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Transformed z-scores


Z-scores have two major disadvantages for a lay audience.  First, negative scores have negative connotations.  Second, z-scores and their associated decimal point presentation can be difficult for others to interpret.  These disadvantages can be mitigated by transforming the z-scores into another metric that removes decimals and negative values.




Transform raw scores in z-scores


Arbitrarily set a mean value that removes negative numbers

Arbitrarily set a standard deviation value

Use the following formula:






 =  Arbitrary mean

 = Arbitrary standard deviation



Fred took an IQ test and correctly answered 70 out of 100 points.  The mean score on this test is 75 with a standard deviation 5.   Calculate Fred’s z-score and transform to a scale where the mean is 100 and a standard deviation is 15.

Sample statistics:                            

Fred’s z-score:          

Transformation:            and 



Fred’s transformed IQ test score is 85.




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