Outline I. What are z-scores? II. Locating scores in a distribution A. Computing a z-score from a raw score B. Computing a raw score from a z-score C. Using z-scores to standardize distributions III. Comparing scores from different distributions

I. What are z scores? You scored 76 How well did you perform?  serves as reference point: Are you above or below average?  serves as yardstick: How much are you above or below? Convert raw score to a z-score z-score describes a score relative to  &  Two useful purposes: Tell exact location of score in a distribution Compare scores across different distributions

II. Locating Scores in a distribution Deviation from  in SD units Relative status, location, of a raw score (X) z-score has 2 parts: Sign tells you above (+) or below (-)  Value tells magnitude of distance in SD units

A. Converting a raw score (X) to a z-score: Example: Spelling bee:  = 8  = 2 Garth X=6  z = Peggy X=11  z =

Example Let’s say someone has an IQ of 145 and is 52 inches tall IQ in a population has a mean of 100 and a standard deviation of 15 Height in a population has a mean of 64” with a standard deviation of 4 How many standard deviations is this person away from the average IQ? How many standard deviations is this person away from the average height? 3 each, positive and negative

B. Converting a z-score to a raw score: Example: Spelling bee:  = 8  = 2 Hellen z = .5  X = Andy z = 0  X = raw score = mean + deviation

C. Using z-scores to Standardize a Distribution Convert each raw score to a z-score What is the shape of the new dist’n? Same as it was before! Does NOT alter shape of dist’n! Re-labeling values, but order stays the same! What is the mean?  = 0 Convenient reference point! What is the standard deviation?  = 1 z always tells you # of SD units from !

An entire population of scores is transformed into z-scores An entire population of scores is transformed into z-scores. The transformation does not change the shape of the population but the mean is transformed into a value of 0 and the standard deviation is transformed to a value of 1.

Example: So, a distribution of z-scores always has:  = 0  = 1 Student X X- z Garth 6 Peggy 11 Andy 8 Hellen 9 Humphry 5 Vivian N = 6 N=6  = 8 = 0  = 2  = 1 So, a distribution of z-scores always has:  = 0  = 1 A standardized distribution helps us compare scores from different distributions

III. Comparing Scores From Different Dist’s Example: Jim in class A scored 18 Mary in class B scored 75 Who performed better? Need a “common metric” Express each score relative to it’s own  &  Transform raw scores to z-scores Standardize the distributions  they will now have same  & 

Example: Class A: Jim scored 18  = 10  = 5 Class B: Mary scored 75  = 10  = 5 Class B: Mary scored 75  = 50  = 25 Who performed better? Jim! Two z-scores can always be compared

Homework Chapter 5 7, 8, 9, 10, 11