**Norming
Distributions and Standardization**

Since
most psychological tests are not mastery tests with criterion references which
determine performance, a different way must be used to classify scores as low
or high.

In order to assess overall performance,
most psychological tests employ a ** standardization sample** which
allows the test makers to create a normal distribution which can be used for
comparison of any specific future test score.

**Standardization
Sample : ** a large sample of test takers who represent
the population for which the test is intended.
This standardization sample is also referred to as the *norm group (or
norming group).*

* *

We convert the raw scores of the sample
group into percentiles in order to construct a normal distribution to allow us
to rank future test takers.

Norms
are not standards of performance, but serve as a frame of reference for test
score interpretation.

Norm
groups can range in size from a few hundred to a hundred thousand people. he
more people we use in our norm group, the close the approximation to a normal
population distribution we get.

**Sampling
methods for selecting a norming group**

Sample
must be representative : Test children
if you are developing a test of children's IQ;
test adults if you are interested in assessing adult interests.

The
closer the match between your sample and your intended population of test
takers, the more accurate the distribution will be as a ranking guide.

** Simple
Random Sampling :** every person in the target population has an equal chance of being in
the standardization sample.

** Stratified
Sampling :**
Test developer takes into account all demographic variables which can
accurately describe the population of interest and then selects individual at
random, but proportional to the demographic portrait of the test population.

Most
accurate way of developing norm group.

Common
demographics to stratify : age, gender,
socioeconomic status, geographic region.

** Cluster
Sampling :**sampling
begins by dividing a geographic region into blocks and then randomly sampling
within those blocks.

More
likely than random sampling to come up
with a representative sample and less time consuming than stratified sampling.

**Item Sampling**

Often,
test developers need to produce more than one version of a standardized test.

This
is particularly important if you believe you will have an individual complete a
psychological test more than once.

Item
sampling refers to the procedure of giving two norm groups different items
from the same exam.

This
allows us to shorten the time it takes to conduct our representative sampling.

Difference
between **group norms** and **local norms :**

Sometimes educators are interested how
students performed relative to other students in the same grade, or other
students in adjacent districts.

For these purposes, test scores will
develop *local norms *for statistical comparison, rather than using the
group norm supplied with the test.

When scoring is done by computer, local
norms can be easily developed.

**Converting
Raw scores into percentile ranks.**

Remember,
one major assumption in both psychology and psychological measurement is that
all variables of psychological interest are **normally distributed**.

Since
these variables fall into a normal distribution, we can specify what proportion
of the population falls at or below (or at or above, or beteen) any score on a
particular test.

The
average value is the midpoint of the distribution and has a percentile rank of
50%.

By
knowing the mean (arithmetic average) and the standard deviation (average
variation) of any psychological test, we can construct the normal distribution.

**68
%** of all
scores fall within +/- 1 standard
deviation from the mean.

**96%** of all scores fall within
+/- 2 standard deviations from the mean

IQ
distribution has a mean of 100 and a standard deviation of 15.

**Specific
Types of Normal Distributions commonly used in psychology.**

Psychologists
refer to these distributions often because there is a common reference for
understanding raw scores of these particular distributions :

**The
Z distribution **: The Z distribution has a mean
of 0 and a standard deviation of 1.

Extremely easy to tell from a Z score :

Whether
a score is above or below average (by the sign, positive or negative)

Whether
the score falls within average or deviate ranges. -1 to +1, an average score,
-1 to -2 and +1 to +2, above or below average, Z scores <-2 or >+2 are atypical scores (outliers).

**The
T distribution**
: Has a mean of 50 and a standard deviation of 10. Easy to tell from a T score:

Whether
a score is above or below average (T<50 below average, T>50 above
average)

How
far above or below because standard deviation is in units of ten.

Sometimes
preferred to Z because negative T values are extremely rare.

**Converting
Raw Scores to Z scores and reverse**

** **

** **

**Z
= (Raw Score - Average) / Standard Deviation**

Through
simple algebra, we can isolate any term we are interested in solving for :

**Raw
Score = ( Z * SD) + Average**

**Average
= Raw Score - (Z * SD)**

**SD
= (Raw Score - Average)/ Z **

Understanding
this relationship, we can convert a z score into any type of distribution we
like.

**T
= 10Z + 50**

**SAT
scores : 100Z +500**

**Parallel and Equated Tests**

** **

** **

When
more than one version of a standardized test is needed, alternate forms must be
developed.

**Parallel
Forms**
: If the two tests have the same types
and numbers of items of equal difficulty, the alternate versions are said to
have parallel form.

Scores
on parallel forms are highly correlated.

Parallel
Forms are difficult to develop because the mean and standard deviation on both
tests must be equivalent.

**Equated
Forms**
: When we can't develop two alternate
forms with the exact same mean and standard deviation, we can still compare
tests of equivalent difficulty through the use of a common metric, for example
the Z score distribution.

**Item
Response Theory** can be used to equate difficulty and discriminability of two tests
through **linking **