\newcommand{\lowwtpobs}{32} 
\newcommand{\nexogobs}{12} 
\newcommand{\excludeobs}{44} 
\newcommand{\lowwtpobswthree}{13} 
\newcommand{\nexogobswthree}{2} 
\newcommand{\woneobs}{350} 
\newcommand{\wtwoobs}{528} 
\newcommand{\wthreeobs}{414} 
\newcommand{\pctpreferzero}{1.2} 
\newcommand{\commiteightrate}{64} 
\newcommand{\commiteightobs}{849} 
\newcommand{\committwelverate}{49} 
\newcommand{\committwelveobs}{1{,}248} 
\newcommand{\commitsixteenrate}{32} 
\newcommand{\commitsixteenobs}{849} 
\newcommand{\gotcontractobs}{122} 
\newcommand{\goalexpmean}{3.34} 
\newcommand{\goalexpsd}{3.64} 
\newcommand{\actexpmean}{-4.17} 
\newcommand{\actexpsd}{6.61} 
\newcommand{\enhinfobcpcoeff}{1.36} 
\newcommand{\bcpinfoctrlmean}{0.66} 
\newcommand{\bcpregmean}{1.17} 
\newcommand{\goalexpbcpcoeff}{0.71} 
\newcommand{\actualexpbcpcoeff}{0.45} 
\newcommand{\enhinfoMCcoeff}{8.0} 
\newcommand{\MCregmean}{0.49} 
\newcommand{\MCregmeanPCT}{49} 
\newcommand{\bcpMCcoeff}{3} 
\newcommand{\goalexpMCcoeff}{3.8} 
\newcommand{\wantgottwelvediff}{3.51} 
\newcommand{\rejectgottwelvediff}{4.04} 
\newcommand{\pctundertwelve}{35} 
\newcommand{\pctmaxed}{7.4} 
\newcommand{\pctovermax}{28} 
\newcommand{\pctatmax}{22} 
\newcommand{\pctbelowmax}{50} 
\newcommand{\pctdeltaneg}{33} 
\newcommand{\pctfemale}{61} 
\newcommand{\pctfemalealt}{61.3} 
\newcommand{\pctmalealt}{38.7} 
\newcommand{\fracfemale}{0.613} 
\newcommand{\fracmale}{0.387} 
\newcommand{\meanage}{34} 
\newcommand{\pctstudent}{57} 
\newcommand{\pctworking}{57} 
\newcommand{\pctmarried}{27} 
\newcommand{\meanpastvisits}{22} 
\newcommand{\meanpastvisitsrecall}{31} 
\newcommand{\pctfailedac}{3.5} 
\newcommand{\pctchosedom}{1.8} 
\newcommand{\pctfailedcc}{4.3} 
\newcommand{\passednumeracy}{95.2} 
\newcommand{\anticommitrate}{31} 
\newcommand{\anticommitrateexcl}{30} 
\newcommand{\anticommitpctmin}{27} 
\newcommand{\anticommitpctmax}{34} 
\newcommand{\wtwothreeobs}{908} 
\newcommand{\avgexpnoinc}{11.5} 
\newcommand{\avgexpseveninc}{17.7} 
\newcommand{\avgexpdiffseven}{6.2} 
\newcommand{\avgactnoinc}{7.2} 
\newcommand{\avgactseveninc}{13.3} 
\newcommand{\avgactdiffseven}{6.1} 
\newcommand{\attcoeff}{0.685} 
\newcommand{\attcoeffse}{0.028} 
\newcommand{\avgbcpcorr}{0.17} 
\newcommand{\avgbcpcorrse}{0.06} 
\newcommand{\avgMCcorr}{0.49} 
\newcommand{\avgMCcorrse}{0.02} 
\newcommand{\avgexpincone}{12.92} 
\newcommand{\avgwtpincone}{18.30} 
\newcommand{\avgdiffincone}{5.38} 
\newcommand{\avgbcp}{2.01} 
\newcommand{\avgbcpexone}{1.20} 
\newcommand{\incentivezeroobs}{413} 
\newcommand{\incentivetwoobs}{293} 
\newcommand{\incentivefiveobs}{75} 
\newcommand{\incentivesevenobs}{342} 
\newcommand{\incentivezeroobsbasic}{105} 
\newcommand{\incentivetwoobsbasic}{112} 
\newcommand{\incentivesevenobsbasic}{121} 
\newcommand{\obsbasictreat}{174} 
\newcommand{\obsbasiccontrol}{166} 
\newcommand{\incentivezeroobsenhanced}{308} 
\newcommand{\incentivetwoobsenhanced}{181} 
\newcommand{\incentivefiveobsenhanced}{74} 
\newcommand{\incentivesevenobsenhanced}{221} 
\newcommand{\obsenhancedtreat}{452} 
\newcommand{\obsenhancedcontrol}{456} 
\newcommand{\incrattinc}{0.67} 
\newcommand{\incrattincse}{0.014} 
\newcommand{\avgbcpinc}{3.00} 
\newcommand{\avgbcpexoneinc}{1.78} 
\newcommand{\wtpbcmean}{1.20} 
\newcommand{\wtpbcsd}{7.08} 
\newcommand{\enhancedtreatobs}{452} 
\newcommand{\controlobs}{622} 
\newcommand{\incentivezeroinfobs}{366} 
\newcommand{\incentivetwoinfobs}{234} 
\newcommand{\incentivefiveinfobs}{75} 
\newcommand{\incentiveseveninfobs}{274} 
\newcommand{\minfoavgobspe}{952} 
\newcommand{\infodropobs}{174} 
\newcommand{\minfoavgnoconfusedobspe}{865} 
\newcommand{\empirDaC}{3.51} 
\newcommand{\empirDaCCI}{(1.38, 5.65)} 
\newcommand{\empirctrlPmeet}{0.22} 
\newcommand{\empirctrlPmeetCI}{(0.10, 0.35)} 
\newcommand{\empirtreatPmeet}{0.65} 
\newcommand{\empirtreatPmeetCI}{(0.52, 0.78)} 
\newcommand{\empirDmeet}{0.42} 
\newcommand{\empirDmeetCI}{(0.26, 0.58)}