Can the ASQ-3 scores be translated into percentile rank and, if so, what is that percentile?

The ASQ-3 cutoff scores are set at 2 standard deviations below the mean. The monitoring zone is between 1 and 2 standard deviations below the mean. Table 18 in the technical appendix (page 171 in the User’s Guide or available here) shows the mean and standard deviations for each ASQ-3 interval. The bell curve is not typical, however, so calculating percentiles is not straightforward.

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ASQ-3(195) User's Guide(37) technical report(4) cutoff score(4)