clear all
import excel "data.xls", sheet("probability estimates data") cellrange(A1:Y376) firstrow

destring _all, replace

tab version_max_prize
tab version_min_prize

/////////// Table 8 ///////////
////// working on the min_prize estimates
tab min_prize_10
tab min_prize_6
tab min_prize_3

sum min_prize_10, detail
sum min_prize_6, detail
sum min_prize_3, detail

 // true probability --> 1/7
replace min_prize_10=1/min_prize_10
tab min_prize_10
sum min_prize_10, detail //median prob.-->.0153409
display 10000000/153409 // --> 1/65 median prob. 
display .0153409/(1/7) // ratio of median to true probability --> 0.11

 // true probability --> 1/8
replace min_prize_6=1/min_prize_6
tab min_prize_6
sum min_prize_6, detail //median prob.-->.025
display 1000/25 // --> 1/40 median prob.
display .025/(1/8) // ratio of median to true probability --> 0.2

 // true probability --> 1/7
replace min_prize_3=1/min_prize_3
tab min_prize_3
sum min_prize_3, detail //median prob.-->.025 
display 1000/25 // --> 1/40 median prob.
display .025/(1/7) // ratio of median to true probability --> 0.18

////// working on the max_prize estimates
tab max_prize_10
tab max_prize_7
tab max_prize_4
tab max_prize_1

sum max_prize_10, detail //median 1.00e+07
sum max_prize_7, detail //median 310000
sum max_prize_4, detail //median 10000
sum max_prize_1, detail //median 80

 // true probability --> 1/8911711
replace max_prize_10=1/max_prize_10
tab max_prize_10
sum max_prize_10, detail //median prob.--> 1.00e-07  
display 10000000/1 // --> 1/10,000,000 median prob.
display 1.00e-07/(1/8911711) // ratio of median to true probability --> 0.89

 // true probability --> 1/40979
replace max_prize_7=1/max_prize_7
tab max_prize_7
sum max_prize_7, detail //median prob.--> 3.23e-06 
display 100000000/323 // --> 1/309,589 median prob.
display 3.23e-06/(1/40979) // ratio of median to true probability --> 0.13

 // true probability --> 1/326
replace max_prize_4=1/max_prize_4
tab max_prize_4
sum max_prize_4, detail //median prob.--> .0001  
display 10000/1 // --> 1/10000 median prob.
display .0001/(1/326) // ratio of median to true probability --> 0.03

 // true probability --> 1/4
replace max_prize_1=1/max_prize_1
tab max_prize_1
sum max_prize_1, detail //median prob.--> .0125  
display 10000/125 // --> 1/80 median prob.
display .0125/(1/4) // ratio of median to true probability --> 0.05
////--------------------////

/////////// Appendix C2 ///////////
///does order of the questions make a difference?

// order: for min_prize grouped into 3 bins- starting with 10, 6 and 3
kwallis min_prize_10, by(version_order) //no Chi(2)=1.659 with 2 d.f.,p = 0.4362
kwallis min_prize_6, by(version_order) //no Chi(2)=2.136 with 2 d.f.,p = 0.3438
kwallis min_prize_3, by(version_order) //no Chi(2)=3.802 with 2 d.f.,p = 0.1494

// order: for max_prize grouped into 4 bins- starting with 10, 7, 4 and 1
kwallis max_prize_10, by(version_order) //no Chi(2)=6.711 with 3 d.f.,p = 0.0817
kwallis max_prize_7, by(version_order) //yes Chi(2)=11.822 with 3 d.f.,p = 0.008
kwallis max_prize_4, by(version_order) //no Chi(2)=6.076 with 3 d.f.,p = 0.108
kwallis max_prize_1, by(version_order) //no Chi(2)=1.194 with 3 d.f.,p = 0.7545

///just to make sure:
// exact order: for min_prize 6 versions (3!)
kwallis min_prize_10, by(version_order_exact) //no 
kwallis min_prize_6, by(version_order_exact) //no
kwallis min_prize_3, by(version_order_exact) //no

// exact order: for max_prize 24 versions (6!)
kwallis max_prize_10, by(version_order_exact) //no 
kwallis max_prize_7, by(version_order_exact) //order makes a diff p=0.01
kwallis max_prize_4, by(version_order_exact) //no 
kwallis max_prize_1, by(version_order_exact) //no 

////--------------------////