Two Test Scores and Twelve Days
A learner has 12 days, one retake, and a requirement of 125 overall with no subscore below 110. Two full practice tests, four days apart, give: Test 1 - Literacy 105, Comprehension 118, Conversation 92, Production 100. Test 2 - Literacy 112, Comprehension 112, Conversation 97, Production 96. She has been practising 9 hours a week, split evenly across the four skills, and feels 'stuck in the nineties' in speaking. She proposes spending all remaining time on Conversation, since it is consistently the lowest. She has one practice test left in her budget and is deciding when to use it.
1. How much of the variation is signal? What can and cannot be concluded from two administrations?
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What cannot be concluded: that any single subscore moved. Differences of 7, 6, 5 and 4 points sit inside normal measurement error for subscores, and two administrations four days apart are not independent samples - fatigue, task content and familiarity all shift results. Treating 105 → 112 in Literacy as 'progress' and 118 → 112 in Comprehension as 'decline' would be reading noise as trend.
What can be concluded:
- Conversation is consistently lowest (92, 97) and below the 110 floor in at least one administration - the one finding that survives both tests.
- Comprehension has never fallen below 110 (118, 112) - the only subscore with clear headroom over the threshold.
- Production straddles the floor (100, 96): both below 110, so it is at least as much at risk as Conversation, and she has been ignoring it because it is not lowest.
- The overall target is not currently met on any plausible aggregation of these numbers.
Implication for the remaining test: use it around day 7–8, not day 1 and not the day before the retake, so there is still time to change course.
2. Where should the 12 days go? Give an explicit split, given the 'no subscore below 110' rule.
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The floor rule changes the objective. She is not maximising an average; she needs two subscores pulled up past a hard line. Reject the 'all Conversation' proposal: it optimises the lowest number, not the binding constraint set.
Suggested split of ~15 hours:
- 45% Conversation (≈7 h). Below the floor on both tests and hardest to move late, so it needs the most contact. Focus on extended turns and interactive-listening register, not vocabulary.
- 30% Production (≈4.5 h). Underrated: 100 and 96 are both below 110. Timed 5-minute responses with forced revision, which is the fastest-moving writing lever.
- 15% Literacy (≈2 h). Fluctuates around the floor; timed cloze and dictation only, no new content.
- 10% Comprehension (≈1.5 h). Maintenance only. At 112–118 it has the most headroom and the lowest marginal return; a full reallocation away from it is defensible.
Rationale to state plainly: the even split she has been running is the reason she is stuck - it spends equal time on the skill that most needs it and the skill that least needs it.
3. What monitoring would tell her by day 6 that the plan is wrong?
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Three pre-committed checkpoints, set now, before the results can be rationalised:
- Conversation fluency proxy: count silent seconds in the first 20 seconds of three recorded responses on day 1 and day 6. If silence has not fallen meaningfully and content coverage has not improved, the method is wrong (probably too much input, not enough recorded output) - change method, not skill.
- Production accuracy under revision: if her revised timed texts show new error types appearing after restructuring, she is being pushed past her control and should bank simpler accuracy instead.
- Score signal: the day 7–8 practice test. Only a shift larger than the noise band seen between Tests 1 and 2 (roughly 7 points) should trigger a reallocation; a 4-point wobble should not.
Also decide in advance what she will stop. A plan with no stated stopping rule becomes an even split again by default, which is the pattern that produced the plateau.