PSY 4310 NORMS
PURPOSE OF NORMS: translate a raw score
into a "normed" score that is based on other
people's performance on the same test
RAW SCORE immediate result of an individual's
responses to a test
NORMED SCORE: the individual's raw score is
compared with scores of individuals in the
normative (standardized) group
CRITERION REFERENCED VS. NORM
REFERENCED: the framework for interpreting
test performance can either be related to a
criterion (like an "A") or other individual scores
NORMREFERENCED TESTING AND
ASSESSMENT: a method of evaluation and a
way of deriving meaning from test scores by
evaluating an individual testtaker's score and
comparing it to scores of a group of testtakers yields information on a testtaker's standing or
ranking relative to some comparison group of
testtakers
CRITERION REFERENCE TEST: a test which uses
a universal score of mastery, ignoring scores of
other testers - no use of normative samples
APPLICABILITY OF CRITERION REFERENCING:
a test must have a well-defined body of
content for it to be criterion referenced
3 MAJOR TYPES OF NORMS
1. percentiles
2. standard scores
3. developmental norms
RELATIONSHIP OF NORMS: most types of
norms are systematically related to one
another and interpreted in the context of the
normal curve
PERCENTILES:
 reflects the percentage of cases in the
norm group falling below a certain
score; range = 1 to 99... median = 50

an expression of the
percentage of people whose score on a
test or measure falls below a particular
raw score
PERCENTAGE CORRECT: the distribution of raw
scores - number of items that were answered
correctly multiplied by 100 and divided by the
total number of items
STRENGTHS OF PERCENTILES: easy to explain
and easy to calculate and thus widely used
3 WEAKNESSES OF PERCENTILES
1. confusion with percentage-right score
(a score of 50 is not failing, it is average)
2. represents an ordinal scale of
measurement (no information of
absolute differences between people)
3. Inequality of units throughout the scale
(percentiles are bunched up in the
middle and spread out in the ends)
STANDARD SCORES: conversion of a z-score
into a new system with an arbitrarily chosen M
and SD (generally these values are convenient
such as M=50 and SD=10)
4 EXAMPLES OF WIDELY USED VERSIONS
OF STANDARD SCORES
Wechsler and SB personality scores (M=50,
SD=10)
SAT scores (M=500, SD=100)
IQ scores (M=100, SD=15)
multilevel scaled scores like the Weschsler and
SB sustests (M=10, SD=3)
EQUATION FOR STANDARD SCORE
SS=SD(s)/SD(r) (X-Mr) + Ms
where:
SS= standard score
SD(s) = standard deviation in the standard
score system
SD(r) = standard score in raw score system
X= raw score
Mr = mean in raw score system
Ms = mean in standard score system
EQUATION OF STANDARD SCORE USING ZSCORE
SS=z(SDs)+Ms
3 CHARACTERISTICS OF STANDARD
SCORES
1. mean is set at a standard value
2. SD is set at a standard value
3. the value of any score expresses it's
location relative to the normal
distribution
LINEAR VS. NONLINEAR STANDARD SCORES:
most standard scores are linear
transformations of raw scores whereas some
standard scores are derived from non-linear
transformations when the raw scores are not
normally distributed
AREA TRANSFORMATION: results in a
normalized standard score when doing a nonlinear transformation
STANDARD SCORES USED IN PERSONALITY
TESTS
t-scores with a mean of 50 and a standard
deviation of 10
2 STRENGTHS OF STANDARD SCORES:
1. avoids the problem of inequality of
units because they are linear
transformations of
2. z-scores amenable to statistical
calculations
WEAKNESSES OF STANDARD SCORES:
difficult to explain and one must know they
mean and standard deviation
DEVELOPMENTAL NORMS: applicable when a
trait develops systematically with time; raw
score can be interpreted in terms of age or
grade
NATIONAL ANCHOR NORMS: norms that we
use nationally for our country & update for
aptitude tests
EQUIPERCENTILE METHOD: method of
establishing norms in which the equivalency of
scores on different tests is calculated with
reference to corresponding percentile scores
AGE EQUIVALENTS: norms created based on
age such as mental age (determined by finding
the median for examinees as successive age
levels)
GRADE EQUIVALENTS: norms created based on
grade such as different tests for different
grades in order to obtain the norm for each
grade)
2 OTHER DEVELOPMENTAL NORMS
1. anthropometric measurements (i.e.
height and weight; **many are
essentially AE)
2. stage theories of human development
(tests based on these theories may
place an individual at a certain stage;
i.e. Piaget's theory of development)
2 STRENGTHS OF DEVELOPMENTAL NORMS
1. natural interpretations (i.e. "he's
reading at 8th grade level")
2. Useful for measuring growth (i.e.
comparing an individual's achievement
level in 1st, then 4th, then 7th grade)
2 WEAKNESSES OF DEVELOPMENTAL NORMS
1. limited to "growth" traits (traits must
have a developmental pattern)
2. uncontrolled standard deviations (SD
changes from level to level and test to
test)
NORM GROUPS: groups which arise from
norming standardization programs and then
provide the basis for norms
TYPES OF NORM GROUPS
1. National
2. Convenience
3. Subgroup Norms
NATIONAL NORM GROUPS: groups that are
representative of the segment of the
population for whom the test is intended (i.e.
people applying to college)
CONVENIENCE NORM GROUPS: groups based
on one or more groups that a conveniently
available for testing
USER NORMS: convenience norms based on
whatever groups actually took the test
(generally within some specified time)
SUBGROUP NORMS: groups based on the
common traits within a larger norm group (i.e.
sex or race); **useful when there are
substantial differences between the
subgroups on the variable measured
by the test
LOCAL NORMS: Norms derived from a
representative local sample, as opposed to a
national sample.
USEFULNESS OF NORM GROUPS: provide a
representative, stable, and meaningful
framework for interpreting the test results
STABILITY OF NORM GROUPS: determined by
the size of the group (larger groups are more
stable)
REPRESENTATIVENESS OF NORM GROUPS:
determined by how well-defined a population
is; if a norm group is not representative one
should get good information about the norm
group – if a norm group is representative one
should compare it with a target group
on key variables
KEY VARIABLES OF INTEREST
Age, sex, racial ethnic group, SES, ability level,
educational level, geographic region, size of
city