{"id":4802,"date":"2025-04-12T21:04:37","date_gmt":"2025-04-12T19:04:37","guid":{"rendered":"https:\/\/www.psyctc.org\/psyctc\/?post_type=docs&#038;p=4802"},"modified":"2025-05-01T12:47:31","modified_gmt":"2025-05-01T10:47:31","password":"","slug":"stanines-the-stanine-transformation-scoring","status":"publish","type":"docs","link":"https:\/\/www.psyctc.org\/psyctc\/glossary2\/stanines-the-stanine-transformation-scoring\/","title":{"rendered":"Stanines &amp; the stanine transformation\/scoring"},"content":{"rendered":"\n<p>I remember reading about these, hm, some time in the 1980s I suspect when I thought they were a rather odd idea.  I have just been reminded of them because I had been doing entries like the five number summary and seven number summaries and a note on wikipedia about them reminded me of them.  I&#8217;ve never seen them used in our fields but I&#8217;m am rather more sympathetic to the motivations behind them and felt they ought to be in the glossary.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Details<\/h4>\n\n\n\n<p>I am drawing heavily on the excellent, and short, page on Wikipedia: <a href=\"https:\/\/en.wikipedia.org\/wiki\/Stanine\" target=\"_blank\" rel=\"noopener\" title=\"\">https:\/\/en.wikipedia.org\/wiki\/Stanine<\/a> but I&#8217;ll summarise it here in case it changes a lot!<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>It is a way of transforming a continuous score to a nine level score (hence stanine, from STAndard NINE).<\/li>\n\n\n\n<li>It&#8217;s a mapping based on quantiles\/percentiles<\/li>\n\n\n\n<li>The stanines are created by ranking (referential) data, so that:\n<ul class=\"wp-block-list\">\n<li>the lowest 4% get a score of 1<\/li>\n\n\n\n<li>the next 7%, i.e. up the 11% percentile get a score of 2<\/li>\n\n\n\n<li>the next 12%, up to 23%, score 3<\/li>\n\n\n\n<li>the next 17%, up to 40%, score 4<\/li>\n\n\n\n<li>the next 20%, up to 60%, i.e. the middle 20% around the median, score 5<\/li>\n\n\n\n<li>the next 17%, up to 77%, score 6<\/li>\n\n\n\n<li>the next 12%, up to 89%, score 7<\/li>\n\n\n\n<li>the next 7%, up to 96%, score 8<\/li>\n\n\n\n<li>the last 4% score 9<\/li>\n\n\n\n<li>The logic behind those funny percentiles was that they pretty much divide a Gaussian distribution into .5 SD steps (except for the end ones that sort of mop up what&#8217;s left at the edges)<\/li>\n\n\n\n<li>That means, as you can see from the percentiles, that the scores won&#8217;t contain the same proportions of the score distribution there are two stories about the reason<\/li>\n\n\n\n<li>It was first used by the U.S. air force in WW-II &#8220;for test scores&#8221; (I&#8217;d be interested to know what tests)<\/li>\n\n\n\n<li>There are two stories about the logic.  One is that, as for any nine level transformation in a decimal number system, it gets you the most levels you can get from one digit so spares you using two digits.  The other, which I love, is that it would &#8220;reduce the tendency to try to interpret small score differences&#8221; (apparently that came from Thorndyke, one of the key figures in mid-20th Century psychometrics).<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p>To me looking at this now, at least thirty years since I first saw it, there are four interesting points about this and they touch on why I think I&#8217;ve never seen stanines used in the therapy change measurement world.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>There is a logic that if you have a score that has more than nine levels you are throwing away information and, even if the reliability of the measure is such that there is little informational value in say a score difference that would map to the same stanine score, it is still true that you lose a tiny amount of statistical precision so if you really need to know if a mean difference between two groups is important or not, then you should never rescale\/transform to a small number of levels in the scores.  (The ultimate example of this is dichotomising scores which we so often do and which can lose a huge amount of statistical power\/precision, transforming to nine levels loses very little by comparison.<\/li>\n\n\n\n<li>However, Thorndike&#8217;s point is important, they probably didn&#8217;t want air force personnel arguing because one was triumphant about scoring say 73 on some score (say from 0 to 85) and another 71 when the difference between 73 and 71 was extremely likely to have been down to imprecision of measurement.  I think our field often overvalues small differences between scores and particularly, going back to dichotomising, when one score is one point above a cut-off point and the other one point below it.<\/li>\n\n\n\n<li>The other important point for our field is that we are often interested in changes in scores <em>over time for just one person<\/em>.  Here all the psychometric and statistical tools that are based on the assumption that measures work in exactly the same way for any individual (as, say, a reasonable weighing scales, or height measure, or a blood test will) may be wrong and we <em>might <\/em>be moderately seriously throwing away meaningful information if we transformed even down to nine levels.  But that opens up a lot of issues that go beyond this glossary entry!<\/li>\n\n\n\n<li>The wikipedia entry is written as if using the stanine principle as a data transform, i.e. using the centiles in your own data to convert raw scores to stanine scores.  However I suspect that in the educational world where stanines are used quite a lot, the mapping will be based on quantiles from large referential samples\/datasets.  To get the scores that mark these 4%, 7%, 12% &#8230; 96% percentiles so they won&#8217;t fluctuate much from one sample\/dataset to the next you need your referential sample\/dataset to be very large, into many thousands.  Our field very, very rarely has such datasets even if we were keen to have stanine mappings for our measure scores.<\/li>\n<\/ol>\n\n\n\n<p>Even small print: a sten transformation\/score (Standardised TEN I assume) is like a stanine but has ten levels (so losing the advantage that you can code it with a single digit.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Try also<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/www.psyctc.org\/psyctc\/glossary2\/accuracy\/\" title=\"\">Accuracy\/precision<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.psyctc.org\/psyctc\/glossary2\/dataset-and-database\/\" title=\"\">Dataset<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.psyctc.org\/psyctc\/glossary2\/distribution\/\" title=\"\">Distribution<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.psyctc.org\/psyctc\/glossary2\/five-number-summary\/\" title=\"\">Five number summary<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.psyctc.org\/psyctc\/glossary2\/gaussian-normal-distribution\/\" title=\"\">Gaussian (&#8220;Normal&#8221;) distribution<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.psyctc.org\/psyctc\/glossary2\/quantiles\/\" title=\"\">Percentiles\/centiles\/quantiles<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.psyctc.org\/psyctc\/glossary2\/reliability\/\" title=\"\">Reliability<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.psyctc.org\/psyctc\/glossary2\/sample\/\" title=\"\">Sample<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.psyctc.org\/psyctc\/glossary2\/seven-point-summaries\/\" title=\"\">Seven number summaries<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.psyctc.org\/psyctc\/glossary2\/sten-scores\/\" title=\"\">Sten scores\/transformation<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.psyctc.org\/psyctc\/glossary2\/transforming-data-variables\/\" title=\"\">Transformations<\/a><\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Chapters<\/h4>\n\n\n\n<p>Not covered in the OMbook.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Online resources<\/h4>\n\n\n\n<p>My <a href=\"https:\/\/www.psyctc.org\/Rblog\/index.html\" target=\"_blank\" rel=\"noopener\" title=\"\">rblog<\/a> post <a href=\"https:\/\/www.psyctc.org\/Rblog\/posts\/2024-12-03-dichotomisation-1\/\" target=\"_blank\" rel=\"noopener\" title=\"\">about dichotomisation<\/a> explains the issue noted above about dichotomisation.<\/p>\n\n\n\n<p>My <a href=\"https:\/\/shiny.psyctc.org\" target=\"_blank\" rel=\"noopener\" title=\"\">shiny apps<\/a> have one (<a href=\"https:\/\/shiny.psyctc.org\/apps\/ECDFplot\/\" target=\"_blank\" rel=\"noopener\" title=\"\">ECDF plot with quantiles and CIs for quantiles<\/a>) that allows you to upload data and shows the imprecision of estimating quantiles.   If you put in:<br>.04, .07, .12, .17, .2, .4, .6, .77, .89, .96<br>for the quantiles you want you are asking for a stanine mapping of your data.  You could pull these CSV files which contain datasets from a standard Gaussian distribution to your machine and upload them to that app to see the effects of dataset size:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/www.psyctc.org\/psyctc\/wp-content\/uploads\/2025\/04\/Gaussian_n100.csv\" target=\"_blank\" rel=\"noopener\" title=\"\"><em>n <\/em>= 100<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.psyctc.org\/psyctc\/wp-content\/uploads\/2025\/04\/Gaussian_n200.csv\" target=\"_blank\" rel=\"noopener\" title=\"\"><em>n <\/em>= 200<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.psyctc.org\/psyctc\/wp-content\/uploads\/2025\/04\/Gaussian_n500.csv\" target=\"_blank\" rel=\"noopener\" title=\"\"><em>n <\/em>= 500<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.psyctc.org\/psyctc\/wp-content\/uploads\/2025\/04\/Gaussian_n1000.csv\" target=\"_blank\" rel=\"noopener\" title=\"\"><em>n <\/em>= 1,000<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.psyctc.org\/psyctc\/wp-content\/uploads\/2025\/04\/Gaussian_n5000.csv\" target=\"_blank\" rel=\"noopener\" title=\"\"><em>n <\/em>= 5,000<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.psyctc.org\/psyctc\/wp-content\/uploads\/2025\/04\/Gaussian_n10000.csv\" target=\"_blank\" rel=\"noopener\" title=\"\"><em>n <\/em>= 10,000<\/a><\/li>\n<\/ul>\n\n\n\n<p>I might create some things that might touch on this though I think they&#8217;d be explanatory rather than of real use for routine data &#8230; for the reasons above including that I&#8217;ve never seen stanines used in our field!<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Dates<\/h4>\n\n\n\n<p>First created 12.iv.25, updated adding link to sten score glossary entry 1.v.25.<\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>I remember reading about these, hm, some time in the 1980s I suspect when I thought they were a rather odd idea. I have just been reminded of them because I had been doing entries like the five number summary and seven number summaries and a note on wikipedia about them reminded me of them. &hellip; <a href=\"https:\/\/www.psyctc.org\/psyctc\/glossary2\/stanines-the-stanine-transformation-scoring\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Stanines &amp; the stanine transformation\/scoring<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","template":"","meta":{"footnotes":""},"doc_category":[],"glossaries":[],"doc_tag":[],"knowledge_base":[],"class_list":["post-4802","docs","type-docs","status-publish","hentry"],"year_month":"2026-04","word_count":1024,"total_views":"1183","reactions":{"happy":"0","normal":"0","sad":"0"},"author_info":{"name":"chris","author_nicename":"chris","author_url":"https:\/\/www.psyctc.org\/psyctc\/author\/chris\/"},"doc_category_info":[],"doc_tag_info":[],"knowledge_base_info":[],"knowledge_base_slug":[],"_links":{"self":[{"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/docs\/4802","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/docs"}],"about":[{"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/types\/docs"}],"author":[{"embeddable":true,"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/comments?post=4802"}],"version-history":[{"count":16,"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/docs\/4802\/revisions"}],"predecessor-version":[{"id":4851,"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/docs\/4802\/revisions\/4851"}],"wp:attachment":[{"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/media?parent=4802"}],"wp:term":[{"taxonomy":"doc_category","embeddable":true,"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/doc_category?post=4802"},{"taxonomy":"glossaries","embeddable":true,"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/glossaries?post=4802"},{"taxonomy":"doc_tag","embeddable":true,"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/doc_tag?post=4802"},{"taxonomy":"knowledge_base","embeddable":true,"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/knowledge_base?post=4802"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}