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

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
Scores for current managers
10, 25, 32, 35, 39, 40, 41, 45, 48, 55, 70
N=11
Need the mean
Need the standard deviation

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

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 OR
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