expected a GAM prevalence of about 12% then you might want a precision of +/- 3% on the estimate. The ENA software for SMART surveys has a good sample size calculator but we will do this by hand. The sample size required would be about:

Prevalence (p) = 12% Precision (e) = 3% Design effect (DEFF) = 1.5 n = DEFF * (p * (1 - p)) / (e / 1.96)^2 n = 1.5 * (0.12 * (1 - 0.12)) / (0.03 / 1.96)^2 n = 676

You'd want to take this using about 30 clusters of:

cluster size = 676/30 = 23 (rounded up)

More small clusters are better than few large clusters.

If you want better precision you will need a larger sample size (either as more smaller clusters or a a bigger overall sample size or both). You will almost never need a sample size greater than n = 900 (i.e. the old 30-by-30 design).

The sample here is for individuals. This can be converted to HHs. If HHs are your unit of interest (e.g. you might want to estimate proportions of HHs with an improved latrine) then you need make no change. If (e.g.) you want to know how many HHs to sample to get a given sample of children then you will need to divide the calculated sample by some estimated mean number of eligible children in each HH. If we expect 1.5 eligible children per HH then (with the above sample size):

n = 676 kids per HH = 1.5 number of HHs = 676 / 1.5 = 450 cluster size = 450 / 30 = 15 HHs

SMART documentation covers sampling issues in useful detail.

REPRESENTATIVE : This is a really BIG question. The answer depends on how you define "representative". There are a number of definitions. I think we can avoid philosophy here. Assuming that you are using a two-stage cluster sample with PPS sampling to select clusters (most SMART surveys use this) then you will need:

(1) A **complete** list of communities from which to sample clusters. If the list is not complete then there will be a selection bias against the communities not listed. Even a good list will usually excluded (e.g.) transhumant groups such as nomadic pastoralists.

(2) A reasonably accurate population estimate for **all** communities. The accuracy does not need to be absolute as weighting only requires that relative sizes are accurate.

(3) The skills needed to take the PPS sample (see SMART documentation).

(4) The ability to reach the communities selected in (3).

(5) Proper application of the within-community sampling procedures.

Failures at any of these points will risk your taking a sample that is not representative.

SMART documentation covers sampling issues in useful detail.

I hope this is of some use.

### Scott Logue

Normal user

2 Apr 2015, 19:39

Thank you Mark for this comprehensive answer. Indeed, you calculate sample size to achieve the minimum level of precision required for interpretation of results in order to make programmatic decisions. To answer your question, there is no minimum sample size for nutrition surveys. Your main concern when running a survey should be to avoid selection bias (as Mark clearly explained) when undertaking cluster and household selection. Kindly refer to page 19 in the 2012 Sampling Methods & Sample size calculation for the SMART methodology for more complete guidance on selecting level of precision based on estimated GAM prevalence.

In situations of emergencies or high insecurity, please refer to the Rapid SMART Guidelines. Minimum number of households and children are also discussed in this document.

Both of these documents can be found at the following link on the SMART Methodology website:

http://smartmethodology.org/survey-planning-tools/smart-methodology/

For any other SMART-related questions, check out the SMART Forum: http://smartmethodology.org/forums/