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A
standardized z-score
represents both the relative position of an individual score in a distribution as compared
to the mean and the variation of scores in the distribution.
A negative z-score indicates the score is below the distribution mean. A
positive z-score indicates the score is above the distribution mean. Z-scores will form a
distribution identical to the distribution of raw scores; the mean of z-scores will equal
zero and the variance
of a z-distribution
will always be one, as will the standard deviation.
To
obtain a standardized score you must subtract the mean from the individual score and
divide by the standard deviation. Standardized scores
provide you with a score that is directly comparable within and between different groups
of cases.
Variableè |
Age |
|
|
Z |
Doug |
24 |
-20.29 |
-20.29/15.86 |
-1.28 |
Mary |
32 |
-12.29 |
-12.29/15.86 |
-0.77 |
Jenny |
32 |
-12.29 |
-12.29/15.86 |
-0.77 |
Frank |
42 |
-2.29 |
-2.29/15.86 |
-0.14 |
John |
55 |
10.71 |
10.71/15.86 |
0.68 |
Beth |
60 |
15.71 |
15.71/15.86 |
0.99 |
Ed |
65 |
20.71 |
20.71/15.86 |
1.31 |
As an
example of how to interpret z-scores, Ed is 1.31 standard deviations above the mean age
for those represented in the sample. Another
simple example is exam scores from two history classes with the same content but
difference instructors and different test formats. To adequately compare student A's score
from class A with Student B's score from class B you need to adjust the scores by the
variation (standard deviation) of scores in each class and the distance of each student's
score from the average (mean) for the class.
Software Output Example
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