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.
Procedure:
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:
where
 = Arbitrary mean
 =
Arbitrary standard deviation
Example
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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