The Two-Phase Approach
Most vocabulary tests ask you to answer definition questions directly. This approach has a fundamental flaw: test-takers can guess, and many people tend to overclaim — marking words as known when they only have a vague familiarity. Our test addresses this with a two-phase design.
Overclaim Detection
The recognition phase includes a controlled proportion of fake words — terms that look and sound like real English words but have no meaning (e.g., crepulent, nargitate). If you mark these as words you know, the test records an overclaim.
Your final vocabulary estimate is adjusted based on your overclaim rate. If you marked 10% of fake words as known, the model assumes you also overclaimed on approximately 10% of real words — and reduces your estimate accordingly. This keeps scores honest even for test-takers who are inclined to be generous with themselves.
Bayesian Item Response Theory (IRT) & Adaptive Selection
The definition phase operates on a mathematically rigorous 2-Parameter Logistic (2PL) Item Response Theory (IRT) framework. Every word in the test bank is dynamically calibrated with two statistical parameters:
- Difficulty ($b_i$): The latent ability level ($\theta$) at which a test-taker has a 50% probability of answering the item correctly.
- Discrimination ($a_i$): The sensitivity of the item in distinguishing between test-takers whose abilities lie just above or below the word's difficulty level.
The probability $P_i(\theta)$ that a user with latent ability $\theta$ will answer a given word $i$ correctly is computed using the 2PL logistic formula:
$$P_i(\theta) = \frac{1}{1 + e^{-a_i(\theta - b_i)}}$$
Instead of hard difficulty steps, the test uses Fisher Information ($I_i(\theta)$) maximization to select the next question. It evaluates which remaining word in the bank will yield the highest mathematical information at your current estimated ability level $\theta$, calculated as:
$$I_i(\theta) = a_i^2 P_i(\theta)(1 - P_i(\theta))$$
After each answer, the system updates your latent ability score ($\theta$) using a Bayesian Expected A Posteriori (EAP) estimator, integrating your response history across an 81-point ability scale. The test dynamically halts when its internal Standard Error of Measurement (SEM) reaches the configured threshold ($SEM \le 0.22$), or when a maximum cap of 20 questions is reached. This threshold describes precision within the model; it has not yet been shown to equal a particular real-world percentage error.
This is intended to make the assessment efficient by matching question difficulty to the model’s current estimate in real time.
Thematic Lexical Profile Breakdown
Upon completing the test, your vocabulary is not just represented as a single number, but also divided into a multidimensional Lexical Profile across five core educational domains:
- Academic: Vocabulary key to scientific, analytical, and scholarly environments (SAT, GRE, and academic publishing).
- Business: Lexicon of professional relations, negotiation, economics, and corporate communication.
- Conversational: Standard daily vocabulary, idioms, and core conversational speech.
- Literary: Narrative richness, historical phrasing, descriptive aesthetics, and rare creative prose.
- Collocations: Common phrasal verbs, idiomatic pairings, and natural native-like collocations.
Your answers are visualized on an interactive SVG Radar Chart across the five categories. The chart summarizes performance on the sampled items; it is not a validated diagnostic profile.
Calibration — Native Speaker Track
The native-speaker word bank is informed by the Brysbaert & Keuleers (2016) lexical decision database, which contains word frequency and familiarity data for more than 60,000 English words collected from over 220,000 participants. Using that research as an input does not make this site's scores directly comparable to the study participant distribution.
Vocabulary estimates are expressed in word families — the standard unit in vocabulary research. A word family includes a base word and its regular inflections and derivations (e.g., run / runs / ran / running / runner = one family).
CEFR Alignment — English Learner Track
The English learner track is aligned with the Common European Framework of Reference for Languages (CEFR). Word difficulty levels correspond to CEFR band vocabulary lists:
- Level 1 (A1) — ~500 most frequent word families
- Level 2 (A2) — 500–1,500 word families
- Level 3 (B1) — 1,500–3,000 word families
- Level 4 (B2) — 3,000–5,500 word families
- Level 5 (C1) — 5,500–8,500 word families
- Level 6 (C2) — 8,500–12,000 word families
The learner track maps the model's latent ability parameter ($\theta$) to a CEFR-oriented vocabulary band. This is an internal educational mapping, not an official CEFR placement, because the test does not assess listening, speaking, writing, grammar, or pragmatic competence.
Accuracy and Limitations
The result is a model-based estimate and this implementation has not yet been independently validated against an external criterion test. Its practical accuracy depends on:
- Honest answering — the overclaim correction assumes a consistent response pattern. Deliberate random answering will produce unreliable results.
- Model precision — the test uses an internal Standard Error of Measurement stopping rule, which measures uncertainty inside the IRT model but is not the same as a validated real-world error margin.
- Word family definition — vocabulary estimates vary depending on how broadly "knowing a word" is defined. Our estimates use a conservative receptive-vocabulary definition.
Use the reported score as an indicative vocabulary band, not a precise inventory. Individual results can vary with fatigue, guessing, interpretation of “knowing” a word, item exposure, and the fit between the word bank and the test-taker.
Word Bank
The native speaker word bank contains words across five difficulty levels, from high-frequency everyday vocabulary through SAT and GRE-level academic words to rare literary and archaic terms. The learner word bank covers A1 through C2 CEFR vocabulary with a focus on receptive knowledge of word meaning.
Both banks are reviewed periodically for item quality and difficulty ordering. Decoy words are constructed to resemble the phonological and morphological patterns of real English words.
Frequently Asked Questions
How accurate is the vocabulary test?
The result is an indicative, model-based estimate. The test uses a 2PL IRT model, Bayesian EAP estimation, and an internal SEM stopping rule, but this specific implementation has not yet been independently validated. We therefore do not claim a fixed real-world margin of error.
What is the Brysbaert corpus and why is it used?
The Brysbaert & Keuleers (2016) lexical decision database contains word frequency and familiarity data for more than 60,000 English words collected from over 220,000 participants. This site uses the research to inform word selection; its own scoring implementation remains independently unvalidated.
How does overclaim detection work?
The recognition phase includes decoy words — terms that look and sound like real English but have no meaning (e.g., crepulent, nargitate). If you mark these as known, the test records an overclaim.
How are CEFR levels assigned in the learner track?
The learner track maps the model's latent ability estimate to an internal CEFR-oriented vocabulary band from A1 to C2. It is not an official CEFR placement or full-skills assessment.