How to convert these test scores into percentiles?

Is this a trade secret? Nothing obvious appears on line.

I have in front of me three test scores:


TONI-3: 117

SAGES: 129

I have no idea how good or bad these test scores are.* I’d like to know what percentiles they fall under, if possible.

Anybody know?

*Well, tha’ts not true–I have good reasons to think they’re good scores. I just don’t know how good.

X Percentile means you did better than X percent of the rest. I.e. if your income puts you in the 85th percentile, you make as much or more money than 85% of the population.

Obviously, to determine percentile, you need to know the distribution of scores.

If (a big if) those scores are normalized to have a mean of 100 and a standard deviation of 15, then the best score is around the 97th percentile and the lowest is near the 87th.

It looks like my guess is right about the NNAT and TONI but I haven’t found out anything about SAGES although it does seem somewhat more likely now.

So the test scores correspond to z-scores of: 30/15, 17/15, and 29/15. I gave the percentiles that go with these in the post above but you can look them up in any stats book.

Somewhere there as to be instructions on how to do that. I don’t remember if it was in the statistics course I took a long time ago. I never took any education courses that should cover it somewhere. You would need a large body of data to establish a mean of 100. I do remember that statistics means little in groups of less than 30, and the more data, the better.