CIs only work with standard scores from norm-referenced tests. They do not apply to:
Percentile ranks (non-linear scale; a 3-point difference at the 50th %ile is not the same as at the 2nd)
Criterion-referenced scores like CORE Phonics Survey (pass/fail by skill, no SEM)
CBM raw scores like DIBELS or easyCBM words correct per minute
Age or grade equivalents (these are ordinal, not interval-scaled)
Screener scores like iReady scale scores or MAP RIT (designed to sort, not diagnose)
Scores at the floor or ceiling of a test (SEM is unreliable at extremes)
If a school is using any of the above to argue your child "doesn't qualify," the confidence interval argument does not apply. Use other strategies from The Parent Investigator's Playbook.