# When was the word “bias” coined to mean $\mathbb{E}[\hat{\theta}-\theta]$?

When was the word “bias” coined to mean
$\mathbb{E}[\hat{\theta}-\theta]$?

The reason why I’m thinking about this right now is because I seem to recall Jaynes, in his Probability Theory text, criticizing the use of the word “bias” used to describe this formula, and suggesting an alternative.

From Jaynes’ Probability Theory, section 17.2 “Unbiased Estimators:”

Why do orthodoxians put such exaggerated emphasis on bias? We suspect that the main reason is simply that they are caught in a psychosemantic trap of their own making. When we call the quantity $(\langle\beta\rangle-\alpha)$ the ‘bias’, that makes it sound like something awfully reprehensible, which we must get rid of at all costs. If it had been called instead the ‘component of error orthogonal to the variance’, as suggested by the Pythagorean form of (17.2), it would have been clear that these two contributions to the error are on an equal footing; it is folly to decrease one at the expense of increasing the other. This is just the price one pays for choosing a technical terminology that carries an emotional load, implying value judgments; orthodoxy falls constantly into this tactical error.

Apparently, the concept of mean bias was coined by:

Neyman, J., & Pearson, E. S. (1936). Contributions to the theory of testing statistical hypotheses. Statistical Research Memoirs, 1, 1-37.

acccording to:

Lehmann, E. L. “A General Concept of Unbiasedness” The Annals of Mathematical Statistics, vol. 22, no. 4 (Dec., 1951), pp. 587–592.

which contains a more extensive discussion on the history of this concept.

It is worth noticing that mean bias is just a type of bias, and there also exists the concept of median bias (which cannot be straightforwardly extended to the multivariate case, which may explain why it is not that popular).