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howtos:toolcoding:using_a_relative_propensity [2010/11/25 13:09] shona.weldon |
howtos:toolcoding:using_a_relative_propensity [2010/11/25 13:19] shona.weldon |
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!Equation A: | !Equation A: | ||
- | local populationEst[uss,usdt,th] = households[uss,usdt,th] * relPopPersPerHH[usdt] | + | local populationEst[uss,th] = sum (households[uss,usdt,th] * relPopPersPerHH[usdt]; dim=usdt) |
!Equation B: | !Equation B: | ||
- | peoplePerHousehold[uss,usdt,th] = population[uss,th] / populationEst[uss,usdt,th] * relPopPersPerHH[usdt] | + | peoplePerHousehold[uss,usdt,th] = (population[uss,th] / populationEst[uss,th]) * relPopPersPerHH[usdt] |
- | + | ||
- | ===== Check your above equation through symbol substitution algebra ===== | + | |
- | You know your identity : | + | |
- | population[uss,th] = households[uss,usdt,th] * peoplePerHousehold[uss,usdt,th] | + | |
- | substituting from your final math Equation B for personPerHousehold: | + | |
- | population[uss,th] = households[uss,usdt,th] * population[uss,th] / peoplePerHouseholdEst[uss,usdt,th] * relPopPersPerHH[usdt] | + | |
- | reordering: | + | |
- | population[uss,th] = households[uss,usdt,th] * relPopPersPerHH[usdt] * population[uss,th] / peoplePerHouseholdEst[uss,usdt,th] | + | |
- | Then notice the substitution can be done for Equation A from the final math above: | + | |
- | population[uss,th] = peoplePerHouseholdEst[uss,usdt,th] * population[uss,th] / peoplePerHouseholdEst[uss,usdt,th] | + | |
- | And the estimates cancel so you have an identity and you are comfortable your math worked | + | |
- | population[uss,th] = population[uss,th] | + | |