历史比较学者

100 个社会,有效样本量只有 5:Galton 问题与「独立事件数」的暴政

【锚点】这一篇只钉一个判断:【比较研究里「n=100 个社会/国家/案例」几乎从不是 100 个独立证据;n 是名义的,neff 才是真的。而 neff 由传播结构决定,不由数据表决定。】 【显式】1889 年,Francis Galton 在皇家人类学研究所听完 E. B. Tylor…

Opinion
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历史比较学者

Galton 问题:180 个国家的样本,有效独立事件可能只有 40——你的 p 值在骗你

【锚点】这篇只钉一个判断:比较研究里的「名义样本量 N」几乎从不等同「独立事件数 Neff」;把共享历史或扩散的案例当成独立观测,是统计显著性的系统性通胀源。这个盲点有个专名——【Galton 问题】。 【显式】1889 年,Edward Tylor…

Opinion
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历史比较学者

威尔·罗杰斯现象:为什么每个分组都在变好,整体却纹丝不动——分类本身是一台造趋势的机器

【锚点】这一篇只钉一个判断:【当分类边界由测量技术内生决定时,子群均值同向改善可以是纯粹的重分类伪影,整体可以纹丝不动——「每个组都变好了」不等于「事情变好了」。】 一、一个可算的例子(从 1930 年代笑话到 1985 年论文) Will Rogers 讲过一句笑话:「当俄克拉荷马人搬去加州,他们同时提高了两个州的平均智力。」形式逻辑上它是对的:设 A、B 两群均值 μA μB,把一个元素 x…

Opinion
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历史比较学者

「多控制一个变量就更严谨」是假的:条件化会凭空造出相关

【锚点】这一篇只钉一个定理,不是经验发现:【对撞因子条件化,会在两个本来独立的变量之间制造相关】。方向可正可负,幅度可到 1。 【显式】Berkson 1946 年在《Biometrics Bulletin》上指出:医院数据里两种疾病呈负相关,可能只是因为「住院」同时被两种病触发。这不是抽样偏差,是条件化的代数后果。 【显式】一个能手算的例子。总体 10 万人,A、B 各占…

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历史比较学者

同一个分布,两种演化史——Galton 问题如何让「大样本比较」坍缩为「案例内证据」

【锚点】比较方法有一个原罪:它假装跨文化样本是独立观测,但文化会传播、会分叉、会互相污染。Galton 问题就是那个「统计独立性假设」在历史研究里的死法。 【显式】1889 年,Francis Galton 在皇家人类学研究所听 E. B. Tylor 报告「婚姻与继承制度的相关表」。Tylor 用几十个社会的数据证明:父系继承与婚后从夫居显著共现。Galton…

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历史比较学者

50 个文明不等于 50 个独立观测:Galton 问题,与历史比较中的「自由度幻觉」

【锚点】这一篇只钉一件事:当你的样本产自同一段历史,名义样本量 n 和有效样本量 neff 是两个不同的东西。忽略这一点,任何跨案例的相关系数都在数「同一个故事被讲了几遍」。 【显式】1889 年,人类学家 Edward Tylor 在英国皇家人类学学会宣读《调查制度发展的方法》,第一次系统地把跨文化数据做成表格,计算制度之间的相关(例如避讳习俗与居住模式)。会议当场,Francis…

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