Page 173 - DEDU504_EDUCATIONAL_MEASUREMENT_AND_EVALUATION_ENGLISH

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

12.8 Summary Notes

• Raw score is an original datum that has not been transformed.
• Standard scores are those scores which have a definite reference point or norm, and this
norm is the Mean (M) of the scale.
• Z-Scores
• Z-scores are those converted scores of raw scores of which the mean (M) is zero (0) and
σ
standard deviation () is one (1). These scores are obtained by linear transformation of
raw scores, so they fall in the category of linear standard scores. The unit of Z-scores is
σ
similar to the standard deviation () .
• Calculation of Z-Scores
• The following formula is used for converting raw scores into Z-scores :
X – M
Z-score, Z =
σ
In which, Z = Z-score
X = Raw score
M = Mean
σ = Standard deviation

• 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.
• T-scores are those converted scores of raw scores of which the mean (M) is 50, standard
σ
deviation () is 10 and the distribution is normal. These scores are always positive (+ve)
and their value is often from 20 to 80.
• 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
X = Raw score
M = Mean
σ = Standard deviation

• The mean (M) of T-scores is 50 and standard deviation () is 10. so, if the range of general
σ
distribution is taken to be 100, the range of T-scale becomes from 0 to 100.
• C-scores are those converted scores of raw scores of which the mean (M) is 5 and standard
σ
deviation () is 2. For it, the range of raw scores is distributed into 11 equal unit-groups
which are displayed on a 11-point scale from 0 to 10.
• There are two methods of converting a raw score into C-score— by Z-score and by percentile
rank. The following formula is used to convert a raw scores into C-score by Z-score :
• C-score, C = 5 + 2Z
• In some situations in the field of education, the use of C-scores is more useful than the use
of Z-scores and T-scores, however such situations are very rare.

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