Lab · Matching匹配练习 · 匹配
Which students remain once prior math is similar?先前数学相近之后，还剩下谁？
The course teacher has 80 students and has to decide whether the faculty should keep paying for an optional statistics workshop. The sheet has three columns: joined or not, a prior-math score, and the later methods grade. Students with higher prior math signed up more often, so a higher grade among joiners can just be that earlier score. Matching pairs a joiner with a non-joiner only when their prior-math scores sit inside the caliper — the widest gap you still count as “close enough.” Students with no such partner drop out of the comparison.任课老师有 80 名学生，要决定院里还要不要继续付钱办这门选修的统计工作坊。表上三列：参加与否、先前的数学分数、后来的方法课成绩。先前数学更高的学生更常报名，所以参加者成绩更好，可能只是那个旧分数。匹配只在两人的先前数学落在卡尺里时，才把参加者和没参加的人配成一对。卡尺就是你还愿意当成“够近”的最大分差。找不到这样的人，就不进入比较。
Why it matters.为什么要紧。 A higher methods grade among joiners can be their higher prior math, not the workshop. Pairing keeps a joiner only when someone who did not join has a similar prior-math score. Students with no partner drop out of the grade gap the teacher would report.参加者方法课成绩更高，可以是他们先前的数学更高，不是工作坊。只有没参加的人也有相近的先前数学时，参加者才留在比较里。没有伙伴的学生，不会出现在老师拿去汇报的那个成绩差里。
Try this试一试 Turn up how strongly prior math pushes joining, and keep the allowed gap wide. Compare the grade gap before pairing with the workshop’s own effect. Then tighten the gap and see who fades out.把先前数学推动报名的力度调高，允许的差距先留宽。把配对前的成绩差和工作坊本身的作用比一比。再把差距收紧，看谁变淡。
How to read the chart怎么读这张图
If you read this wrong要是读错了
If the teacher reports the matched grade gap as proof the workshop worked, the faculty may keep paying for it. A tight caliper has already dropped students who had no partner with a similar prior-math score. The gap is only among students who could be paired.如果老师把配对后的成绩差写成“工作坊有效”，院里可能会继续付钱。卡尺一收紧，找不到先前数学接近的伙伴的学生已经被丢掉。这个差距只存在于能够配成对的学生之间。
What this picture is enough for这张图够说明什么
Enough to see that tightening the allowed gap in prior math changes which of the 80 students stay in the grade comparison.看得出：把先前数学允许的差距收紧，会改变 80 名学生里谁还留在成绩比较中。
Not enough to decide the workshop stays. The note still has to match on more than prior math, and say which students the tight rule left out of the grade gap.还不够拿来决定工作坊留下。说明仍要比先前数学更多的列，并写明收紧之后，哪些学生被留在了成绩差外面。
The equation, and where it stops式子、假设和边界
Prior math, X, is a standard normal. The propensity is one number for how likely joining was, given the columns on the sheet. Here it is logistic(γX). Joining is then a yes-or-no draw from that chance. The grade is Y = τT + X + 0.5e. The weight on prior math is fixed at 1, so if joiners are one point ahead on prior math, the grade gap before pairing moves by about one point too.先前数学 X 是一个标准正态。倾向得分是一个数字：按表上的列，这个人有多可能参加。这里它是 logistic(γX)。参加与否，再按这个机会做一次是或否的抽取。成绩是 Y = τT + X + 0.5e。先前数学的权重固定为 1，所以参加者的先前数学如果领先 1 分，没配对时的成绩差大约也跟着动 1 分。
The grade gap before pairing is the difference in average grades. Matching is one to one and does not reuse a partner. Joiners are considered from the most extreme prior-math score inward, and each takes the nearest unused non-joiner inside the caliper. There is only one column besides joining and the grade, so matching on prior math and matching on the propensity line the students up in the same order.没配对时的成绩差，就是两组平均成绩之差。匹配是一对一，同一个人不重复使用。参加者按先前数学离平均有多远，从最远的开始，各自在卡尺里找最近的、还没用过的未参加者。除了参加和成绩，表上只有一列，所以按先前数学匹配，和按倾向得分匹配，学生的顺序是一样的。
Easy to get wrong.容易踩的坑。 A tight caliper can make the prior-math gap look small and still answer a different question: the grade gap among joiners who had a nearby non-joiner. Joiners left unmatched are not in that average. Another mistake is to treat “balanced on prior math” as “balanced on everything.” If something else differs between joiners and the rest, this picture will not show it. The page also does not reweight by the inverse propensity. It only pairs neighbors.卡尺很紧时，先前数学的差距可以看起来很小，同时回答的已经是另一个问题：在附近找得到没参加的人的那些参加者之间，成绩差多少。没配上的参加者不在这个平均里。另一个错，是把“先前数学上配平了”当成“什么都配平了”。如果参加者和其余人在别的事情上不同，这张图不会显示。这一页也不按倾向得分的倒数去加权。它只是把邻居配成对。