Statistics
| Statistic | Meaning | Good range (placement / proficiency) |
|---|---|---|
| Facility (p) | Proportion answering correctly | 0.2-0.9 overall; each level's items easiest for that level and above |
| Discrimination (D, upper-lower 27%) | Do stronger test-takers get it right more often? | 0.30+ good; 0.20-0.29 acceptable; under 0.20 revise; negative = fault |
| Distractor share | % choosing each wrong option | Each distractor chosen by at least 5% |
| Distractor direction | Weaker group chooses it more than stronger group | Always |
| KR-20 / Cronbach's alpha | Internal consistency of the whole test | 0.80+ for placement; 0.90+ for high-stakes |
Item statistics need data: under 30 test-takers treat them as indications; under 10 they are noise.
Diagnosing problem items
| Pattern | Likely cause | Fix |
|---|---|---|
| Negative D, one distractor popular with the top group | Miskeyed, or two defensible answers | Check the key; rewrite the option |
| D near zero, facility near 0.5 | Item measures something else (trick, culture, reading load) | Rewrite or drop |
| Facility above 0.9 | Too easy for this population | Keep only if it targets A1 in a test for beginners too |
| Facility below 0.2, D low | Too hard or ambiguous | Check level and wording |
| A distractor nobody picks | Implausible option | Replace with a real learner error |
| Higher-level item easier than lower-level items | Item mis-levelled, or tests a familiar chunk | Re-tag or rewrite |
Improving reliability
- More good items (reliability rises with length).
- Remove items with low or negative discrimination.
- Spread item difficulty to match the levels you separate.
- Clear instructions and examples; avoid speededness unless intended.
Workflow
- Pilot the test with 30+ learners across the levels (existing classes are ideal).
python scripts/item_analysis.py responses.csv.- Fix or drop IA001 and IA002 items; replace non-working distractors.
- Re-pilot changed items or run them as unscored trial items in live tests.
- Recalculate cut scores if items changed.
academic-english-eap-course-planner
Plan English for Academic Purposes (EAP) courses: pre-sessional, in-sessional, foundation, IELTS preparation and discipline-specific EAP, with syllabus strands (academic reading, lecture listening and note-taking, essay and report writing, paraphrase, summary and synthesis, referencing and plagiarism, seminars and presentations, academic vocabulary, critical thinking), a 10-week pre-sessional outline, exit assessment, IELTS-CEFR alignment and academic style (formality, hedging, cohesion, reporting verbs). Estimates study hours and weeks to close an IELTS gap from overall or per-skill scores (IELTS rounding, minimum per skill, priority skills, feasibility before a deadline), and checks learner texts for contractions, informal words with academic alternatives, unhedged claims, 'you', And/But/So starts, rhetorical questions and missing citations.
actfl-proficiency-curriculum-mapper
Map world language curricula to the ACTFL framework: proficiency levels (Novice, Intermediate, Advanced, Superior, Distinguished with sublevels), functions, contexts, text types and accuracy, proficiency vs performance, the three modes of communication (interpretive, interpersonal, presentational), the 5 Cs World-Readiness Standards, backward-designed thematic units with Integrated Performance Assessments, typical programme targets and FSI time estimates. Looks up approximate ACTFL-CEFR-ILR equivalences with what each level can do, and checks a unit map for missing modes, rehearsed skits mislabelled as interpersonal, translation or word lists as interpretive tasks, and units without an integrated performance assessment.
adult-literacy-esl-lesson-builder
Build lessons for adult ESL learners who are developing literacy (LESLLA learners: pre-literate, non-literate, semi-literate, literate in a non-Roman script): learner profiles and sensitive initial assessment, principles (oral language first, known to new, systematic phonics with adult-relevant text, repetition, classroom skills, respect for experience), a lesson routine (oral warm-up, review, new grapheme, blending, segmenting, decodable text, writing, functional literacy, Language Experience Approach), a phonics sequence for adults, sight words, functional literacy targets (forms, signs, medicine labels) and portfolio assessment. Checks whether a reading text is decodable with the letter-sound patterns and sight words taught so far, catching untaught digraphs, listing non-decodable words with the untaught part, and suggesting the most useful next patterns.
authentic-material-lesson-adapter
Turn authentic material (news articles, podcasts, videos, songs, menus, timetables, adverts, social media posts, forms, infographics) into language lessons by grading the task rather than the text. Selects texts for interest, relevance, exploitability, coverage, cultural load and rights; finds the 4-6 words to pre-teach, words to gloss on the page and words learners can ignore, plus names and cultural references to explain, with reading time by level; and builds a lesson shape (lead-in, pre-teach, gist or scanning, graded detail task, language focus on chunks and register, response) with task ideas per material type and level from A1 to C1. Covers copyright, fair dealing and fair use, Creative Commons and attribution.
can-do-statement-writer
Write and review can-do statements for language courses, units, lessons and learner self-assessment, CEFR or NCSSFL-ACTFL style: action (observable verb) + text or situation + level-specific conditions, learner ('I can') and descriptor ('Can') versions, progressions of one activity from A1 to C1, and coverage of reception, production, interaction and mediation. Includes a verb bank by mode and level and condition and text-type banks. Lints statements for teacher-centred phrasing, knowledge instead of use (learn, know, understand the passive), missing context, two skills in one statement, vague quality words, grammar items as outcomes, overlong statements and missing modes in a set.
cefr-aligned-syllabus-builder
Build language course syllabuses aligned to the CEFR (A1-C2, plus levels, Companion Volume 2020): entry and exit levels, guided learning hours and course length (with an L1-distance adjustment), syllabus type (topic, functional-notional, task-based, skills-based, multi-strand), unit-by-unit can-do outcomes, grammar from a core inventory by level, vocabulary, functions, pronunciation, balance of reception, production, interaction and mediation, recycling and assessment points. Checks a syllabus for units without can-do statements, core grammar for the level not covered, items above the course level, skills missing from most units and units with no vocabulary or functions.