## 1 Introduction  
Many education systems globally have adopted the English Proficiency Test (EPT) as an effective mechanism to evaluate English as a Foreign Language (EFL) speakers' comprehension levels [1, 2]. It is also used to determine the success or failure of pedagogies and English learning performances [3, 4]. Hence, any exploration of EPT can help stimulate EFL practitioners and learners' further interest [5, 6]. With the advancement of Information and Communications Technology (ICT), EPT has gradually developed towards digitalization. For example, internationally well-known English certification tests, such as the Test of English as a Foreign Language (TOEFL) and the International English Language Testing System (IELTS), are implemented online [7]. Because the Online English Proficiency Test (OEPT) naturally offers many benefits, including random selection of test items, easy-to-update-and-expand test banks, and the fact that the evaluation process of EFL learners' academic performance is more flexible and ubiquitous (e.g., [8, 9]), many educational institutes have developed OEPT for facilitating EFL students' English learning performance (e.g., [10, 11]). Since OEPT is used to test EFL students' English proficiency, in order to effectively evaluate their learning performance, the literature has brought forth various derived issues, including whether the test is objective, its reliability and validity, its difficulty tendency, and so on (e.g., [9, 12]). When it comes to tests, most people in education think of the item response theory (IRT), along with test response patterns and theories, test reliability and validity, test construction, item banking, computer adaptive test (CAT), and so on [13; 14; 15]. IRT embraces two basic concepts: (1) test-takers' performances in test items can be predicted or explained by a single (or a group of) factor(s), which are called \"latent traits\" or \"abilities\"; and (2) test-takers' performances and their latent traits can be represented by a continuous increasing mathematical function, which is called the item characteristic curve (ICC) [16]. IRT has achieved remarkable results in the development of test banks and CAT systems (e.g., [13; 14; 17]). Its advantages include the ability to effectively define the reliability and validity of test items, classify the difficulty of test items, and conduct an integrated analysis of students' ability and test questions [18]. IRT tools or CAT systems rely on statistical experts or in-service teachers who have the relevant statistical expertise (e.g., [13; 14; 15; 17; 18]), which may not be easily implemented by Teaching English for Speakers of Other Languages (TESOL) faculty. Moreover, establishing the CAT system of OEPT requires considerable resources and funds, which may not be accepted by most schools. Thus, seeking a low-cost and efficient approach to explore the composition of EPT or even OEPT and defining its lexical difficulty tendency would undoubtedly be a boon for English language learning and teaching. Language ability is multidimensional and includes three different concepts: (1) standards describe language performance in specific contexts at different proficiency levels; (2) language competence includes lexical and grammatical competence; and (3) language skills comprise listening, reading, speaking, and writing [12]. EPT is used as the standard to assess whether EFL learners can understand English language knowledge (i.e., lexicon and grammar) when those pop up in real-world English contexts [19; 20]. In addition, EPT is fundamentally composed of a bunch of lexical items (i.e., vocabularies). From the perspective of corpus linguistics, the difficulty level and classification of vocabularies have been processed by many linguists. Furthermore, many word lists have been developed for corpus-based analysis to date. For example, [PERSON] [21] compiled the general service list (GSL), [PERSON] [22] compiled the academic word list (AVL), [PERSON] et al.