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

is evident that the scores obtained from educational measurements cannot be analysed on their Notes
own basis. So, in statistics, these raw scores are converted into several types of new scores and by
these new scores, the raw scores are analysed. These converted scores are called derived scores in
statistics.
Standard scores indicate where your score lies in comparison to a norm group. For example, if
the average or mean score for the norm group is 25, then your own score can be compared to this
to see if you are above or below this average.

12.1 Meaning of Raw Scores

Raw score is an original datum that has not been transformed. This may include, for example, the
original result obtained by a student on a test (i.e., the number of correctly answered items) as
opposed to that score after transformation to a standard score or percentile rank or the like.
Often the conversion must be made to a standard score before the data can be used. For example,
an open ended survey question will yield raw data that cannot be used for statistical purposes as
it is; however a multiple choice question will yield raw data that is either easy to convert to a
standard score, or even can be used as it is.

12.2 Standard Scores

Standard scores are those scores which have a definite reference point or norm, and this norm is
σ
the Mean (M) of the scale. Besides, it has a definite standard deviation () . Several standard
σ
scores can be obtained using mean (M) and standard deviation () . The chief among them are Z-
scores, T-scores, C-scores and Stanine scores.
Suppose that you have just completed your midterm for this class and you were told that you had
a score of 55. How would you feel ? The first question you might ask is how many points were
possible ? If you were told that 85 points were possible you might not feel too well since you
correctly answered about 64% of the questions.
Now let’s assume that the test was very difficult and the instructor didn’t expect anyone to have
mastered all of the content on it. What other information might you wish to know ? Perhaps you
would like to know the average (mean) grade on the test. If you were to discover that it was 50,
you might feel better about your performance because you were above average.
You might be interested to know how the scores were spread above and below the average
(mean). In particular, you are probably wondering how far above the mean you were compared
to others in the class. Were most of the grades close to the mean, or were students’ grades far
above or below the mean. One way to measure the dispersion or spread of scores is with the
range (subtract the low score from the high score). Suppose the range were 30 points with the
high being 75 and the low being 45. You might not feel to well about your grade even though it
was above the average. The problem with the range is that one extreme score can influence it
very much. In this case, maybe only one person earned 75 and the next high was 56 with everyone
else falling between 46 and 56, a range of 10.
Instead of using the range, we use the standard deviation when we talk about the spread of
scores. In the midterm example, suppose you were told that 68% of the people who took the test
has a score from 48 to 52. In other words, 68% of the people fell 2 points above or 2 points below
the mean. In that case, we would say that the test scores had a standard deviation of 2. Assuming
that the scores fell into a normal distribution, we would also know that 95% of the students
would have scores within two standard deviations above or below the mean. In our case that
would 4 points above (54) or 4 points below (46) the mean (50). You would feel rather good about
your score of 55. Knowing the mean and standard deviation makes it possible to interpret raw
scores and compare different individuals’ performances with each other or an individual’s
performance on one test with his or her performance on another test.

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