In minority language revitalisation contexts, the determination of proficiency in the minoritised language is a sensitive social issue that affects citizens regardless of their linguistic background. From a psychometric perspective, since the target population is heterogeneous, competence assessment instruments must ensure score validity for each linguistic subgroup. Focused on the Basque Autonomous Community (Spain), in this paper, we introduce the Basque Competence Assessment examination (known by its acronym EGA) and assess the factorial invariance of the writing section using a structural equation modelling approach. Data were collected from 2554 candidates classified into three groups according to mother tongue: Spanish, Basque, and Basque/Spanish. The results show the near invariance of the writing section of the EGA and that the highest performance was found in the Basque mother-tongue examinees. Results also reinforce the importance of validation analysis in language diversity contexts to guarantee fairness in test-based decisions.