Case 742: A Story of Growth
The biometric laboratory at University College London houses the records of 1,000 families, specifically the measurements of stature between fathers and sons. Look at the entry for Case 742. The father stands 68.2 inches; the son stands 69.1 inches. This single pairing contains no information. It is a story. It suggests a narrative of growth, perhaps an improvement in Victorian diet or a personal triumph of lineage. Such stories are the enemies of science.
The null hypothesis states that there is no linear relationship between the height of the father and the height of the adult son. To test this, the entire contingency table must be constructed. The correlation coefficient $r$ for this series is 0.51. The standard error is small due to the sample size of 1,000 pairings. The p-value falls far below the 0.01 threshold. The null hypothesis is rejected. This is the signal. It is a mathematical description of the pressure of heredity.
The 0.35% average return premium during equity index options expiration weeks functions on the same mechanical rigor. The null hypothesis states that opex weeks are indistinguishable from non-opex weeks. The data rejects this null. The premium is a persistent deviation. Market participants attempt to wrap this signal in a story about “gamma hedging” or “mechanical rebalancing.” These are mere causal ghosts. They are the same as the “dietary improvements” attributed to Case 742. The statistician does not require the story to validate the signal. The signal is the measured frequency of the event against the distribution of pure chance.
If the sample were reduced to ten weeks, the test would likely fail to reject the null. This failure would not prove the premium is non-existent. It would prove the observation lacked the power to overcome the noise. We do not accept the null; we merely find the evidence insufficient to convict. The 0.35% premium is a directional finding with a specific effect size. It exists as a structural feature of the frequency distribution. I shall record the coefficient and discard the narrative explanation.