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FA25_QTM_110_1 Quiz #5: Randomization and Inference

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Suppose we are interested in the effect of being a 1st round pick in the NBA draft (as opposed to a 2nd round pick or being undrafted) on minutes played in a person's NBA career.  The theory is that 1st round picks are given more chances to show that they can be a successful player and are less likely to be cut than another player, all else equal.  Those who are drafted in the first round are treated (T = 1) and all other NBA players are untreated (T = 0).  You observe that there is a large positive difference in the average number of minutes played by first round picks and the average number of minutes played by other NBA players . You are worried, though, that skill as a basketball player confounds this relationship.  You believe that a player's skill is positively correlated with receiving the treatment.  Additionally, you believe that in a world where there is no NBA draft, highly skilled players are more likely to play more minutes than less skilled players. Given this information (and assuming that this is the only confounding variable that matters), the observed difference in averages [选择] is unbiased for overestimates underestimates the true effect of being a first round pick. 

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The question asks about how the observed difference in minutes between first-round picks (T = 1) and others should be interpreted as an estimate of the true causal effect, given a confounding variable (player skill) that is positively correlated with both treatment and the outcome (minutes). First, recognize the core issue: confounding by skill. If highly skilled players are more likely to be first-round picks and also tend to play more minutes regardless of draft status, then the observed gap in minutes combines both the causal effect of being a first-round pi......Login to view full explanation

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Suppose we are interested in the effect of being a 1st round pick in the NBA draft (as opposed to a 2nd round pick or being undrafted) on minutes played in a person's NBA career.  The theory is that 1st round picks are given more chances to show that they can be a successful player and are less likely to be cut than another player, all else equal.  Those who are drafted in the first round are treated (T = 1) and all other NBA players are untreated (T = 0).  You observe that there is a large positive difference in the average number of minutes played by first round picks and the average number of minutes played by other NBA players . You are worried, though, that skill as a basketball player confounds this relationship.  You believe that a player's skill is positively correlated with receiving the treatment.  Additionally, you believe that in a world where there is no NBA draft, highly skilled players are more likely to play more minutes than less skilled players. Given this information (and assuming that this is the only confounding variable that matters), the observed difference in averages overestimates the true effect of being a first round pick. 

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