Evaluating Intercourse Ratios: Revisiting a Well-known Statistical Drawback from the 1700s | by Ryan Burn | Aug, 2024

What can we are saying concerning the distinction of two binomial distribution possibilities

18th century Paris and London [12]

Contemplate two unbiased binomial distributions with possibilities of successes p_1 and p_2. If we observe a_1 successes, b_1 failures from the primary distribution and a_2 successes, b_2 failures from the second distribution, what can we are saying concerning the distinction, p_1 – p_2?

Binomial mannequin variations like this have been first studied by Laplace in 1778. Laplace noticed that the ratio of boys-to-girls born in London was notably bigger than the ratio of boys-to-girls born in Paris, and he sought to find out whether or not the distinction was vital.

Utilizing what would now be referred to as Bayesian inference along with a uniform prior, Laplace computed the posterior chance that the start ratio in London was lower than the start ratio in Paris as

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