# How to convert these test scores into percentiles?

**URL:** <https://boards.straightdope.com/t/how-to-convert-these-test-scores-into-percentiles/573913>\
**Category:** Factual Questions\
**Created:** [March 8, 2011, 1:11pm UTC](https://boards.straightdope.com/t/how-to-convert-these-test-scores-into-percentiles/573913 "2011-03-08T13:11:26Z")\
**Posts on this page:** 5\
**Page:** 1

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**Author:** ![Frylock](https://avatars.discourse-cdn.com/v4/letter/f/ce7236/32.png) [@Frylock](https://boards.straightdope.com/u/Frylock)\
**Post date:** [March 8, 2011, 1:11pm UTC](https://boards.straightdope.com/t/how-to-convert-these-test-scores-into-percentiles/573913/1 "2011-03-08T13:11:26Z")

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

I have in front of me three test scores:

NNAT:130

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.

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**Author:** ![md2000](https://avatars.discourse-cdn.com/v4/letter/m/73ab20/32.png) [@md2000](https://boards.straightdope.com/u/md2000)\
**Post date:** [March 8, 2011, 1:43pm UTC](https://boards.straightdope.com/t/how-to-convert-these-test-scores-into-percentiles/573913/2 "2011-03-08T13:43:41Z")

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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.

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**Author:** ![Lance\_Turbo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lance_turbo/32/6156_2.png) [@Lance\_Turbo](https://boards.straightdope.com/u/Lance_Turbo)\
**Post date:** [March 8, 2011, 2:01pm UTC](https://boards.straightdope.com/t/how-to-convert-these-test-scores-into-percentiles/573913/3 "2011-03-08T14:01:09Z")

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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.

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**Author:** ![Lance\_Turbo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lance_turbo/32/6156_2.png) [@Lance\_Turbo](https://boards.straightdope.com/u/Lance_Turbo)\
**Post date:** [March 8, 2011, 2:11pm UTC](https://boards.straightdope.com/t/how-to-convert-these-test-scores-into-percentiles/573913/4 "2011-03-08T14:11:50Z")

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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.

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**Author:** ![thelabdude](https://avatars.discourse-cdn.com/v4/letter/t/dc4da7/32.png) [@thelabdude](https://boards.straightdope.com/u/thelabdude)\
**Post date:** [March 8, 2011, 2:17pm UTC](https://boards.straightdope.com/t/how-to-convert-these-test-scores-into-percentiles/573913/5 "2011-03-08T14:17:39Z")

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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.