Four metrics, one distance from average.

The conversions

None of that is clever. Two things about doing it at scale are worth saying out loud, because both are places the arithmetic quietly goes wrong.

Percentiles lose precision at the extremes

0 and 100 have no finite z. A report printing “<1” or “>99” means “somewhere past here”, and converting that to a number invents the rest of the sentence.

Casebook clamps those, and the clamping is visible in the workings rather than silent — so a domain mean pulled by a clamped value shows why it was pulled.

A score is not worth more because it was reported precisely

A z of −1.53 and an index of 77 are the same claim at different apparent resolutions, and the decimal places on the first do not make it a better measurement. Holding everything in one metric makes that obvious, which is an argument for the conversion rather than against it.

What the conversion must not do is lose the original. Every score in Casebook keeps the metric and the value it arrived in; z is computed for comparison and displayed beside the score as it was reported, not instead of it. A score arrives already computed by whichever platform you licensed, and is stored as it arrived.

The harder half

Putting a battery on one axis is arithmetic. Two things that follow are judgment, and both have their own page:

• Which way each measure points — a BRIEF-2 T of 80 and a WISC-V index of 80 are opposite facts, and averaging them as they stand cancels a real problem out.
• Whether a composite and its own subtests are both in the average — counting one testing twice, weighted by how many parts it happens to have.