# Uncategorized

In the comments to my first post on severity, Professor Mayo noted some apparent and some actual misstatements of her views.To avert misunderstandings, she directed readers to two of her articles, one of which opens by making this distinction:

“Error statistics refers to a standpoint regarding both (1) a general philosophy of science and the roles probability plays in inductive inference, and (2) a cluster of statistical tools, their interpretation, and their justiﬁcation.”

In Mayo’s writings I see  two interrelated notions of severity corresponding to the two items listed in the quote: (1) an informal severity notion that Mayo uses when discussing philosophy of science and specific scientific investigations, and (2) Mayo’s formalization of severity at the data analysis level.

One of my besetting flaws is a tendency to take a narrow conceptual focus to the detriment of the wider context. In the case of Severity, part one, I think I ended up making claims about severity that were wrong. I was narrowly focused on severity in sense (2) — in fact, on one specific equation within (2) — but used a mish-mash of ideas and terminology drawn from all of my readings of Mayo’s work. When read through a philosophy-of-science lens, the result is a distorted and misstated version of severity in sense (1) .

As a philosopher of science, I’m a rank amateur; I’m not equipped to add anything to the conversation about severity as a philosophy of science. My topic is statistics, not philosophy, and so I want to warn readers against interpreting Severity, part one as a description of Mayo’s philosophy of science; it’s more of a wordy introduction to the formal definition of severity in sense (2).

It’s not great, but, as my mother-in-law sometimes says, it’ll do in the dark:

$\Phi\left(x\right)\approx\tilde{\Phi}\left(x\right)=\frac{\phi\left(0.87x-0.89\right)}{2\phi\left(0.89\right)},\,-3\le x<0.$

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