↓请看题↓When you think of airforce in the Second World War there’s at least one name worth remembering. Not a pilot or commander, but a statistician, Abraham Wald. In a series of eight memoranda, while working at the Statistical Research Group within the US military (yes they had an applied mathematics department), Wald worked out the secret to placing armour on aircraft bombers in a way that saved countless lives.Here’s the problem Wald was confronted with. The commanders wanted to place armour on their bombers, but clearly couldn’t put it everywhere because it was too heavy. So where is it best to armour a plane to maximise its chance of survival? Wald looked at all the planes that returned from missions and saw a pattern of bullet holes like this (in black):
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So, where should you put the armour? Have a think before reading on.The commanders saw it clearly. Put the armour where the most bullet holes are. That’s where the planes are getting shot the most. And, of course, that would have been a complete disaster. Wald showed that actually, you should put the armour where the bullet holes aren’t.
Why? Well the commanders had fallen for the classic fallacy of survivorship bias. They were only examining the aircraft that made it back to base, the survivors. The missing aircraft, with their locations of bullet holes, were never seen by the commanders, and therefore not taken into account. Wald showed that it was very likely that those missing aircraft had holes in very different places, on average, than the surviving aircraft.
In short, what Wald’s diagram showed was the places an aircraft could take hits and still get home. These were the places you didn’t have to put armour on, the exact opposite to what the military designs intended to do.
The essence of survivorship bias is the difficulty to see the failures, in business, in life, and in war. And sometimes it’s the failures that have the most important lessons. Like the planes that didn’t make it back. Wald’s reasoning went on to save lives not only in World War Two, but also in Korea and Vietnam.
Which of the following are true according to the passage?A. The concept is proposed by the commander of a war time statistician, called Abraham Wald.B. This bias is consistent with the solution proposed by Wald.C. The way to maximise the use of armour is to cover it on the area where the survival airplanes have most bullet holes.D. People normally make such bias because failures are often not easy to identify.E. The survivorship theory is only applicable in military areas and weaponry designs.做题学姿势在看答案之前，同学们可以先了解一下这个有趣的定义。
Survivorship Bias在中文中被称为“幸存者偏差”，稍微有些拗口。大致的意思是，人们会过于关注幸存的个体，并忽略失败的个体，最终得出一个有所偏差的结论。
文中的故事可以算是这个理论的一个典故：1941年,第二次世界大战中，美国哥伦比亚大学统计学沃德教授(Abraham Wald)应军方要求,利用其在统计方面的专业知识来提供关于《飞机应该如何加强防护，才能降低被炮火击落的几率》的相关建议。沃德教授针对联军的轰炸机遭受攻击后的数据，进行研究后发现:机翼是最容易被击中的位置，机尾则是最少被击中的位置。沃德教授的结论是“我们应该强化机尾的防护”，而军方指挥官认为“应该加强机翼的防护，因为这是最容易被击中的位置”。
沃德教授坚持认为：(1)统计的样本，只涵盖平安返回的轰炸机；(2)被多次击中机翼的轰炸机，似乎还是能够安全返航；(3)而在机尾的位置，很少发现弹孔的原因并非真的不会中弹，而是一旦中弹，其安全返航的概率就微乎其微。军方采用了教授的建议，并且后来证实该决策是正确的,看不见的弹痕却最致命!
这个故事有两个启示：一是战死或被俘的飞行员无法发表意见，所以弹痕数据的来源本身就有严重的偏误；二是作战经验丰富的飞行员的专业意见也不一定能提升决策的质量，因为这些飞行员大多是机翼中弹而机尾未中弹的幸存者。
看完这么详细的解释，这道题的答案是否也非常明显了呢？
本题的正确答案就是D选项：People normally make such bias because failures are often not easy to identify. (可以根据文中的这句话判断：The essence of survivorship bias is the difficulty to see the failures, in business, in life, and in war.）
题外话举一个很简单的例子：“每个成功者都很努力，所以只要努力就能成功。”这种说法在日常中似乎非常常见。如果这个逻辑成立的话，我们是不是可以类比出这样一个推论：“每个少年犯都喜欢吃饭，所以只要喜欢吃饭就会成为少年犯。”
嗯，明显后一个听起来不那么正确。
问题出在哪里呢？原因很简单，第一个例子没有提出努力却失败的人，直接无视了失败者。在生活中，无可否认的是成功的人很少，而失败的人则比较多，在没有分析过失败的人们是否努力之前，我们并不能得出后面的结论。
第二个例子没有提出没有成为少年犯的人，因而也无视了另一个因素。现实中，明显成为罪犯的人比较少，而没有成为罪犯的人比较多，因此逻辑也很难立证。
Key Vocabulary? Commander n. 指挥官记忆：Command命令 + er的人 = Commander 指挥官? Statistician n. 统计学家
记忆：Statistic统计 + ian的人 = Statistician 统计学家? Memoranda n. （复） 备忘录
记忆：Memor + andum名词 = Memorandum 备忘录（单数）? Bombers n. （复）轰炸机
记忆：Bomb炸弹 + er的人 = Bombers 轰炸机? Countless adj. 数不尽的，无数的
记忆：Count数 + less否定 = Countless 无数的? Confronted v. （被）面对
记忆：Con共同 + front向前 = Confront 面对? Survival adj. 生存的
记忆：Surviv(e)生存 + al形容词 = Survival 生存的? Fallacy n. 谬论，谬误
记忆：Fal错误的 + acy名词 = Fallacy 谬误? Armour n. 铠甲
? Missions n. （复）任务
? Pattern n. 规律，图案
? Bullet Holes n. （复）弹孔
? Disaster n. 灾难，悲剧 |
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