Z-Scores and Standardized Distributions

Question 1

define z-scores

Answer 1

• specify the precise location of each X value within a distribution
• can interpret a single score
• can compare 2 scores on different distributions
• can be used in inferential test to compare one sample to a population

Question 2

how do you create a standardised distribution?

Answer 2

• convert x-scores into z-scores
• subtract the population score from each raw score and set the mean of the transformed scores to 0
• divide each raw score by the population standard deviation and set the standard deviation of the transformed scores to 1

Question 3

how does linear transformation affect a standarized distribution?

Answer 3

it has no linear effect on the shape of the distribution, just changes the scale being used

Question 4

what are some rescaling examples?

Answer 4

t-scores: mean of 50 and SD of 10
IQ-scores: mean of 100 and SD of 15

Question 5

is standard or raw scores better?

Answer 5

standard scores are preferable to raw scores because they express where a score is relative to other scores and allow us to compare scores from different scales