Sampling for Impact Evaluation. Maria Jones 24 June 2015 ieconnect Impact Evaluation Workshop Rio de Janeiro, Brazil June 22-25, 2015

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1 Sampling for Impact Evaluation Maria Jones 24 June 2015 ieconnect Impact Evaluation Workshop Rio de Janeiro, Brazil June 22-25, 2015

2 How many hours do you expect to sleep tonight? A. 2 or less B. 3 C. 4 D. 5 E. 6 F. 7 G. 8 H. 9 I. 10 J. 11 or more 2 or less 4% 4% 0% 3 4 1% % 29% 23% 8% or more 2% 0%

3 WHY IS SAMPLE SIZE IMPORTANT?

4 Why is sample size important? Imagine you had to sample letters to estimate what the sentence says: 4

5 Why is sample size important? Imagine you had to sample letters to estimate what the sentence says: 5

6 Intuition Think of sample size as the accuracy of a measuring device: The more observations you have The more precise is your measuring device The more confident you are about your conclusions Common sense: the more complicated is the sentence, the more letters you would need Below, we discuss the sense in which impacts can be complicated to detect and would require larger samples. 6

7 A practical illustration A real-time experiment! Must have many of you respond for this to work How many hours do you expect to sleep tonight? round to the nearest whole number If less than 2 choose A! If more than 11 choose G!

8 A practical illustration Now let s have some fun in stata! Randomize into treatment and control Assign treatment intervention Randomly select samples of different sizes, see how close the treatment effect we estimate from our sample is to the true effect

9 HOW BIG SHOULD MY SAMPLE BE? 9

10 Answer is N 4 2 ( z / 2 2 D z ) 2 1 ( H 1)

11 A better question What influences the sample size I need? 1. Expected size of impact 2. Variation in outcome 3. Clustering 4. Take-Up

12 1. expected impact Who is taller??? EASY! HARD! Big differences are easy to identify Small differences require more precision Larger sample needed

13 1. expected impact What is the smallest effect size that, if it were any smaller, the intervention would not be worth the effort? Called Minimum Detectable Effect Size (MDES) larger sample more precise measuring device easier to detect smaller effects 13

14 1. expected impact With two assumptions, we can directly calculate trade-offs in MDES and sample size likelihood of type 1 error reject the null when true α =.05 likelihood of type 2 error fail to reject null when false a.k.a. power β = 80%

15 1. expected Impact

16 2. variance of outcomes Of the two (circled) populations, which animals are bigger? How many observations from each would you need to decide? 16

17 2. variance of outcomes Of the two (circled) populations, which animals are bigger? How many observations from each would you need to decide? 17

18 Applies to more than farm animals! Ex. a transport subsidy increases employment by 10% (average) Case A: HHs are very similar, likelihood of employment concentrated Case B: HHs are quite different, likelihood of employment spread out Which instance requires a more precise measuring device? 18

19 2. variance of outcomes In sum: More underlying variance (heterogeneity) more difficult to detect difference need larger sample size Tricky: How do we know about heterogeneity before we decide our sample size and collect our data? Ideal: pre-existing data but often non-existent Can use pre-existing data from a similar population Example: data routinely collected by govt, satellite imagery Common sense 19

20 3. level of clustering Unit for sample size calculation depends on both: Level of intervention AND Level of measured impacts Example: intervention at village level, interested in impacts at HH level Level of intervention ( cluster ) most important for sample size calculation If few clusters, precision will be limited, regardless of number of HHs sampled

21 3. level of clustering Ex. Randomize transport voucher at village level, in 6 villages. Sample 1,000 HHs per vlg. Sample size: 6,000 HHs that s a lot, right?!! Key sample size number is 6 Adding clusters is always a better way to increase precision than adding HHs within clusters How much precision the 1,000 HHs buys you depends on intra-cluster correlation

22 3. level of clustering Intracluster correlation (ICC): measure of similarity of units within clusters ICC & sample size If ICC is high, increasing number of HHs from 10 to 100 will have small impact on precision but big impact on budget! If ICC is low, increasing number of HHs from 10 to 100 can improve precision

23 High ICC 3. level of clustering Village 1 Village 3 Village 2 Village 4

24 3. clustering Low ICC Village 1 Village 3 Village 2 Village 4

25 Small number of clusters high ICC (.50) low ICC (.05)

26 Large number of clusters high ICC (.50) low ICC (.05)

27 3. clustering Takeaway High intra-cluster correlation (HHs in same cluster similar) lower marginal value per extra sampled unit in the cluster More clusters needed Rule of thumb: at least 40 clusters per treatment arm

28 4. take-up Low take-up (rate) for intervention lowers precision Effectively decreases sample size Example: Offer transport voucher, but cannot force HHs to use it Offer voucher to 1,000 HHs Only 403 participate In practice, because of low take up rate, we end up with a less precise measuring device We won t be able to detect differences with precision Can only find an effect if it is really large 28

29 Sample size Take up vs. sample size Proportion of HHs taking up voucher 29

30 5. data quality Poor data quality effectively increases required sample size Missing observations quality of data collection, attrition, migration High measurement error: answers not always precise e.g. self-reported land size, agricultural production e.g. recall bias, framing, pleasing Poor data quality can be partly addressed with field coordinator on the ground monitoring data collection 30

31 conclusions The smaller effects that we want to detect The more underlying heterogeneity (variance) The higher the level of clustering The lower take up The larger the sample size has to be The lower data quality 31

32 To keep in mind this week What is the level of randomization (clustering)? Expected effect size? Variation within target population? How to ensure High take-up? Good data quality?

33 If you like the graphs you saw here You can make your own with Optimal Design, a free download from Univ. of Michigan

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