= Egon Pearson
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<Egon Pearson> developed the theory of <statistical hypothesis testing> with <Jerzy Neyman>. Their framework distinguishes controlling <type I error> under a <null hypothesis> from maximizing <statistical power> against a specified <alternative hypothesis>. University College London's institutional history identifies this collaboration as a central contribution.https://www.ucl.ac.uk/mathematical-physical-sciences/statistics-old/department-information/our-early-history[Departmental history, Egon Pearson and collaboration with Neyman]{ref}
The <Neyman-Pearson lemma> makes the tradeoff precise for two simple hypotheses with densities $f_0$ and $f_1$. At a fixed allowed <type I error>, the most powerful test rejects where the <likelihood ratio> $f_1/f_0$ is largest, with boundary <randomization> if needed. To see the principle, compare its test function $\phi_*$ with another admissible $\phi$: the product $(\phi-\phi_*)(f_1-cf_0)$ is nonpositive pointwise. Integrating and using the size constraint shows that $\phi$ cannot have greater <statistical power>.
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