Page 167 - DEDU504_EDUCATIONAL_MEASUREMENT_AND_EVALUATION_ENGLISH

Unit 12 : Conversion of Raw Scores into Standard Scores, T-scores, C-scores, Z-scores, Stanine Scores, Percentiles

Notes

If raw scores are to be found out from Z-scores, the following formula is used :

Raw scores, X = M + ( × )Z σ
Example 3

σ
In a test, the mean (M) of the scores is 65, and standard deviation () is 10. In this test, the Z-
score of Student A is 2.5 and that of Student B, -3. Find out raw scores of students A and B.
Calculation

Raw score of Student A, (X) = M + ( × )Z σ
= 65 + (2.5 x 10)
= 65 + 25
= 90
Raw score of Student B, (X) = 65 + (– 3 x 10)
= 65 – 30

= 35

There are no standard units to measure non-physical qualities of a person such as
intelligence, aptitude, personality, and ability, etc. The measures of these are unit less,
for example, obtained score of a student in an examination as 40 and his IQ as 110.

Utility of Z-Scores
In the field of education, the Z-scores are used in meaningful analysis of scores of a student,
comparison of scores of two students and for comparison of marks of a student in-two subjects,
Generally, the meaning of Z-scores is considered as follows :
Table—1
Meaning of Z-scores

Z-Score Meaning

More than + 2.00 very good
+ 1.00 to + 2.00 good
+ 0.50 to + 1.00 above average
– 0.50 to + 0.50 average
– 1.00 to – 0.50 below average
– 2.00 to – 1.00 low
– 2.00 lowest

In comparison two qualities or abilities of a student in the reference group, the Z-scores of the
scores in the two subjects are calculated and then they are compared.

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