history – Andi Fugard (∧⇒)

Your control group can be sensible

There’s nothing in theories of experiments requiring that researchers use a ridiculous control group. An example of such a ridiculous (and unethical) control would include randomising people who are living in abject poverty either to a regular sufficient social security payment or leaving them in poverty. Hmmm, what group will have a better outcome…?

The first example Rubin gave in his classic “Estimating causal effects of treatments in randomized and nonrandomized studies” (Rubin, 1974, p. 689) had the following two groups:

“… we will restrict discussion to the very simple study consisting of 2N units (e.g., subjects), half having been exposed to an experimental (E) treatment (e.g., a compensatory reading program) and the other half having been exposed to a control (C) treatment (e.g., a regular reading program).”

Lind’s (1753) study of scurvy treatments compared six treatments, including cider, vinegar, and sea water, as well as the oranges and lemons. Potentially unclear what the theoretical rationale was for all of those, so not ideal I’ll admit.

It’s pretty common now to use “business as usual”, “treatment as usual”, “teaching as usual”, etc., controls and to avoid waitlist controls. But this is not a new idea.

Additionally, Rubin didn’t use Y(1) and Y(0) for the two potential outcomes, but Y(E) and Y(C). It’s a very subtle difference; however, I wonder if ditching the zero helps people’s understanding. My preference would be something even closer to the names of the actual programs, e.g., if we are evaluating whether the Acme Compensatory Reading Programme is better than regular reading, Y(Acme) and Y(Regular) to emphasise the contrast. (Also now we would use “participants” rather than “subjects”.)

References

Rubin, D. B. (1974). Estimating causal effects of treatments in randomized and nonrandomized studies. Journal of Educational Psychology, 66(5), 688–701.

Lind, J. (1753). A treatise of the scurvy. In three parts. Containing an inquiry into the nature, causes and cure, of that disease. Together with a critical and chronological view of what has been published on the subject. Edinburgh: Printed by Sands, Murray and Cochran for A. Kincaid and A. Donaldson.

Oral history: Henry Faulk

“British officer served as interpreter with Intelligence Corps and as Chief Executive Field Officer of Prisoner of War Division of Foreign Office in German Prisoner of War camps in GB, 1944-1948”

Source: Imperial War Museum

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Obit

James Lind (1753), A treatise of the scurvy – key excerpts

Excerpts from the Lind (1753), with help on the ye olde English from others who have quoted him (Hughes, 1975; Bartholomew, 2002; Weber & De Vreese, 2005).

Lind’s study is sometimes presented as an RCT, but it’s not clear how his patients were assigned to groups, just that the cases “were as similar as I could have them” (see discusison in Weber & De Vreese, 2005). Bartholomew (2002) argues that Lind was convinced scurvy was a disease of the digestive system and warns against quoting the positive outcomes for oranges and lemons (and cider) out of the broader context of Lind’s other work.

Here’s what Lind said he did:

“On the 20th May, 1747, I took twelve patients in the scurvy on board the Salisbury at sea. Their cases were as similar as I could have them. They all in general had putrid gums, the spots and lassitude, with weakness of their knees. They lay together in one place, being a proper apartment for the sick in the fore-hold; and had one diet in common to all, viz., water gruel sweetened with sugar in the morning; fresh mutton broth often times for dinner; at other times puddings, boiled biscuit with sugar etc.; and for supper barley, raisins, rice and currants, sago and wine, or the like.”

Groups (n = 2 in each):

“ordered each a quart of cyder a day”
“twenty five gutts of elixir vitriol three times a day upon an empty stomach, using a gargle strongly acidulated with it for their mouths.”
“two spoonfuls of vinegar three times a day upon an empty stomach”
“a course of sea water”
“two oranges and one lemon given them every day. These they eat with greediness”
“The two remaining patients took the bigness of a nutmeg three times a day of an electuray recommended by an hospital surgeon made of garlic, mustard seed, rad. raphan., balsam of Peru and gum myrrh, using for common drink barley water well acidulated with tamarinds, by a decoction of which, with the addition of cremor tartar, they were gently purged three or four times during the course”

Excerpt from the study outcomes:

“The consequence was that the most sudden and visible good effects were perceived from the use of the oranges and lemons; one of those who had taken them, being at the end of six days fit for duty”
“Next to the oranges, I thought the cyder had the best effects”

References

Bartholomew, M. (2002). James Lind’s Treatise of the Scurvy (1753). Postgraduate Medical Journal, 78, 695–696.

Hughes, R. E. (1975). James Lind and the cure of Scurvy: An experimental approach. Medical History, 19(4), 342–351.

Weber, E., & De Vreese, L. (2005). The causes and cures of scurvy. How modern was James Lind’s methodology? Logic and Logical Philosophy, 14(1), 55–67.

“A Handbook of Integer Sequences” Fifty Years Later

New paper by N. J. A. Sloane.

Abstract: Until 1973 there was no database of integer sequences. Someone coming across the sequence 1, 2, 4, 9, 21, 51, 127, . . . would have had no way of discovering that it had been studied since 1870 (today these are called the Motzkin numbers, and form entry A001006 in the database). Everything changed in 1973 with the publication of A Handbook of Integer Sequences, which listed 2372 entries. This report describes the fifty-year evolution of the database from the Handbook to its present form as The On-Line Encyclopedia of Integer Sequences (or OEIS), which contains 360,000 entries, receives a million visits a day, and has been cited 10,000 times, often with a comment saying “discovered thanks to the OEIS”.

I’m proud to have a couple of sequences in OEIS:

A140961 (2008, with thanks to Vladeta Jovovic, whom I found via A051588, for the interpretation in terms of binary matrices). This arose when I was counting finite models of categorical syllogisms, thinking this might be useful for the psychology of reasoning. It wasn’t.
A358693 (1 Jan 2023) – whilst looking for properties of the number 2023. Trivial extension of A001102.

Earliest Uses of Symbols of Set Theory and Logic

In case you too were wondering about the history of ⊢, ⊨, and friends, try this MacTutor page at the University of St Andrews, Scotland.

Kharkiv, statistics, and causal inference

As news comes in (14 May 2022) that Ukraine has won the battle of Kharkiv* and Russian troops are withdrawing, it may be of interest to know that a major figure in statistics and causal inference, Jerzy Neyman (1894-1981), trained as a mathematician there 1912-16. If you have ever used a confidence interval or conceptualised causal inference in terms of potential outcomes, then you owe him a debt of gratitude.

“[Neyman] was educated as a mathematician at the University of Kharkov*, 1912-16. After this he became a Lecturer at the Kharkov Institute of Technology with the title of Candidate. When speaking of these years he always stressed his debt to Sergei Bernstein, and his friendship with Otto Struve (later to meet him again in Berkeley). His thesis was entitled ‘Integral of Lebesgue’.” (Kendall et al., 1982)

* Харків (transliterated to Kharkiv) in Ukrainian, Харькoв (transliterated to Kharkov) in Russian.