THE MYSTERIOUS T SCORE - Plymouth State University
THE MYSTERIOUS T SCORE
================================
Before computing the T Score, one must
compute the Z Score.
But before computing the Z Score, one must
compute the Standard Deviation.
(By this time, most people have probably
lost interest and stopped reading this article.)
Anyway, for those who are still interested,
here is what you do:
1. Add up all the test scores. Call the result SUM.
2. Add up all the squares of the test scores.
Call this result SUMSQ.
3. Divide SUM by the number of students, giving AVE.
4. Divide SUMSQ by the number of students, giving AVESQ.
5. Multiply AVE by itself, giving SQD.
6. Subtract SQD from AVESQ and take the square root of the result.
7. You now have the Standard Deviation. Call this S.
8. Look at the individual test scores. For each student,
subtract the above AVE from the student’s score, giving DIFF.
9. Divide each DIFF by the standard deviation, S. Negative answers
are OK. Keep these handy.
10. You now have a list of Z scores. Call each a Z.
11. Multiply each Z by 10 and add 50.
12. Congratulations! You have the T Scores.
“So now that I have them, what do they tell me?”
Here is how it works: If the T Score is 50, the student is average.
Above 50 means above average; below 50 means below average.
Generally, a T Score of above 60 means that a student is in the top
one-sixth of the class; above 63, the top one-tenth. Also, a T Score
below 40 indicates a lowest one-sixth class standing; below 37, the
lowest one-tenth.
Generally, two-thirds of the students will receive T Scores in the
40 to 60 range. These figures apply to classes with large numbers
of students, where a “Normal” or “Bell” curve of results is exhibited.
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\/
Mathematically,
i = n
\
\
SUM = / X
/ i
/_____
i = 1
.
_i = n
\
\ 2
SUMSQ = / ( X )
/ i
/______
i = 1
.
AVE = SUM / n
AVESQ = SUMSQ / n
2
SQD = ( AVE )
____________________
/
S = \ / AVESQ - SQD
\/
DIFF = X - AVE
i
Z = DIFF / S
T = ( 10 )( Z ) + 50
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