How do we go about investigating test fairness

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The many dimensions of algorithmic fairness in educational applications (2019, background): “Any consistent differences in scores between different non-random groups of test-takers that result from other factors not immediately related to the construct (i.e., “construct-irrelevant”) may indicate that the test is unfair (Xi, 2010; Zieky, 2016).”
Building Better Open-Source Tools to Support Fairness in Automated Scoring (2017, background): “For example, Xi (2010) discusses how familiarity with the subject matter in an English language proﬁciency test may impact test performance and, thus, would require an explicit analysis of fairness for a group de-ﬁned by test-taker ﬁelds of study.”