Z-Scores

2. Also known as standard scores
It is used to identify and describe the exact
location of each score in a distribution
A score by itself does not necessarily provide
much information about its position within a
distribution
It tells the exact location of the original X value
The number tells the distance between the
score and the mean

3. 𝑧 =
𝑥− 𝑥
𝑠𝐷
𝑠𝐷 =
𝑥−𝑅𝑠
𝑧
𝑥 = 𝑅𝑠 − 𝑠𝑑 ⋅ 𝑧
Standardized Score = 50 + 10(z)

4. Z-Scores will have exactly the same shape as the
original distribution of scores
Z-scores will always have a mean of zero
The distribution of Z-scores will always have a
standard deviation of 1
One advantage of standardizing distributions is
that it makes it possible to compare different
individuals even though they are from
completely different distributions.

5. You are doing a research with homeless people.
You want to be able to identify those who are
depressed so they can be referred to treatment.
You used the Beck Depression Inventory.
With n = 50, 𝑥 = 15 and 𝜎 = 2.
The following are the scores obtained:
Participant Original
Score
Z-Score T-
score/Sta
ndardized
Alicia 16.5
Christina 14
Chelsea 13
Sabrina 16
Kim 19

6. Alicia:
16.5−15
2
= +0.75
Christina:
14−15
2
= −0.50
Chelsea:
13−15
2
= −1.00
Sabrina:
16−15
2
= +0.50
Kim:
19−15
2
= +2.00

7. Alicia: 50 + 10 +0.75 = 57.50
Christina: 50 + 10 (-0.50) = 45.00
Chelsea: 50 + 10 (-1.00) = 40.00
Sabrina: 50 + 10 (+0.50) = 55.00
Kim: 50 + 10 (+2.00) = 70.00