Minimum detectable effect size for main outcomes (accounting for sample design and clustering)
Using the TAPRA data, collected by Tegemeo Institute in 2010, our power calculations suggest the following Minimum Detectable Effects (MDEs): in Western/ Nyanza, δ_yield∈ (0.5, 0.3) and δ_income∈ (0.4, 0.3), where δ denotes the standardized effect size.* Given the means and standard deviations of yield and income respectively, this translates into MDEs for yields of 15-26% of the average 2010 yield, and 25-35% of the average 2010 household income, depending on the amount of variation in the outcome variables that can be explained by baseline values of covariates.** In Central/Eastern, δ_yield∈ (0.6, 0.45) and δ_income∈ (0.6, 0.45), implying MDEs corresponding to 30-35% increases in yields and incomes. These should be conservative estimates of MDEs, as they are calculated using formulas for a 3-level cluster-randomized trial, while the liquidity treatment arm will be randomized at the individual level.
* Using Optimal Design’s notation, the statistics used for power calculations in Western/Nyanza province are as follows: n (the number of households in each village) in each treatment arm is 9 (17 households are sampled in each village, but that number will be halved by the voucher-treatment); J (the number of clusters per site) equals 3, and there are 24 sites, K; the intra-class correlations for level-2 and level-3 in Western are ρ_π=0.083,ρ_β=0.072 (yields) and ρ_π=0.059,ρ_β=0.043 (income). In Central/Eastern, n=17, J=3, K=12, ρ_π=0.085,ρ_β=0.076 (yields) and ρ_π=0.09,ρ_β=0.07 (income).
** In the TAPRA panel data, level-3 covariates from the previous round explain between 15-40% of the variation in current-period outcome variable.