  Data-driven algorithms play a large role in decision making across a variety
of industries. Increasingly, these algorithms are being used to make decisions
that have significant ramifications for people's social and economic
well-being, e.g. in sentencing, loan approval, and policing. Amid the
proliferation of such systems there is a growing concern about their potential
discriminatory impact. In particular, machine learning systems which are
trained on biased data have the potential to learn and perpetuate those biases.
A central challenge for practitioners is thus to determine whether their models
display discriminatory bias. Here we present a case study in which we frame the
issue of bias detection as a causal inference problem with observational data.
We enumerate two main causes of bias, sampling bias and label bias, and we
investigate the abilities of six different fairness metrics to detect each bias
type. Based on these investigations, we propose a set of best practice
guidelines to select the fairness metric that is most likely to detect bias if
it is present. Additionally, we aim to identify the conditions in which certain
fairness metrics may fail to detect bias and instead give practitioners a false
belief that their biased model is making fair decisions.
