z-scores for Non-Normal Distributions Flashcards
Non-normal distributions can be transformed into sets of
unit-free, standardized z scores
Non-normal distributions can be transformed into sets of unit-free, standardized z scores
In these cases, the standard normal table cannot be used
The distribution of the z scores will match the non-normal distribution
In other words, if the non-normal distribution is positively skewed, then the z-score distribution will also be skewed
Regardless of the shape of the distribution, what happens during the
the shift to z scores always produces a distribution of standard scores with a mean of 0 and a standard deviation of 1
Under most circumstances, z scores provide efficient descriptions of
relative performance on one or more tests.
The use of z scores can help you identify a person’s relative
strengths and weaknesses on several different tests
z scores reflect performance relative to some group rather than
an absolute standard
Any unit-free scores expressed relative to a known mean and a known standard deviation
standard scores
Transformed standard score
A standard score, that unlike a z score, usually likes negative signs and decimal points
Used when reporting test results to a wide audience
z’ = desired mean + (z) (desired standard deviation)
z’ (called z prime) is the transformed standard score and z is the original standard score
Use the following formula to convert any original standard score, z, have a distribution with any desired mean and standard deviation