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Causal因果

Two exercises. The first is 300 workers, a retraining subsidy, and pay a year later. The second is 80 students, an optional statistics workshop, and a later grade. The first asks whether the rising line is the subsidy or the family’s savings. The second asks who is still in the comparison once each joiner is paired with someone of similar prior math.两页练习。第一页是 300 名工人、再培训补贴，和一年后的月薪。第二页是 80 名学生、选修的统计工作坊，和后来的成绩。第一页问：往上的线是补贴，还是家里的积蓄。第二页问：每个参加者都配上先前数学相近的人之后，比较里还剩下谁。

Savings can push both subsidy use and later pay, so the line rises even when the subsidy adds nothing. Pairing is a different repair: keep a joiner only when a non-joiner has a close prior-math score, instead of putting savings or prior math into the line.积蓄可以同时推动领补贴和后来的月薪，所以补贴本身没加钱时线仍会上升。配对是另一种修法：只在未参加者也有相近的先前数学时才留下参加者，而不是把积蓄或先前数学放进那条线。

Watch out.容易看错的地方。 Putting savings into the line, or tightening the allowed gap in prior math, does not by itself hand you the program’s own effect. Look at who is still in the comparison.把积蓄放进线里，或把先前数学允许的差距收紧，并不会自动给你项目本身的作用。要看比较里还剩下谁。

Labs练习

• Lab练习 Confounding混杂 Is the pay gap the subsidy, or the family’s savings?工资差距是补贴，还是家里的积蓄？
• Lab练习 Matching匹配 Which students remain once prior math is similar?先前数学相近之后，还剩下哪些学生？

Summarize, then compare先概括，再比较 arrives here after a text summary: first an adjustment, then a match on one score.从一段文本概括走到这里：先做调整，再在一个分数上匹配。