![]() Just to be thorough, we can check the psychologist’s work by computing the Z score ourselves. With these pieces of information in place, we’re good to go. The standard deviation of that distribution.The mean of the distribution that this raw score came from.The raw score we are trying to convert into a Z score.To calculate a Z score you need to know three things: But the Z score gives us an answer., and it’s all because of how Z scores are calculated. Should we be impressed by Benny? Should we be sad for him? Who knows. We don’t know if everyone else also had scores that were about 310, or if lots of other people scored way higher than Benny or way lower than Benny. You might have noticed that when the psychologist told us that Benny’s raw spelling score was 310, she didn’t tell us anything about the variability of the scores among all the test takers. Whether you realize it or not (yet) this way of conveying information about Benny’s score is actually much more informative than just knowing his raw score of 310. She informs us that Benny’s spelling test result is a Z score of -1.4. Because our psychologist knows that this score of 310 isn’t super informative, she instead decides to report Benny’s spelling score as a standardized score. What exactly does this score tell us about Benny? Turns out, not much. A local psychologist comes along and analyzes some of the student data and learns that Benny earned a score of 310 on this spelling test.Ĭool… I guess. The test was administered to 500 students across the district. This spelling test is a brand new measure one that was made up by the education “expert” (whatever that means) at some school district. The Z score is arguably the most common type of standardized score, and its what we’ll work with here to make things easier for us.Įxample: We want to know how well a student named Benny did on a test of spelling. Put simply, to say that a score is standardized means that it has been converted from its original scale/metric into standard deviation units, more commonly known as a Z score. My code is shared at the end, if you’re interested in how I did everything) What does standardized mean? (Side note: I used R to put together the data for this tutorial. ![]() Here’s a rundown for your statistical woes. ![]() Many students have a difficult time understanding standardization when starting out in learning statistics. ![]()
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