What the pilot establishes
At 20% capacity, rural priority reaches 25.31% of students below basic proficiency. Random allocation reaches 20%. The difference is +5.31 percentage points, with a preliminary 95% interval of +3.55 to +7.08.
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Findings / access to support
What the pilot shows. Which decisions it informs.
The pilot compares offers of places at equal capacity. It helps identify which allocation rules merit further study and establish limits on spending for additional screening.
01Whom to offer a place
CAPACITY SCENARIO
How many places can we offer?
Of 200 recipients of offers, how many are below basic mathematics proficiency?
0200 offers
The full gray bar represents 200 offers. The colored portion shows expected recipients below basic proficiency. The black marker is the preliminary 95% confidence interval.
A simple rule is a meaningful benchmark.
At 200 places, the pilot does not establish a statistically significant difference between rural priority and the more complex family-resource index. This does not prove equivalence.
Illustrative group: 1,000 students. Calculations use weighted Ukrainian PISA data; capacities of 100 and 300 are exploratory checks. Chart data ↗
Which decision this can inform
A more complex selection process should be compared with a simple rule. The pilot has not established a clear advantage of the family-resource index, ESCS, over rural priority. Its collection cost should be weighed against the range of possible gains.
Three measures: what do the percentages mean?
| Rule | Coverage of students below basic proficiency | Their share among recipients of offers | Share of the initial skill deficit held by recipients |
|---|---|---|---|
| Random allocation | 20.00% | 45.96% | 20.00% |
| Rural priority | 25.31% | 58.17% | 28.83% |
| Low ESCS | 25.43% | 58.44% | 28.48% |
| Parental education | 23.39% | 53.74% | 24.47% |
The first measure asks “what share of students in need receives an offer?” The second asks “who receives the offers?” The third accounts for the depth of the initial skill deficit, not learning gaps eliminated. All rules have the same expected capacity.
The coverage difference between rural priority and low ESCS is −0.12 percentage points, with a 95% interval of −2.22 to +1.99. A statistically insignificant difference does not prove equivalence.
02Incomplete family information
A missing answer
changes access.
ESCS is missing for 7.11% of the represented population. Leaving these cases without priority changes how the rule allocates support.
The practical implication is to provide a way to clarify information and track coverage of these cases separately. The reasons for missingness are unknown; a missing value does not itself establish poverty.
Low ESCS; missing values receive no priority25.43%
Low ESCS or a missing value27.29%
Difference: +1.86 pp
95% interval: +1.27 to +2.45 pp
Some places can remain open to everyone
One scenario allocates 25% of capacity through open random selection and 75% through rural priority. Coverage of students below basic proficiency is 23.99%, compared with 25.31%. The cost of broader access is 1.33 percentage points of coverage. This illustrates a trade-off, not an established optimum.
03How to spend the budget
Better targeting.
Fewer places.
Move the slider: screening can improve the composition of recipients, but it leaves less money for tutoring.
SCENARIO MODEL · TEST ACCURACY AND COST ARE ASSUMED, NOT MEASURED
Better information also costs money
The initial budget covers 200 places per 1,000 students. Screening is paid for all 1,000.
As a percentage of the cost of one tutoring place.
What do these two measures mean?
Sensitivity is the probability of identifying a student below basic proficiency. Specificity is the probability of correctly identifying other students. These are assumed test properties; PISA is not a ready-to-use screening tool for selecting individual children.
The same total budget
Screening: 20.0% of the total budget
160places remaining
≈142offers to students below basic proficiency
+25 versus the baseline
Compared with approximately 116 such offers under rural priority without an additional test.
Price limit at the selected accuracy: 6.85% of the cost of one place, per person screened.
The model targets offers to students with insufficient skills. Each place costs the same; allocation among positive test results is random. Participation, learning gains and the instructional value of assessment are not included. Even perfect information gives only an upper bound on justified spending. Formulas and assumptions ↗
The upper bound is already calculated
Compared with rural priority, perfect knowledge of students’ status justifies spending at most 8.37% of the cost of one place per person screened. The preliminary 95% interval is 7.39–9.34%.
At an initial capacity of 20%, that is approximately 41.8% of the total budget for places. These percentages use different denominators.
What this bound does not mean
It is not a recommended test price or measured cost saving. A specific instrument requires evidence on its accuracy and price. The value of assessment for grouping students or adapting instruction is outside this model.
From findings to decisions
The price exceeds even the perfect-information ceilingPreserve funding for places, under the model’s stated objective.
The price is below the ceiling, but accuracy is unknownValidate the instrument before adoption. A low price alone is insufficient.
Differences between rules remain uncertainWeigh information costs against the range of possible targeting gains.
Recommendations are conditional. Actual programs may differ in participants, costs, attendance and effects. Explore the full research design ↗