STANDARD SCORES Flashcards
a raw score that has been converted from one scale to
another scale, where the latter scale has some arbitrarily set mean and standard deviation.
standard score
Why
convert raw scores to standard scores?
standard scores are more easily
interpretable than raw scores.
Different systems for standard scores
z scores
T scores
stanines
etc
First for consideration is the type of standard score scale that may be thought
of as….
it has a mean set at 0 and a standard
deviation set at 1.
zero plus or minus one scale
Raw scores converted into standard scores on this scale (zero plus or minus one scale)
results from the conversion of a raw score into a number indicating how many
standard deviation units the raw score is below or above the mean of the distribution.
z scores
Z = X − X
s
z score is equal to the difference between a particular raw score and the
mean divided by the standard deviation.
raw score is converted to a z score
If the scale used in the computation of z scores is called
zero plus or minus one scale
scale used in the computation of T scores can be
a scale with a mean set at 50 and a standard deviation set at 10. (W. A.
McCall)
fifty plus or minus ten scale
a scale that ranges from 5 standard deviations below the
mean to 5 standard deviations above the mean. (E. L. Thorndike)
T score
advantage in using T scores
none of the scores
is negative
By contrast, in a z score distribution
scores can be positive and negative; this can
make further computation
a
standard score with a mean of 5 and a standard deviation of approximately 2
Divided into
nine units, the scale was
term that was a contraction of the words
standard and nine
stanine
Standard scores converted from raw scores may involve
linear or nonlinear
transformations.
one that retains a
direct numerical relationship to the original raw score.
magnitude of differences between
such standard scores exactly parallels the differences between corresponding raw scores.
linear transformation
when the data under consideration are not
normally distributed yet comparisons with normal distributions need to be made.
resulting standard score does not necessarily have a direct numerical
relationship to the original, raw score.
resulting standard score does not necessarily have a direct numerical
relationship to the original, raw score.
nonlinear transformation
involves “stretching” the skewed curve into the shape of a normal
curve and creating a corresponding scale of standard scores
a scale that is technically referred
to as a normalized standard score scale.
normalizing a distribution
