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Table 2 Example of random allocation for two states

From: Do federal and state audits increase compliance with a grant program to improve municipal infrastructure (AUDIT study): study protocol for a randomized controlled trial

PANEL A: generating the random allocation sequence of “Winning Digits”
Lottery 3/1/2011 Lottery 2/22/2011    
Number Prize (millions) Number Prize (millions)    
23862 5 36625 5    
19186 0.4      
54595 0.2 Sort order (ascending)     
02437 0.08 3     
09502 0.08 6     
42585 0.08 2     
45776 0.08 5     
PANEL B: randomization of municipalities
ID State Municipality FISM transfer (millions) “Ticket” Digits ASF EFSL
07022 Chiapas Comitán de Domínguez 69 0-1   
07028 Chiapas Chenalhó 61 2-3 1  
07076 Chiapas Ocozocoautla de Espinosa 68 4-5   1
07092 Chiapas San Cristóbal de Las Casas 65 6-7   
07111 Chiapas Tecpatán 59 8-9   
08012 Chihuahua Carichí 12 0-1   
08021 Chihuahua Delicias 15 2-3 1  
08030 Chihuahua Guazapares 11 4-5   
08032 Chihuahua Hidalgo del Parral 13 6-7   
08066 Chihuahua Uruachi 13 8-9   1
  1. The sequence of random numbers from Panel A is: 23862, 19186, 54595, 42585, 02437, 45776, 09502. We use the first 17 winning digits to allocate one municipality by state to an audit by ASF. For example, the first winning digit in the random sequence is a 2. Because Chenalhó was allocated that “ticket” (see Panel B, Digits column), it is selected to be audited by ASF. The second winning digit in the random sequence is a 3, and so Delicias is selected, and so on for the remaining 15 states. To allocate EFSL we begin at the top again, starting with the 18th digit in the random sequence, a 5. Accordingly, Ocozocoautla de Espinosa is allocated to EFSL, and so on. Had the 18th digit been a 2 or a 3, we would have skipped that digit, moved to the next digit different from 2 or 3, and used that digit to allocate the first municipality to EFSL. One municipality cannot be assigned to both ASF and EFSL.