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\newcommand{\lowwtpobs}{32} 
\newcommand{\nexogobs}{12} 
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\newcommand{\nexogobswthree}{2} 
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\newcommand{\commiteightrate}{64} 
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\newcommand{\commitsixteenrate}{32} 
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\newcommand{\actexpsd}{6.61} 
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\newcommand{\bcpinfoctrlmean}{0.66} 
\newcommand{\bcpregmean}{1.17} 
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\newcommand{\pctfemalealt}{61.3} 
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\newcommand{\fracmale}{0.387} 
\newcommand{\meanage}{34} 
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\newcommand{\passednumeracy}{95.2} 
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\newcommand{\avgexpincone}{12.92} 
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\newcommand{\avgdiffincone}{5.38} 
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\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} 
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\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)} 
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\newcommand{\empirDmeet}{0.42} 
\newcommand{\empirDmeetCI}{(0.26, 0.58)}