The error law and its generalisation per Fechner and Pearson - A rejoinder
The error law and its generalisation per Fechner and Pearson - A rejoinder
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DOI：
10.1093/biomet/4.1-2.169
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发表时间：
1905-01-01
期刊：
影响因子：
2.7
通讯作者：
Pearson, K
中科院分区：
文献类型：
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作者：
Pearson, K
170 Skew Variation，根据我的批评者的说法，这是一个奇怪的词，它实际上写于 1895 年，其内容在同年或次年的学术讲座中给出；直到几年后，由于缺乏空闲时间为媒体准备材料，这本书才得以出版，而每位每天必须讲课四个小时的老师都会欣赏这一点。兰克博士表示，如果这篇论文已经写出来，就不会影响他的判断。这是很有可能的，我在这里引用这个问题只是为了表明我的批评者所采用的语气。 KE Ranke 博士对我对 J. Ranke 教授的 900 Altbaierisch 颅骨数据进行拟合的处理中出现了一个非常相似的例子。我特意使用这个例子，因为 Stieda 已经使用过它。 1 我自己不应该混合，即使是头颅指数，/和？数据和斯蒂达一样，但我希望将广义曲线达到的结果与高斯曲线达到的结果进行比较。实际上，我在回忆录中谈到了所得曲线，无论是广义曲线还是高斯曲线，都“对于此类统计数据非常有用”。我的目的当然是证明，广义方法并没有在高斯方法成功的地方失败，而是超越了它。那么兰克博士如何治疗这个例子呢？他引用了 Palin Elderton 的回忆录中的一个例子（实际上是我插入的 f！），给出了 Ranke'sche Messungen，作为我在正态曲线情况下测试拟合优度的方法的说明。毫无疑问，正如我在 1894 年所说，高斯曲线对于 J. Ranke 的数据来说相当好，但它并不遵循 IV 型曲线。频率曲线没有给出更好的拟合，并且对于高斯过程无法处理的常数来说并不显着。现在，Ranke 博士可以测试给出的众数到均值的距离值、偏度以及 Altbaierisch 颅骨情况下的其他常数。我在我的回忆录中给出了这些常数的可能错误：论数学-
170 Skew Variation, a Bejoinder worden according to my critics, it was actually written in 1895 and its substance given in academic lectures of the same or the following year; it was not published till some years afterwards owing to that want of leisure'for preparing matter for press which every teacher who has to lecture four hours a day will appreciate. Dr Ranke says that had the paper been written, it would not have influenced his judgment. That is quite possible, and I only cite the matter here to indicate the tone adopted by my critics.A very similar instance occurs in Dr KE Ranke's treatment of my fitting of Professor J. Ranke's data for 900 Altbaierisch crania. I used this example purposely because it had already been used by Stieda. 1 should not myself have mixed, even for the cephalic index,/and? data as Stieda did, but I wished to compare the results reached by the generalised curve with those reached by the Gaussian curve. I actually spoke of the resulting curves in my memoir, whether the generalised curve or the Gaussian, as being" quite good for this type of statistics*." My object of course was to show that the generalised method did not fail where the Gaussian succeeded, but surpassed it. Now how does Dr Ranke treat this instance? He cites an example (actually inserted f by me!) in a memoir by Palin Elderton giving the Ranke'sche Messungen as an illustration of my method of testing goodness of fit in the case of the normal curve. Undoubtedly as I said in 1894 the Gaussian curve is quite good for J. Ranke's data, but it does not follow that the Type IV. frequency curve does not give a better fit, and is not significant for constants which the Gaussian process cannot deal with. Now it was open to Dr Ranke to test the values given for the distance from mode to mean, the skewness and the other constants in the case of the Altbaierisch crania. I have given the probable errors of these constants in my memoir: On the Mathe-