  Recent critiques of Physics Education Research (PER) studies have revoiced
the critical issues when drawing causal inferences from observational data
where no intervention is present. In response to a call for a "causal reasoning
primer", this paper discusses some of the fundamental issues underlying
statistical causal inference. In reviewing these issues, we discuss
well-established causal inference methods commonly applied in other fields and
discuss their application to PER. Using simulated data sets, we illustrate (i)
why analysis for causal inference should control for confounders but not
control for mediators and colliders and (ii) that multiple proposed causal
models can fit a highly correlated data set. Finally, we discuss how these
causal inference methods can be used to represent and explain existing issues
in quantitative PER. Throughout, we discuss a central issue: quantitative
results from observational studies cannot support a researcher's proposed
causal model over other alternative models. To address this issue, we propose
an explicit role for observational studies in PER that draw statistical causal
inferences: proposing future intervention studies and predicting their
outcomes. Mirroring a broader connection between theoretical motivating
experiments in physics, observational studies in PER can make quantitative
predictions of the causal effects of interventions, and future intervention
studies can test those predictions directly.
