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Table 1. 
Models Used to Statistically Test the Effects of Congruency, Caffeine, and Reward-Prospect on the Behavioral and Neural Dependent Variables
Behavioral analysis p(hit)n = logit−10.j + β1congruencyj[n] + β2rewardj[n] + β3caffeinen + β4sessionj[n] + β5congruencyn × rewardn + β6congruencyn × caffeinen + β7reward × congruencyn + β8congruency × reward × caffeinen + ϵn
RTsn = β0.j + β1congruencyj[n] + β2rewardj[n] + β3caffeinen + β4sessionj[n] + β5congruencyn × rewardn + β6congruencyn × caffeinen + β7rewardn × caffeinen + β8congruencyn × rewardn × caffeinen + ϵn 
Cue interval analysis Markern = β0.j + β1rewardj[n] + β2caffeinen + β3sessionj[n] + β4reward × caffeinen + ϵn 
Target interval analysis μVn = β0.j + β1congruencyj[n] + β2rewardj[n] + β3caffeinen + β4sessionj[n] + β5congruencyn × rewardn + β6congruencyn × caffeinen + β7rewardn × caffeinen + β8congruencyn × rewardn × caffeinen + ϵn 
Sustained alpha power alpha powern = β0.j + β1caffeinen + β2sessionj[n] + ϵn 
Behavioral analysis p(hit)n = logit−10.j + β1congruencyj[n] + β2rewardj[n] + β3caffeinen + β4sessionj[n] + β5congruencyn × rewardn + β6congruencyn × caffeinen + β7reward × congruencyn + β8congruency × reward × caffeinen + ϵn
RTsn = β0.j + β1congruencyj[n] + β2rewardj[n] + β3caffeinen + β4sessionj[n] + β5congruencyn × rewardn + β6congruencyn × caffeinen + β7rewardn × caffeinen + β8congruencyn × rewardn × caffeinen + ϵn 
Cue interval analysis Markern = β0.j + β1rewardj[n] + β2caffeinen + β3sessionj[n] + β4reward × caffeinen + ϵn 
Target interval analysis μVn = β0.j + β1congruencyj[n] + β2rewardj[n] + β3caffeinen + β4sessionj[n] + β5congruencyn × rewardn + β6congruencyn × caffeinen + β7rewardn × caffeinen + β8congruencyn × rewardn × caffeinen + ϵn 
Sustained alpha power alpha powern = β0.j + β1caffeinen + β2sessionj[n] + ϵn 

Within the formulas the subscript n indicates single trials, the subscript j indicates the individual participant. For instance, the notation β0.j indicates the intercept, which varies by participant (the random effect).

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