Here’s a nice overview of causal inference by Scott Cunningham. Yes, you get an entire book as a free download, and it’s got you covered from probability to Pearl’s directed acyclical graphs, from instrumental variables to synthetic control. It comes across quite friendly, but has enough econometrics to scare many off. I quite enjoyed the historical bits thrown in here and there to explain where the methods came from.
With the advent of easy internet surveys, some of which quite powerful, survey experiments have experienced a boom. The promise of stronger claims to causality (due to internal validity) may play another role. A particular kind of survey experiments are vignettes: a short description is presented to respondents, followed by a question (or a few). In a vignette experiment, the description is systematically varied (e.g. black woman, white woman), while the question is not (e.g. how like you is this person). Questions of external validity are too often brushed aside, but for someone looking for a short introduction, look no further than the Little Green Book (as usual). It’s an accessible manual/introduction.
To my taste, there is a bit too much about D-efficient designs, but I might be glad one day given how practical the advice is in the respective sections. I was a bit puzzled about how critical the authors are of conjoint analysis, but it turns out that this has more to do with the kind of analysis usually undertaken than the design (conjoint analysis presents information as a table, factorial surveys use vignettes, but there are other terms in use).
Auspurg, Katrin, and Thomas Hinz. 2015. Factorial Survey Experiments. Quantitative Applications in the Social Sciences (QASS) 175. Seven Oaks: SAGE Publications.