Skulls of the seventeenth-century Londoners unearthed from the Farringdon Street

Skulls of the seventeenth-century Londoners unearthed from the Farringdon Street plague pit in 1903 lie in rows upon the laboratory benches at University College. Measurement of the cephalic index across nine hundred specimens provides the basis for a distribution of cranial breadth. The mean stands at 140.2 millimetres. The standard deviation is 5.3. These are raw descriptions of a finite population. The problem arises when the investigator moves from the table to the press. To publish a correlation of 0.25 between cranial capacity and orbital height before the sampling error is fully constrained is an act of intellectual recklessness. The null hypothesis states that no such correlation exists in the parent population from which these Farringdon remains were drawn. The probable error must be calculated. If the coefficient is less than thrice its probable error, the result is indistinguishable from the fluctuations of random sampling.

A finding published prematurely is a permanent toxin in the scientific record. The April 12 battery sweep of the L19 and L20 series demonstrates this fragility. The initial confidence of 0.88 collapsed to 0.55 when subjected to a held-out replication. This is the load-bearing downgrade. A correlation that vanishes under the pressure of a larger n is not a discovery; it is a phantom of small-sample noise. The investigator must maintain the threshold of the razor. Below the significance level, one retains the null. Above it, one rejects. There is no middle ground of “suggestive” evidence. A p-value of 0.06 is a failure to reject. It is a statement that the data do not yet possess the power to overcome the null assumption. To publish such a result as a “trend” is to abandon the mathematical discipline of the Biometric school for the vagaries of the old naturalists. The effect size must be paired with the p-value to distinguish a massive sample measuring a triviality from a small sample capturing a profound shift. The Farringdon data stay in the ledger until the chi-squared goodness-of-fit test confirms the normality of the distribution. I will not release the coefficients for the long-headedness of the plague-dead until the mathematical probability of error is reduced to a negligible fraction. Accuracy is the only morality in statistics.