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Designing an impact evaluation: Randomization, statistical power, and some more fun…

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Designing a (simple) RCT in a couple steps You want to evaluate the impact of something (a program, a technology, a piece of information, etc.) on an outcome. Example: Evaluate the impact of free school meals on pupilss schooling outcomes. You decide to do it through a randomized controlled trial. – Why? The questions that follow: – Type of randomization – What is most appropriate? – Unit of randomization – What do we need to think about? – Sample size > These are the things we will talk about now.

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I. Where to start You have an HYPOTHESIS Example: Free meals => increased school attendance => increased amount of schooling => improved test scores. Or could it go the other way? To test your hypothesis, you want to estimate the impact of a variable T on an outcome Y for an individual i. In a simple regression framework: How could you do this? – Compare schools with free meals to schools with no free meals? – Compare test scores before the free meal program was implemented to test scores after? Y i =α i +βT+ε i

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You decided to do use a randomized design. Why?? – Randomization removes the selection bias > Trick question: Does the sample need to be randomly sampled from the entire population? – Randomization solves the causal inference issue, by providing a counterfactual = comparison group. While we cant observe Y i T and Y i C at the same time, we can measure the average treatment effect by computing the difference in mean outcome between two a priori comparable groups. We measure: ATE=E[Y T ]- E[Y C ] II. Randomization basics

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What to think of when deciding on your design? – Types of randomization/ unit of randomization Block design Phase-in Encouragement design Stratification? The decision should come from (1) your hypothesis, (2) your partners implementation plans, (3) the type of intervention! Example: What would you do? Next step: How many units? = SAMPLE SIZE. Intuition --> Why do we need many observations? II. Randomization basics

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Remember, were interested in Mean(T)-Mean(C) We measure scores in 1 treatment school and 1 control school > Can I say anything?

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Now 50 schools:

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Now 500 schools:

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But how to pick the optimal size? -> It all depends on the minimum effect size youd want to be able to detect. Note: Standardized effect sizes. POWER CALCULATIONS link minimum effect size to design. They depend on several factors: – The effect size you want – Your randomization choices – The baseline characteristics of your sample – The statistical power you want – The significance you want for your estimates Well look into these factors one by one, starting by the end… III. Sample size

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When trying to test an hypothesis, one actually tests the null hypothesis H 0 against the alternative hypothesis H a, and tries to reject the null. H 0 : Effect size=0 H a : Effect size0 Two types of error are to fear: III. Power calculations (1) Hypothesis testing TRUTH YOUR CONCLUSION Effective (reject H 0 )No effect (cant reject H 0 ) Effective TYPE II ERROR POWER No effectTYPE I ERROR SIGNIFICANCE

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SIGNIFICANCE= Probability that youd conclude that T has an effect when in fact it doesnt. It tells you how confident you can be in your answer. (Denoted α) – Classical values: 1, 5, 10% – Hypothesis testing basically comes down to testing equality of means between T and C using a t-test. For the effect to be significant, it must be that the t-stat obtained be greater than the t-stat of the significance level wanted. Or again: must be greater or equal to t α =1.96 III. Power calculations (1) Significance

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POWER= Probability that, if a significant effect exists, you will find it for a given sample size. (Denoted κ) – Classical values: 80, 90% To achieve a power κ, it must be that: Or graphically… In short: To have a high chance to detect an effect, one needs enough power, which depends on the standard error of the estimate of ß. III. Power calculations (2) Power

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Intuition = the higher the standard error, the less precise the estimate, the more tricky it is to identify an effect, the higher the need for power! – Demonstration: How does the spread of a variable impact on the precision a mean comparison test?? We saw that power depended on the SE of the estimate of ß. But what does this standard error depend on? – Standard deviation of the error (how heterogenous the sample is) – The proportion of the population treated (Randomization choices) – The sample size III. Power calculations (3) Standard error of the estimate

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We now have all the ingredients of the equation. The minimum detectable effect (MDE) is: As you can see: – The higher the heterogeneity of the sample, the higher the MDE, – The lower N, the higher the MDE, – The higher the power, the lower the MDE Power calculations in practice, will correspond to playing with all these ingredients to find the optimal design to satisfy your MDE.in practice – Optimal sample size? – Optimal portion treated? III. Power calculations (4) Calculations

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Several treatments? – What happens when more than one treatment? – It all depends on what you want to compare !! Stratification? – Reduces the standard deviation Clustered (block) design? – When using clusters, the outcomes of the observations within a cluster can be correlated. What does this mean? – Intra-cluster correlation rhô, the portion of the total variance explained by within variance, implies an increase in overall variance. – Impact on MDE? – In short: the higher rhô, the higher the MDE (increase can be large) III. Power calculations (5) More complicated frameworks

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When thinking of designing an experiment: 1.What is your hypothesis? 2.How many treatment groups? 3.What unit of randomization? 4.What is the minimum effect size of interest? 5.What optimal sample size considering power/budget? => Power calculations ! Summary

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