PYB110 Week Five Revision Notes
Standardisation and Z Scores
Interpretation of raw scores usually requires some sort of standardisation.
Converting a raw score into a standard score (also called a Z score) allows us to determine
the relative position of a person on a measure.
In order to obtain a Z score, we need to know the Mean and Standard Deviation of a sample
of people who have also completed the measure.
Essentially, standardisation enables us to compare two scores on varying tests (for example)
and be able to directly compare them. Similarly, it can tell us a person’s standing on a test as
compared to others on the same test.
What is a Z Score?
A Z score is how many ‘standard deviations a score is away from the mean’ AKA how many
SDs the X is from the M.
It is a way of transforming scores so that the new score represents the person’s place in the
The size of the Z score tells us how many standard deviations they are from the mean.
The sign (+/-) tells us if it is bigger or smaller than the mean.
How to Calculate a Z Score from a Raw Score
Each ordinary score is called a raw score (x).
Subtract the mean (M) from the raw score (x). This will give you the deviation score.
Divide the deviation score by the standard deviation.
Interpreting Z Scores