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.

**Percentile Scores**

A percentile score is another type of converted score. Your raw
score is converted to a number indicating the percentage of the
norm group who scored below you. For example, a score at the 60th
percentile means that the individual's score is the same as or
higher than the scores of 60% of those who took the test. The 50th
percentile is known as the median and represents the middle score
of the distribution.

Percentiles have the disadvantage that they are not equal units of measurement. For instance, a difference of 5 percentile points between two individualâ€™s scores will have a different meaning depending on its position on the percentile scale, as the scale tends to exaggerate differences near the mean and collapse differences at the extremes.

Percentiles can not be averaged nor treated in any other way
mathematically. However, they do have the advantage of being
easily understood and can be very useful when giving feedback to
candidates or reporting results to managers.

If you know your percentile score then you know how it compares
with others in the norm group. For example, if you scored at the
70th percentile, then this means that you scored the same or
better than 70% of the individuals in the norm group.

This is the score most often used by organizations when comparing
your score with that of other candidates because they are so
easily understood they are very widely used when reporting results
to managers.

The characteristic way that test scores tend to bunch up around
the average and the use of percentiles in the interpretation of
test results, has important implications for you as a job
candidate. This is because most aptitude tests have relatively few
questions and most of the scores are clustered around the mean.
The effect of this is that a very small improvement in your actual
score will make a very substantial difference to your percentile
score.

To illustrate this point, consider a typical aptitude test
consisting of 50 questions. Most of the candidates, who are a
fairly similar group in terms of their educational background and
achievements, will score around 40. Some will score a few less and
some a few more. It is very unlikely that any of them will score
less than 35 or more than 45.

Looking at these results in terms of percentiles is a very poor way of analyzing them and no experienced statistician would ever use percentiles on this type of data. However, nine times out of ten this is exactly what happens to these test results and a difference of three or four extra marks can take you from the 30th to the 70th percentile. This is why preparing for these tests is so worthwhile as even small improvements in your results can make you appear a far superior candidate.

**Different Norming Systems
**There are several different norming systems available for use,
which have strengths and weaknesses in different situations. These
can be grouped into two main categories; rank order and ordinal.

To overcome the problems of interpretation implicit with percentiles and other rank order systems various types of standard scores have been developed. One of these is the Z-score which is based on the mean and standard deviation. It indicates how many standard deviations above or below the mean your score is.

The Z-score is calculated by the formula: Z=X-M/SD Where:

Z =
standard score

X = individual raw score

M = mean score

SD = standard deviation

The illustration shows how Z-scores in standard deviation units
are marked out on either side of the mean. It shows where your
score sits in relation to the rest of the norm group. If it is
above the mean then it is positive, and if it is below the mean
then it is negative. As you can see from the illustration,
Z-scores can be rather cumbersome to handle because most of them
are decimals and half of them can be expected to be negative.

**T Scores (Transformed Scores)**

T-scores are used to solve this problem of decimals and negative
numbers. The T-score is simply a transformation of the Z-score,
based on a mean of 50 and standard deviation of 10. A T-score can
be calculated from a Z-score using the formula:

T = (Zx10) + 50

Since T-scores do not contain decimal points or negative signs
they are used more frequently than Z-scores as a norm system,
particularly for aptitude tests.

**Stens (Standard Tens)**

The Sten (standard ten) is a standard score system commonly used
with personality questionnaires. Stens divide the score scale into
ten units. Each unit has a band width of half a standard deviation
except the highest unit (Sten 10) which extends from 2 standard
deviations above the mean, and the lowest unit (Sten 1) which
extends from 2 standard deviations below the mean.

Sten scores can be calculated from Z-scores using the formula:
Sten = (Zx2) + 5.5.

Stens have the advantage that they enable results to be thought of
in terms of bands of scores, rather than absolute scores. These
bands are narrow enough to distinguish statistically significant
differences between candidates, but wide enough not to over
emphasize minor differences between candidates.

You may also be interested in: **Aptitude Tests Introduction****, Question Types & Scoring, The Difference between Speed & Power Tests, Verbal Ability Tests, Numerical Ability Tests, Abstract Reasoning Tests, Spatial Ability Tests, Mechanical Aptitude Tests, Data Checking Tests, Work Sample Tests, Interpreting Aptitude Test Results, Different Types of Scoring Systems, Standard Scores, Percentiles & Norming and Using the Results to Make Selection Decisions. **

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