Why z-scores?

• Transforming scores in order to make

comparisons, especially when using different

scales

• Gives information about the relative standing

of a score in relation to the characteristics of

the sample or population

– Location relative to mean

– Relative frequency and percentile

What does it tell us?

• z-score describes the location of the raw score

in terms of distance from the mean, measured

in standard deviations

• Gives us information about the location of

that score relative to the “average” deviation

of all scores

Z-score Distribution

• Mean of zero

◦ Zero distance from the mean

• Standard deviation of 1• Standard deviation of 1

• Z-score distribution always has same shape as

raw score. If distribution was positively skewed to

begin with, z scores made from such a

distribution would be positively skewed.

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