HOW TO MAKE ASSUMPTIONS NEEDED FOR SAMPLE SIZE CALCULATION

One of the most difficult aspects of determining a sample size is deciding what values to include in the formula for precision, the prevalence of the outcome and the design effect. Below is some gui- dance for making these assumptions.

Precision.If survey workers want greater precision, the sample size must be lar- ger, as described above. To determine just how much precision you need, you must consider what question the survey is designed to answer. If a survey is meant to determine whether there is a

large problem with malnutrition, then you may not need much precision. On the other hand, if you will compare this survey to a baseline or a follow-up sur- vey, you may want much more precision to ensure that a difference detected bet- ween the two surveys has statistical significance. Also, if precise subgroup estimates are needed, such as males vs. females, or by age, then a larger sample size would be required. In fact, desired precision and expected prevalence are interconnected. Therefore, if you expect a high level of malnutrition or mortality in the population to be surveyed, you will have to use a larger sample size to achieve a given precision.

However, you often will not need such high precision for common outcomes or indicators. For example, if the prevalen- ce of stunting is 50 percent, there may be no programmatic decision which would change if the prevalence were 45 percent or 55 percent, so very narrow confidence intervals may not be neces- sary; ±10 percentage points may be sufficient. On the other hand, rarer out- comes may need greater precision. If the prevalence of wasting is estimated to be 10 percent, confidence intervals of ±10 percentage points would not be very useful. This would mean that the true prevalence of wasting is somewhe- re between 0 percent and 20 percent. The difference here is significant: 0 per- cent is excellent and no additional fee- ding programs are needed, while 20 percent is a catastrophe, requiring widespread food aid and supplementa- ry and therapeutic feeding programmes. To distinguish between these possibili- ties and make programmatic decisions, you will need much greater precision, such as ±3 or ±4 percentage points so that the confidence interval is 7 percent - 13 percent or 6 percent - 14 percent.

DESIGNING A SURVEY CHAPTER

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The important point is that there is no standard precision to be used, nor any way to calculate the desired precision. You must consider why the survey is being conducted and what questions need to be answered. Then think about possible results and whether wide confidence inter- vals will be acceptable when making pro- gram decisions.

Expected malnutrition prevalence or mortality rate

You can use various techniques to obtain a gross estimate of the prevalence of mal- nutrition or the rate of mortality before you conduct a survey. Surveillance data, for example, may include counts of the number of children presenting to clinics with malnutrition or the number of deaths. A prior survey may have estimated these outcomes, and persons who have worked in this population since that sur- vey may be able to give you a general idea if malnutrition or mortality have changed since that survey. An overall impression of the extent of malnutrition or mortality also can be obtained by more qualitative means. You can ask health workers if they see many thin children, or you can ask religious leaders if they recently have been called upon to conduct more than the usual number of funerals.

In general, a prevalence of wasting of 20 percent is very high. In such a situation, you will have already received many reports of serious malnutrition while organizing the survey. The traditional 30 x 30 survey assumes a prevalence of 50 percent, a level of wasting seen only very rarely in the worst emergency situations. However, if you have only the most imprecise estimate of the prevalence of malnutrition, use an estimate closer to 50 percent than you think is the true preva- lence. This will overestimate the sample size required, ensuring that you have a

large enough sample size to get the nee- ded precision.

Design effectis a measure of how evenly or unevenly the outcome (for example, wasting, stunting, anaemia, or mortality) is distributed in the population being sam- pled. For example, if you think that malnu- trition is about the same in all parts of the population, then the design effect is proba- bly low. In many populations, the design effect for malnutrition is usually in the range of 1.5-2.0. On the other hand, if you think an outcome such as mortality is quite different in different parts of the population, then the design effect may be quite high. For example, in emergencies where violen- ce causes a large proportion of deaths and the violence is not evenly distributed, the design effect can be in the range of 4-10. Probably the best source for estimates of design effect are prior surveys done in the same or similar populations. However, because the design effect changes with the number of units of analysis in each cluster, design effects from prior surveys should not be used in the calculation of sample size for a survey which will have a very different cluster size. In general, the greater the number of units of analy- sis in each cluster, the larger the DEFF. There are some published papers which can give some indication of the range of possible design effects for various outco- mes other than the prevalence of wasting and mortality rates.

Sample size calculation accounting for non-response

Sample size calculations should also account for non-response. If we assume that, at most, 10 percent of households will be gone or will refuse participation, then we must select enough households for the initial sample so that, if we lose 10 percent of selected households to