What we asked

States require ELA of every student, including English learners. WIDA ACCESS is the English-language proficiency test used to decide whether a student can access content in English.

The working claim:

• At low WIDA (roughly Levels 1–2), ILEARN ELA behaves like noise: floor pile-up, near-independence of the two ranks.
• At higher WIDA a signal appears: ILEARN distributions that start to look like they can access English-language content.

If that transition is real, it is evidence about where an exit criterion should sit. It is not itself the legal exit rule.

Indiana’s exit anchors

Source: IDOE, Exit Criteria for English Learners Guidance 2025–2026 (April 2025).

WIDA LONG already stores L1–L4, L4.3 (4.3–4.9 collapsed), L5, L6.

A fitted change-point describes where the content test starts to move with ACCESS. It may or may not equal the legal exit rule.

Data and windows

Same-year, same-grade join: ILEARN STUDENT_ID = WIDA ID. Grades 3–8. Placeholder floors dropped (ILEARN < 5000, WIDA == 100).

Window	Years	Role
Primary	2021–2025	Stable ILEARN scale. The estimand.
Ranks only	2026	Both scales reset. Percentiles, not proficiency.
Contrast	2017–2019	ISTEP / first ILEARN year. Not pooled.

2026 ILEARN SCALE_SCORE in the combined LONG is the equated old scale. Ranks agree; the proficiency classifier does not.

The two tests are not independent

Primary-window Kendall’s τ is 0.51–0.61 (median 0.55) — strong in every grade and year.

The signal-versus-noise claim is therefore local, not global. What changes with WIDA level is where EL students sit on ILEARN, not whether the two ranks suddenly start moving together.

The signal is location, not correlation

WIDA level	N	Within-level τ	Median ILEARN percentile	P(ILEARN proficient)
1	6,048	0.03	17	0.00
2	7,057	0.10	24	0.00
4.3 (provisional)	9,220	0.14	81	0.24
5 (auto-exit)	3,610	0.18	93	0.60

Location moves; correlation does not. From L3 the ILEARN distribution walks up the grade — median percentile climbs from the high teens at L1 to the low 90s at L5 — while the within-band τ stays modest the whole way (restriction of range). The signal is where students sit, not a tightening rank correlation.

Reading a WIDA cut as a classifier

Any candidate cut turns WIDA ACCESS into a yes/no test: WIDA ≥ cut predicts “ILEARN-proficient.”

• Sensitivity — of the ILEARN-proficient students, the share the cut catches (true-positive rate).
• Specificity — of the not-proficient students, the share correctly left below (true-negative rate).

Youden’s J = sensitivity + specificity − 1. J runs from 0 (a coin flip) to 1 (perfect separation); on an ROC curve it is the vertical height above the chance diagonal. The J-optimal cut best separates the two groups.

Youden and the exit cut

The J-optimal WIDA cut is the score that best sorts EL students into ILEARN-proficient vs not. It is a descriptive answer — where the content signal separates best — not a legal rule.

• Across 2021–2025 the J-optimal cut against ILEARN proficiency sits near 4.1 (grade medians 3.9–4.6): inside the 4.3 committee band, never at 5.0.
• At 5.0 the proficient EL students below the cut are so few that sensitivity collapses — the cut misses most of the students it should flag, so J falls.
• Youden weights a false exit and a false hold equally. A policy that treats an early exit as the costlier error would rationally sit above the J-optimal cut — one reading of why 5.0 is defensible even though J prefers 4.3.

The best statistical cut lands near 4.3, not 5.0

Primary-window Youden-optimal WIDA cuts (same-year proficiency) have median 4.05.

Grades 4–5 sit near the start of the 4.3 band; 3 and 6–8 sit a little below it. None of the Youden optima are at 5.0. That is not an argument that 5.0 is the wrong legal exit — ILEARN proficiency is a high bar, and even students first reaching 5.0 are only about 0.40 ILEARN-proficient that year.

Most of the climb happens before auto-exit

Students first reaching a cut while they still have a WIDA score:

Most of the ILEARN location gain has already happened by the time a student hits auto-exit. This is still the stayer sample.

Why symmetric copulas hide the story

The confirmatory families in step 03 — t, Frank, Gaussian — are all exchangeable and radially symmetric. Two consequences, both by construction:

• They force lower-tail dependence to equal upper-tail dependence: $\lambda_L = \lambda_U$.
• They treat the lower-left corner (both tests low — the WIDA floor) as a mirror of the upper-right corner (both high).

But the signal-vs-noise hypothesis is exactly the claim that those corners are not mirror images: low WIDA is noise, high WIDA is signal. A radially symmetric copula cannot represent that — so the departure from symmetry is not a nuisance to smooth away. It is the hypothesis, written in dependence-structure terms.

A picture of the asymmetry

The both-high signal corner and the both-low noise corner are not mirror images — the surface is far from flat, and the coupling is pulled toward high WIDA.

Blue marks where high-scorer pairs cluster more tightly than low-scorer pairs — structure the symmetric t / Frank / Gaussian families cannot represent.

The signal corner couples more than the noise corner

Deep in the tail, upper-tail concordance $\lambda_U$ runs well above lower-tail $\lambda_L$: both-high pairs co-occur more than both-low pairs. The gap $\lambda_U-\lambda_L$ grows from 0.11 (2021) to 0.22 (2025) — stable in sign, strengthening in size, and invisible to any t / Frank / Gaussian fit.

A second, independent signature of the same access story.

Testing-pattern exit

Exit is the complementary event: ILEARN + WIDA at t, ILEARN only at t+1.

Who actually leaves ACCESS

• Almost every inferred exit comes from ≥5.0 — auto-exit is doing the work.
• The 4.3–4.9 committee band barely fills in until 2024, then jumps.
• <4.3 disappearances stay in the low hundreds every year — mobility or a missed test, not a policy pathway.

The classification flag agrees only at 5.0

Share of inferred exiters whose ILEARN EL_STATUS moves LEP → Not an English Language Learner:

>=5.0 testing-pattern matches the official classification. 4.3–4.9 and <4.3 mostly do not — ACCESS non-takers, still classified EL.

No post-exit collapse

No. ≥5.0 leavers sit ~9–10 percentile points above the never-EL median and hold or rise. 4.3–4.9 leavers sit near never-EL and dip about 2 points. <4.3 disappearances stay on the ILEARN floor — like the students who never left.

Exit-year growth sits at or above 50

ILEARN SGP at t+1 is growth in the first year without ACCESS. ≥5.0 leavers post a median 58 — a right shift, not a left one. 4.3–4.9 leavers post ~50. Only <4.3 disappearances are left-shifted (median 41), which is what an unexpected drop among still-low students looks like.

The recipe that gets proposed

Find the WIDA ACCESS Overall score such that a student has better than a 50-50 chance of being ILEARN ELA-proficient the following year.

Read the joint through a copula $C(U_t^{\mathrm{WIDA}}, V_{t+1}^{\mathrm{ILEARN}})$. Let $v^*$ be the ILEARN proficiency cut on the paired rank scale. Invert

$$P(V \ge v^* \mid U = u) = \tfrac{1}{2}$$

and map $u^*$ back to a WIDA proficiency level.

Also report the empirical local-window version: the first cut $c$ at which $P(\text{proficient}_{t+1} \mid \mathrm{WIDA}_t \approx c) \ge 0.5$.

Why we do not recommend it

If the bar is “50-50 on next year’s ELA test,” a substantial share of never-EL students fail it. Using that bar to decide English-learner status asks ACCESS to predict a content outcome that English itself does not guarantee.

We still run the recipe. It is part of the conversation. It is filed as a contrast.

What the copula actually returns

The copula conditional (solid) and the local empirical rate (points) both rise with WIDA and cross the 0.50 line only near the top of the scale. The dotted line is the never-EL rate — the bar even fluent English speakers do not all clear.

Where the 50-50 cut sits

Quantity	Value
Pooled copula cut (WIDA PL at t)	4.70
Pooled local-empirical cut	5.10
P(prof t+1 | WIDA ≥ 4.3)	0.42
P(prof t+1 | WIDA ≥ 5.0)	0.59
Local P(prof t+1 | WIDA ≈ 4.3)	0.27
Local P(prof t+1 | WIDA ≈ 5.0)	0.48
Never-EL P(ILEARN proficient)	0.43

How the pieces fit

1. ILEARN ELA is not informative about English access below WIDA Level 3. L1–L2 is noise in the sense of the hypothesis.
2. Signal is clearly present by the 4.3–4.9 provisional band. That is also where Youden against ILEARN proficiency peaks.
3. 5.0 auto-exit selects students already at the top of the ILEARN distribution. It is a conservative access standard, not the first point at which ILEARN stops looking like noise.
4. Students who leave ACCESS from 5.0 hold their ILEARN location and post slightly-above-typical growth. The classification flag agrees they exited.
5. Students who disappear from ACCESS at 4.3–4.9 also hold location — but most are still classified EL. The committee-band “exiter” cell is thin and contaminated.
6. The 50-50 next-year-proficiency recipe is in the JSON and the figures. It is not the recommended exit rule.

Reproducible artifacts

Rscript run_all.R    # rebuild 00–09 + manifests
./docs/render.sh     # re-render this deck

Open the black box: WIDA’s four domains

The same rank / copula / threshold machinery, run on Listening, Speaking, Reading, and Writing separately (pulling the domain subscores from the ACCESS source files), would ask which skill the ILEARN signal is actually attached to.

• Hypothesis: Reading and Writing carry most of the ILEARN-ELA dependence; Listening and Speaking far less.
• A vine copula on the four domains plus ILEARN would isolate the content signal conditionally — the dependence that survives after the other domains are held fixed.

Is the low-WIDA “noise” real — or measurement error?

• Disattenuate the τ and the copula using each test’s conditional standard errors of measurement (CSEMs), where the source files carry them — noise from unreliability is not the same as noise from access.
• Model the ILEARN floor explicitly with a censored / two-part (Tobit-style) specification, separating “cannot yet access the test” from “low measured ability.”

Direction and dynamics

• A random-intercept cross-lagged panel model (RI-CLPM) on WIDA$_t \rightarrow$ ILEARN$_{t+1}$ versus ILEARN$_t \rightarrow$ WIDA$_{t+1}$ tests the directional ordering of the access relationship.
• Add time in program (years since a student’s first ACCESS administration, recoverable from the panel) as a moderator: does the WIDA→ILEARN coupling strengthen with exposure?

Beyond the median, beyond one cut

• Quantile / distributional regression of ILEARN on WIDA PL models the whole conditional distribution — where the lower tail crosses proficiency, not just the center.
• Finite-mixture / latent-class copulas ask whether newcomers, long-term ELs, and students with interrupted schooling follow different WIDA→ILEARN maps that a single cut averages away.
• A Bayesian or bootstrapped interval on the τ(u) change-point would give the transition “region” an honest width.

From a threshold to a decision rule

• Cost-weighted Youden: recompute the optimal cut as a function of the false-exit / false-hold cost ratio, making the value judgment explicit instead of fixing it implicitly at equal weights.
• Multistate / survival modeling of exit → reclassification → long-term-EL risk: what happens years after a student leaves, not only at $t{+}1$.
• Subgroup invariance: does the WIDA→ILEARN relationship hold across home language, grade of entry, and disability status, or does one cut carry hidden differential impact?

The through-line

The domain decomposition asks which language skill gates access; the measurement-error and distributional work ask how sharply and for whom; the panel and decision-analytic work ask in what direction and at what cost. None of them replaces the ILP committee — they give it a better-instrumented map of the band where the content test becomes a content test.