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AADAPT Workshop South Asia Goa, December 17-21, 2009 Kristen Himelein 1

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The goal of this presentation is not to make you a sampling expert – rather to give an overview of the issues faced in designing a sample for your impact evaluation. (Generally it is recommended that you consult a sampling expert.) Using randomization as a benchmark - I will not deal with non-experimental designs in general, though what follows can be straightforwardly adapted to cover that case Main Question: how do we construct a sample to credibly detect a given effect size within our evaluation budget constraints? 2

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Experiments can be seen as lotteries that randomly assign subjects to separate groups, each of which is offered a different “treatment” Randomizing subjects to experimental groups eliminates all systematic preexisting group differences, as only chance determines which subjects are assigned to which group After the experiment, we compare the outcome of interest in the treatment and the control group Effect = Mean in treatment - Mean in control 3

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The design of each experiment differs, but generally we use a “two stage” approach to selecting a random sample for an impact evaluation. First we select larger areas called “primary sampling units” [PSU] into treatment and control. Then we select “units of analysis” (such as households or farms or clinics) within the selected PSUs. These resulting groups have no systematic differences and will be what we compare in the analysis. 4

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To select these groups in real life we need to have a “sampling frame”. A sampling frame is a list of all the eligible groups at each stage of the sampling. For example: If your PSU is villages in your project district, you would need a complete list of all villages in that district. If you are using households within a village in the second stage, you would need a recent list of all the households in the villages selected in the first stage. 5

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Now all you need to know is how many PSUs and units of analysis you need to credibly measure the impact of your project. 6

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8 Sigma (σ) is the variance in population outcome metric Basically means how wide of a range of differences you expect in the outcome that you will measure. This can be difficult to calculate – the best way is if you have data collected previously (national household survey, project assessment, piloting data, etc). If not, estimations can be made using “(high-low)/4” as a rule of thumb.

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9 D is the effect size or how much of an impact your project will have. Trade off between sample size and effect – the smaller an effect is the bigger a sample size that you will need. Be careful about picking too big of an effect size as you are setting yourself up for failure.

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10 Z’s are from standard normal cumulative distribution function and they relate to the certainty of your conclusions. The values of z are taken from a table depending on the values of α and β. α relates to “type I error” and β relates to “type II error”

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Significance level: Probability that you will falsely conclude that the program has an effect when in fact it does not. Type I error: Conclude that there is an effect, when in fact there are no effect. You select level of 5%, you can be 95% confident in the validity of your conclusion that the program had an effect For policy purpose, you want to be very confident of the answer you give: the level will be set fairly low. The more confident you want to be in your answer, the lower level you will need to select and the bigger your sample will need to be. 11

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Power: Probability to find a significant effect if there truly is an effect Type II error: Fail to reject that the program had no effect when it fact it does have an effect Common values used are 80% or 90%. One minus the power is the probability to be disappointed. (So if you pick a power of 80%, there is a 20% chance that even though your project does have an impact, the evaluation will fail to detect it.) The more power you want your test to have, the larger a sample size you will need. 12

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13 This part of the equation relates to how many clusters and households you select into your sample. Rho (ρ) is the intracluster correlation effect. This is a measure of how similar your observations within each PSU tend to be. H is the number of observations in each cluster. The more similar households are to each other and the more households you have in each cluster, the higher overall sample size you will need.

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14 The reason that ρ raises your sample size is because to more alike this are within a cluster, the less likely they are to be representative of the whole area. ρ‘s are generally high for infrastructure projects, because either the whole village has assess to a road or water source, or the whole village does not. ρ‘s for contraceptive projects tend to be low, because while a neighbor’s actions might influence a woman, decisions about children are generally made within the family.

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15 Final note: Beware the square! There is not a 1 to 1 relationship between sample size and most of the terms that are used to calculate it. So halving the size of the effect that you are looking for will raise required sample size by 4 times!

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Stratification Partition sample to ensure sufficient number of observations in all categories Oversampling Larger proportion of observations from certain strata than proportion in overall population Sample Weights Used to account for oversampling when making inferences about overall population 16

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Treatment Arms: Having multiple treatment arms in a program increases the required sample size quickly. For example, if the sample size calculations indicate that you will need 500 households in your treatment group and 500 households in your control group, and you want to add another type of treatment, you will need 500 households in treatment 1, 500 households in treatment 2 and 500 households in your control to maintain the power of your estimations. 17

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In reality there are generally finite resources available to do impact evaluations. Many time we end up doing a series of calculations varying the components to see just how much power and certainty we can afford. While there is a certain amount of guesswork involved in calculations, it is important to spend effort on them: Avoid launching studies that will have no power at all: waste of time and money, potentially harmful Devote the appropriate resources to the studies that you decide to conduct (and not too much) 18

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Questions? 19

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A 95% confidence interval for an effect size tells us that, for 95% of any samples that we could have drawn from the same population, the estimated effect would have fallen into this interval If zero does not belong to the 95% confidence interval of the effect size we measured, then we can be at least 95% sure that the effect size is not zero The rule of thumb is that if the effect size is more than twice the standard error, you can conclude with more than 95% certainty that the program had an effect 22

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Sometimes impacts are measured as a standardized mean difference Example: outcomes in different metrics must be combined or compared The standardized mean effect size equals the difference in mean outcomes for the treatment group and control group, divided by the standard deviation of outcomes across subjects within experimental groups 23

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