XX

1. Z-SCORES (STANDARD
SCORES)
 We can use the SD (s) to classify people on any
measured variable.
 Why might you ever use this in real life?
 Diagnosis of a mental disorder
 Selecting the best person for the job
 Figuring out which children may need special
assistance in school



X
z

2. EXAMPLE FROM I/O
 Extraversion predicts managerial
performance.
 The more extraverted you are, the
better a manager you will be (with
everything else held constant, of
course).

3. AN EXTRAVERSION TEST TO
EMPLOYEES
1
)( 2
2




N
N
X
X
s
 Scores for current managers
 10, 25, 32, 35, 39, 40, 41, 45, 48, 55,
70
 N=11
 Need the mean
 Need the standard deviation
N
X
X



4. Let’s Do It
X X2
10 100
25 625
32 1024
35 1225
39 1521
40 1600
41 1681
45 2025
48 2304
55 3025
70 4900
440 20030
40
11
440



N
X
X
58.15
111
11
)440(
20030
1
)(
2
2
2








N
N
X
X
s

5. SOMEBODY APPLIES FOR A
JOB AS A MANAGER
 Obtains a score of 42.
 Should I hire him?
 Somebody else comes in and has a
score of 44? What about her?
 What if the mean were still 40, but the
s = 2?

6. HARDER EXAMPLE:
 Two people applying to graduate school
 Bob, GPA = 3.2 at Northwestern Michigan
 Mary, GPA = 3.2 at Southern Michigan
 Whom do we accept?
 What else do we need to know to
determine who gets in?

7. SCHOOL PARAMETERS
 NWMU mean GPA = 3.0; SD = .1
 SMU mean GPA = 3.6; SD = .2
 THE MORAL OF THE STORY: We can
compare people across ANY two tests
just by saying how many SD’s they are
from the mean.

8. ONLY ONE TEST
 it might make sense to “rescore”
everyone on that test in terms of how
many standard deviations each person
is from the mean.
 The “curve”

9. z-SCORES & LOCATION IN A
DISTRIBUTION
 Standardization or Putting scores on a test
into a form that you can use to compare
across tests. These scores become known as
“standardized” scores.
 The purpose of z-scores, or standard scores,
is to identify and describe the exact location
of every score in a distribution
 z-score is the number of standard deviations
a particular score is from the mean.
(This is exactly what we’ve been doing for the
last however many minutes!)

10. z-SCORES
 The sign tells whether the score is
located above (+) or below (-) the
mean
 The number (magnitude) tells the
distance between the score and the
mean in terms of number of standard
deviations

11. WHAT ELSE CAN WE DO WITH z-
SCORES?
 Converting z-scores to X values
 Go backwards. Aaron says he had a z-
score of 2.2 on the Math SAT.
 Math SAT has a m = 500 and s = 100
 What was his SAT score?

12. USING Z-SCORES TO STANDARDIZE
A DISTRIBUTION
 Shape doesn’t change (Think of it as re-
labeling)
 Mean is always 0
 SD is always 1
 Why is the fact that the mean is 0 and the SD is 1
useful?
 standardized distribution is composed of
scores that have been transformed to create
predetermined values for m and s
 Standardized distributions are used to make
dissimilar distributions comparable

13. DEMONSTRATION OF A z-SCORE
TRANSFORMATION
 here’s an example of this in your book (on pg. 161).
I’m not going to ask you to do this on an exam, but I
do want you to look at this example. I think it helps
to re-emphasize the important characteristics of z-
scores.
· The two distributions have exactly the same shape
· After the transformation to z-scores, the mean of
the distribution becomes 0
· After the transformation, the SD becomes 1
· For a z-score distribution, Sz = 0
· For a z-score distribution, Sz2 = SS = N (I will not
emphasize this point)

14. FINAL CHALLENGE
 Using z-scores to make comparisons
(Example from pg. 112)
 Bob has a raw score of 60 on his psych exam
and a raw score of 56 on his biology exam.
 In order to compare, need the mean & the
SD of each distribution
 Psych: m = 50 and s=10
 Bio: m = 48 and s=4

15. FINAL CHALLENGE II
 You could
 sketch the two distributions and locate his score in
each distribution
 Standardize the distributions by converting every score
into a z-score
 OR
 Transform the two scores of interest into z-scores
 PSYCH SCORE = (60-50)/10 = 10/10 = +1
 BIO SCORE = (56-48)/4 = 8/4 = +2
 *Important element of this is INTERPRETATION*

16. OTHER LINEAR
TRANSFORMATIONS
 Steps for converting scores to another
test
 Take the original score and make it a z-
score using the first test’s parameters
 Take the z-score and turn it into a “raw”
score using the second test’s parameters.
 Standard Score = mnew + zsnew
 See “Learning Checks” in text, these are
a general idea of what might be on the
exam