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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.^[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 ${\varphi }_{\ast }$ with another admissible $\varphi$: the product $(\varphi -{\varphi }_{\ast })(f_1-c{f}_0)$ is nonpositive pointwise. Integrating and using the size constraint shows that $\varphi$ cannot have greater statistical power.

Jerzy Neyman helped formulate statistical inference in terms of procedures with stated sampling guarantees. With Egon Pearson, he developed hypothesis testing that controls type I error while seeking high statistical power, embodied in the Neyman-Pearson lemma. His confidence-interval theory interprets a confidence level through repeated-sampling coverage rather than a posterior probability for a fixed unknown parameter. He also contributed to stratified sampling and the Neyman Type A distribution.

Neyman moved from University College London to Berkeley in 1938. The university's statistics department grew out of the programme he established there and became a department in 1955. Berkeley's departmental history connects that institutional development to his work on testing, confidence intervals and sampling design.^[ref]