*Continuing with posts on E.S. Pearson in marking his birthday:*

**Egon Pearson’s Neglected Contributions to Statistics**

by** Aris Spanos**

**Egon Pearson** (11 August 1895 – 12 June 1980), is widely known today for his contribution in recasting of Fisher’s significance testing into the * Neyman-Pearson (1933) theory of hypothesis testing*. Occasionally, he is also credited with contributions in promoting statistical methods in industry and in the history of modern statistics; see Bartlett (1981). What is rarely mentioned is Egon’s early pioneering work on:

**(i) specification**: the need to state explicitly the inductive premises of one’s inferences,

**(ii) robustness**: evaluating the ‘sensitivity’ of inferential procedures to departures from the Normality assumption, as well as

**(iii) Mis-Specification (M-S) testing**: probing for potential departures from the Normality assumption.

Arguably, modern frequentist inference began with the development of various finite sample inference procedures, initially by William Gosset (1908) [of the **Student’s t** fame] and then **Fisher** (1915, 1921, 1922a-b). These inference procedures revolved around a particular statistical model, known today as *the simple Normal model*:

X_{k} ∽ NIID(μ,σ²), k=1,2,…,n,… (1)

where ‘NIID(μ,σ²)’ stands for ‘Normal, Independent and Identically Distributed with mean μ and variance σ²’. These procedures include the ‘optimal’ estimators of μ and σ², Xbar and s², and the pivotal quantities:

(a) τ(**X**) =[√n(Xbar- μ)/s] ∽ St(n-1), (2)

(b) *v*(**X**) =[(n-1)s²/σ²] ∽ χ²(n-1), (3)

where St(n-1) and χ²(n-1) denote the Student’s t and chi-square distributions with (n-1) degrees of freedom. Continue reading