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. 多重下拉选择题

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Imagine that in a large observational study comparing people who regularly take >=400 IU of vitamin D per day with people with no supplemental vitamin D intake, the crude incidence rate ratio of multiple sclerosis was 0.34. Smokers are less likely to take vitamin supplements and they are more likely to develop multiple sclerosis. If the authors of the observational study further adjust for smoking, the resulting adjusted incidence rate ratio may be  

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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