What can we are saying concerning the distinction of two binomial distribution chances
Take into account two unbiased binomial distributions with chances 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 important.
Utilizing what would now be known 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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