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Standardized Z-Scores

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.

 

Variable

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

 

Interpretation

         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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