Friday, October 5, 2012
Chapter 5: Scales, Transformations, and Norms
- raw scores, which represent simple counts of the behaviours sampled by the test or
measuring procedure, do not always provide useful information
- it is often necessary to re-express, or transform, raw scores into some more
informative scale
Scale - the set of scores that might be reported for a test
- scales are very often transformations of the original raw scores
Transformations
- the simplest transformation is one that expresses scores in terms of percentage rather
than raw units
- this simple transformation has 3 characteristics than many of the most useful
transformations exhibit:
1. It does not change the personʼs score; it simply expresses that score in different units
2. It takes into account information not contained in the raw score itself-here, the
number of items on the test
3. It presents the personʼs score in units that are more information or interpretable than
the raw score
Linear Transformations
- Transformed score = constant + (weight x raw score)
- this form of a transformation guarantees a simple, direct relationship between raw
scores and transformed scores that can be depicted using a straight line
- the z transformation is extremely useful for a number of reasons
- ﬁrst, the z score indicates each personʼs standing as compared with the group mean
- when the distribution of raw scores is reasonably normal, z scores can be directly
converted to percentiles
- z scores are very useful in interpreting most psychological tests and measurements
Variations of the Z Transformations
- there are 2 features of z scores that are undesirable: half of the z scores in a
distribution will be negative and z scores often have fractional values, even when they
exceed 11 or 21
- several score transformations can overcome these disadvantages
- the T score is a simple transformation of z that takes the following form:
- T score - (z score x 10 ) + 50
Area Transformations
- uses the normal curve to create scale score values
- linear transformations simply change the units of measurement
- e.g. changing Fahrenheit to Celsius
- rather than simply changing the units of measurement, area transformations change
the point of reference
- these transformations express a personʼs score in terms of where it falls on a normal
curve, rather than simply providing a new unit of measurement Friday, October 5, 2012
- percentile transformation/percentile rank
- area transformations do not change the rank order of scores, but they do change the
intervals between scores
- you can easily convert z scores to percentile ranks
- the transformation to percentile ranks is one of the most common and useful
transformations of raw scores
Stanine - a contraction of the term standard nine and represents one of the simplest
transformations available - raw scores are transformed to a single digit between 1 and 9
Equating Scale Scores
- in many instances, it is not possible or desirable to use the same test across different
groups of examinees or for the same group of examinees at different times
- if the same test is used twice, there are a variety of factors that complicate the
interpretation of factors (student remembers the questions)
- rather than using the same test twice, educators are likely to use alternative forms of
the same achievement test
- the question is whether the test published can be sure that both forms are equal in
terms of their psychometric characteristics (difﬁculty)
- there is growing interest in the problem of equating scores on different versions of the
same test that use different testing technologies
Equating Alternate Forms Administered to the Same Examinees
- the simplest way to equate 2 alternative forms of a test is to distribute both forms of
the test randomly to a large representative sample of examinees
- random assignment is crucial to accuracy
- the next step is to generate the descriptive statistics on both forms of the test
- ﬁnally, a straightforward linear transformation (z scores) can take place, equating a
speciﬁc raw score from one test to the scale score that it would equal on the second
test
Equating Alternative Forms Administered to Different Examinees
- we actually have 3 tests: the old test, the new set, plus the common set of items given
to both groups of people
- the mechanism for equating the new test for to the old test form is through this
common collection of item,s referred to as an anchor test
- the information obtained from the anchor test provides data that allows one to equate
the 2 test forms
- if people perform differently on test forms A and B, it might be difﬁcult to determine
whether this outcome reﬂects differences in people taking the test or differences in the
tests themselves
- the use of a common anchor test, which is taken by both groups of examinees, allows
us to separate differences among examinees form differences between the test forms
Norms
- scores on psychological tests rarely provide absolute, ratio scale measures of
psychological attributes Friday, October 5, 2012
- it rarely makes sense to ask how much intelligence, motivation, depth perception a
person had
- scores on psychological tests do provide useful relative measures
- it makes sense to ask if Scott is more intelligent than Peter
- one of the most useful ways of describing a personʼs performance on a test is to
compare his or her test score with the test scores of some other person or group
- a personʼs score is interpreted by comparing that score with the scores of several
other people, this comparison is referred to as a norm-based interpretat

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