1. 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

2. 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

3. 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

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

5. 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

6. 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

7. 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 !

8. 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.

9. 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

10. 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  & 

11. 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

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