cognitive psychology. PhD 
I think the thread is full of empirical hypotheses about type system design, but that few of them are plausibly testable.
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"Empirical analysis of programming language adoption" (https://dl.acm.org/citation.cfm?id=2509515 …) is a good one. It's more a reflection of user preferences/demography than deep insights on language design, but it's a start.
"Studying the Language and Structure in Non-Programmers’ Solutions to Programming Problems" (http://alumni.cs.ucr.edu/~ratana/PaneRatanamahatanaMyers00.pdf …) is a creative approach towards understanding cognitive models of programming.
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PL @ CHI workshop notes have a lot more references (https://docs.google.com/document/d/1-GUt5oVPpi7rlObbU1WbA5V1OQBX1iaghryLJ6-ND9o/edit# …). But I do feel like it's still pretty surface-level so far, e.g. the static. vs dynamic typing work (https://danluu.com/empirical-pl/ ).
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