Transformed
zscores
Zscores
have two major disadvantages for a lay audience. First,
negative scores have negative connotations. Second,
zscores and their associated decimal point presentation can be difficult for others to
interpret. These disadvantages can be
mitigated by transforming the zscores into another metric that removes decimals and
negative values.
Procedure:
Transform
raw scores in zscores
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 zscore and transform to a scale where the mean is 100
and a standard deviation is 15.
Sample statistics:
Fred’s zscore:
Transformation:
and
Fred’s transformed IQ test score is 85.
