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
raw scores in z-scores
set a mean value that removes negative numbers
set a standard deviation value
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 Freds z-score and transform to a scale where the mean is 100
and a standard deviation is 15.
Freds transformed IQ test score is 85.