Page 168 - DEDU504_EDUCATIONAL_MEASUREMENT_AND_EVALUATION_ENGLISH

Educational Measurement and Evaluation

Notes Example 4
The marks obtained by Student A in the mathematics and language tests of maximum marks 100,
each are 80 and 70 respectively. If the mean (M) of mathematics scores of the class students is 60
and standard deviation () 8, and in the language test 40 and 10 respectively; then find out in
σ
which subject the student A is more able as compared to other students.
Calculation
X – M
Z-score of mathematics marks of Student A, (Z) =
σ
80 – 60
=
8
20
=
8
= 2.5
X – M
Z-score of language marks of Student A, (Z) =
σ
70 – 40
=
10
30
=
10
= 3
Analysis
Because Student A’s Z-score in language is more than that of mathematics, so he is more able in
language in the class as compared with mathematics.
The first thing to be seen here is that his obtained score in mathematics is more than that of
language, but Z-scores reveal that he is more able in language than mathematics in the class.
Secondly, the table reveals that the student falls in Very Good category in both subjects. However,
Z-scores tell that despite being Very Good in both subjects, he is comparatively better placed in
language.
Z-scores are both positive and negative and they are calculated to two numerals of fraction, so
they are a little difficult to use. However, from the viewpoint of the above qualities and utility,
they are most used in the field of education.

12.4 T-Scores (Transformed Scores)

Meaning of T-scores
T-scores are those converted scores of raw scores of which the mean (M) is 50, standard deviation
σ
() is 10 and the distribution is normal. These scores are always positive (+ve) and their value is
often from 20 to 80.
Calculation of T-Scores
The following formula is used for converting raw scores into T-scores :

+
T-Score, T = 50 10 ⎛ ⎜ X – M ⎞ ⎟
⎝ σ ⎠
In which, T = T-score

162 LOVELY PROFESSIONAL UNIVERSITY