Norms and Criteria:
According to
Pythagorean tradition
the circle represents
the spiritual realm;
the square represents
material existence.
So the ideal human
body represents the
marriage of matter and
spirit, reflected in its
geometric proportions.
A first norm?
A first criteria?
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Topics
 Basic Issues or Decisions to be made
 Should we “adjust” the raw score before proceeding?
 Norm or Criteria Interpretation . . . Or both?
 Types of Norms
 Percentiles
 Standard Scores
 Developmental norms
 Norm groups
 Criterion-referencing and Performance Standards
 Dynamic Assessment and Self-referencing on
Repeated Measures
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“Adjusting” The Raw Score
 We have already noted the most immediate result from an assessment
or test is the raw score. Sometimes, before we proceed to discuss the
meaning of the score (i.e., interpret it from either a norm or criteria
perspective), the raw score is adjusted. Usually this is done by
researchers, not classroom teachers. Two special considerations
 Correction for Guessing
 Only for selected-response items
 Use has faded
 Factoring in Item Difficulty
 Students get a higher “Theta” Score based on doing well on the
more difficult items of a test.
 In fact, you may be looking at a test score report given in
percentiles or standard scores and not realize you are looking
at a transformation from a Theta score rather than the
traditional raw score.
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Interpreting Student Performance
Norms or Criteria . . . .
 Intelligent interpretation of student performance is crucial for the
use of educational assessment information. We are building
toward this with previous discussions of
 Building / choosing good tests
 Determining reliability
 Determining validity
 So now we are set to explore some methods of interpretation.
These methods fall into two basic categories or approaches:
 Norm-referenced
 Compare this student with others.
 Criterion-referenced
 Compare this student with some judgment regarding
expected performance level irrespective of others.
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Percentile Rank
at or below . . .
 Percentiles and Percentile Rank




Definition: % of cases “at or below”
As we noted earlier, these two terms are different
conceptually, however, in practice often both terms are used
interchangeably.
Strengths:
 Easy to describe
 Easy to compute
Weaknesses
 Confusion with a “percentage-right score”
 Inequality of units [see next slide]
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The illustration of the
Inequality of Units in Percentiles
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Norm-Referenced Systems
Transforming Scores
 Remember, the z score tells how many standard deviation units
a score is away from the mean. I can take any set of scores I want
to “norm” (i.e. make judgments by comparing scores to each other)
and create the z distribution. But z scores are hard for lay people
to interpret (a range from -3 to +3 has little meaning to them).
 So, how about if I transform them! Zowee, Batman!
 You will hear people call these transformed scores many names,
names like: “standard scores”, “norms”, “normed scores”, “scaled
scores”. Double Zowee!
 Becoming a standard score
Definition - conversion from z-score into system with a “nice, arbitrarily
chosen” M and SD
(see illustration of conversion process on the next slide)
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Illustration of the conversion from . . .
Raw Score to Standard Score
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Cherchez la femme . . .
 Look for the woman, er . . . table


In ordinary practice, you simply use a table in
the test manual to convert a raw score to a
standard score.
Thus, it is important to understand how this
works, but you would likely never do this
yourself (unless you developed your own test,
e.g. The “McEwing Test of Procrastination”
which I will someday get around to
constructing).
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Standard Scores
really a family of scores . . . some examples
Intelligence . . . The IQ Score:
 One of the most widely implemented,
controversial and misunderstood test scores
ever used and abused.
 Historically, schools (and the public)
used the ratio IQ
 (IQ = MA/CA X 100)
 Today, we use the deviation IQ
 (most appropriately called the
“school ability index”);
 M = 100 and SD = 15 or 16
 The “father” of the IQ test was Alfred Binet.
Binet developed the test at the request of a
national commission who wanted to identify
students in need of help in coping with the
school curriculum. (see next slide)
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Alfred Binet (1857-1911)
self-taught French psychologist
In 1905 Binet had children do tasks such as follow commands,
copy patterns, name objects, and put things in order. He gave the
test to Paris schoolchildren and created a standard “intelligence
scale” based on his data. For example, a 6-year-old child who
passed all the tasks usually passed by 6-year-olds (but no tasks
beyond) would have a mental age that exactly matched his
chronological age, 6.0. In accordance with the commission’s
charge, he reasoned that students testing below age level should
be given help to achieve at levels more like their age peers.
Binet stressed that intellectual development progressed at
variable rates and could be impacted by the environment
(therefore not based solely on genetics). He also argued that
intelligence was malleable rather than fixed and IQ testing could
only be used on children with comparable backgrounds.
Along with collaborator Théodore Simon, Binet published
revisions of his intelligence scale in 1908 and 1911, the last
appearing just before his death.
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Lewis M. Terman (1877-1956)
school principal; college professor at Stanford
Terman admired Binet’s work. During World War I, Terman served in the
United States army conducting psychological tests. He and his students
developed the Alpha and Beta tests which were used to allocate
soldiers into the most appropriate areas of military service.
Terman also adopted William Stern's suggestions to multiply the mental
age / chronological age ratio times 100 (to get rid of the decimal) and
call the score be called an intelligence quotient or IQ. Today we
usually refer to this approach to intelligence as the ratio IQ.
In keeping with his army experiences, when Terman moved to testing
classroom children, he proposed using his “Stanford-Binet IQ Test” to
classify children and put them on the appropriate job-track. Terman
believed IQ was inherited and was the strongest predictor of one's
ultimate success in life. By the way, Terman “claimed” that he himself
had an IQ of 180 . . .
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Terman the Researcher
 Terman administered IQ tests, written in English, to Spanish-speakers
and non-schooled African-Americans. From his research he
concluded:
“High-grade or border-line deficiency . . . is very, very common
among Spanish-Indian and Mexican families of the Southwest and
also among negroes. Their dullness seems to be racial, or at least
inherent in the family stocks from which they come . . . . Children of
this group should be segregated into separate classes . . . . They
cannot master abstractions but they can often be made into
efficient workers . . . from a eugenic point of view they constitute a
grave problem because of their unusually prolific breeding.”
(The Measurement of Intelligence, 1916, p. 91-92).
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Part of the stated goals of the
Stanford-Binet IQ Test
Use of the Stanford-Binet scale in American
schools would (according to Chapter I of the
test manual itself) “allow for the scientific
diagnosis and classification of children to be
placed in special classes; bring tens of
thousands of high-grade defectives under
the surveillance and protection of society;
reduce delinquency; help the schools
respond to children of superior intelligence;
assist in assigning children to school
grades; and help determine vocational
fitness . . . .” (White, 2000)
NEXT A table related to the deviation IQ is on the
next slide. What do you notice?
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DEVIATION IQ REFERENCE CHART
Wechsler, D. (1944). The Measurement of Adult Intelligence. Baltimore: The Williams & Wilkins Company.
Reber, A.S. (1995). The Penguin Dictionary of Psychology, 2nd ed. Toronto: Penguin Books.
I.Q. Basics – I.Q. Comparison Site
Deviation IQ Reference Chart
% Of Pop. Under Level
Point Value (15SD)
Idiot
~0.0000001%
<10
Profound Moron
~0.000001%
<16
Exceptional Moron
~0.00001%
<22
Moron
~0.0001%
<29
Extremely Retarded
~0.001%
<36
Highly Retarded
~0.01%
<44
Retarded
~0.1%
<54
Significantly Below Average ~1%
<65
Below Average
~10%
<81
Average
~50%
~100
Above Average
~90%
>119
Significantly Above Average ~99%
>135
Gifted
~99.9%
>146
Highly Gifted
~99.99%
>156
Extremely Gifted
~99.999%
>164
Genius
~99.9999%
>171
Exceptional Genius
~99.99999%
>178
Profound Genius
~99.999999%
>184
Savant
~99.9999999%
>190
Intelligence Level
Point Value (16SD)
<4
<10
<17
<24
<32
<40
<50
<63
<79
~100
>121
>137
>150
>160
>168
>176
>183
>190
>196
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Got Vygotsky?
self-taught Russian psychologist (1896-1934)
Lev Vygotsky graduated with a law degree at Moscow
University. After graduation, he taught literature in
secondary school and psychology at a teacher’s college.
While Vygotsky had no formal training in psychology, ideas
related to developmental psychology fascinated him.
Vygotsky’s thoughts were influenced by Marxist theorists.
Marxists believe that one can only understand individuals in
the context of their social-historical environment. Similarly,
mental abilities and processes were viewed in terms of the
historical sequence of events that produced them.
Upon his death from tuberculosis, his ideas were
repudiated by the Soviet government. They banned his
work because he did some research with intelligence tests
(intelligence tests were condemned by the Communist
Party). Vygotsky was actually criticizing the tests when he
was using them in his research, but this point was lost on
the government officials. When the Cold War ended,
Vygotsky's works were opened to the West.
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Vygotsky and IQ
IQ is culturally inherited . . . not genetically inherited . . .
Rather than seeing intelligence as much the same across cultures, Vygotsky saw
intellectual abilities as being much more specific to the culture (think “family,
community, nation”) in which the child was reared (Vasta,R., Haith, M.M.,
Miller,S.A., 1995). Culture makes two sorts of contributions to the child’s intellectual
development. First, children acquire much of their thinking (e.g., knowledge) from it.
Second, children acquire the processes or means of their thinking (e.g., tools of
intellectual adaptation) from the surrounding culture. Therefore, culture provides the
child with the means to decide both “what” to think and “how” to think.
Vygotsky elaborates this “culture as intelligence” idea as follows: “Every function in
the child’s cultural development appears twice: first, between people (interpsychological) and then inside the child (intra-psychological). All the higher
functions originate as actual relationships between individuals.” (Vygotsky, 1978)
One might conclude, the “richer” the personal interactions, then the “richer” the mind
of the person. We will come back to this idea later, for now let us look at more
examples of standard scores.
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More Standard Scores of Interest . . . .



T-scores, SATs, GREs
NCEs (Normal Curve Equivalent)
 Recall that the percentile rank scale is not an equal-interval
scale; NCEs solve this problem by converting percentile ranks
to an equal-interval scale. NCEs range from 1 to 99 with a
mean of 50. The major advantage of NCEs over percentile
ranks is that NCEs can be averaged.
 Used almost exclusively by federal reporting requirement for
achievement testing.
Stanines
 Widely used in schools so we will look at them in more detail in
the next slide.
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More on Stanines
contraction of “standard nine” . . .

Stanines divide the normal distribution into 9 units each of which cover the same
length along the base of the normal curve (except the units which cover the two
tails). Stanines have a M = 5 and SD = 2 and range 1 (lowest) – 9 (highest).

Stanines can be used to convert any test score into a single digit number. This
was valuable when paper punch cards were the standard method of storing this
kind of information. However, because all stanines are integers, two scores in a
single stanine are sometimes further apart than two scores in adjacent stanines.
This reduces their value.

Stanine scores are useful in comparing a student's performance across different
content areas. For example, a 6 in Mathematics and an 8 in Reading generally
indicate a meaningful difference in a student's learning for the two respective
content areas. While stanine scores are good at signifying broad differences in
performance, they should be used cautiously when making any finer distinctions
about performance.
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Stanines Defined Descriptively:
NOT RECOMMENDED
Stanines facilitate using words rather than numbers in presenting
statistical data. Most people like words, but this practice is arbitrary
and less accurate: “Bill tested considerably below average."
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Pros & Cons of Standard Scores
 Strengths
Wide applicability
 Nice statistical properties
 Teachers often build their narrative reports on
these standard scores using the “accepted
descriptive words” rather than the numbers.
 Weaknesses
 May be hard to explain to laypersons
 Need to know M and SD of original test
 Teachers often build their narrative reports on
these standard scores using the “accepted
descriptive words” rather than the numbers.

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Developmental Norms
Another area of real and potential misuse . . .
 Main examples:
Grade equivalents
 4.5 Fourth Grade, Fifth Month
 Mental ages (age equivalents)
 5.10 Fifth Year, Tenth month
 Others: stage theories (Piaget), physical measures (height in
relation to age)
 Strengths
 “Natural” interpretation (is this really a strength?)
 Looks at multi-level growth parents / teachers want
 Weaknesses
 Limited to growth functions
 Commonly misused (see next slide)

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According to:
Margaret J. Kay, Ed.D. Psychologist
 The practice of using grade equivalency scores to identify learning
disabled children in educational reports and IEP’s is wide spread and
misleading.
 The normative data for most tests are usually collected at one point
every year. How, then, are grade equivalents obtained for every
month? They are extrapolated at the upper and lower ends of the
growth curve. This estimation produces scores that are systematically
too low in the Fall and too high in the Spring. Problems associated with
this practice are:


A high probability of over-identifying learning disabled children exists
if screening is conducted in the Fall.
A high probability of under-identifying learning disabled children
occurs if screening is conducted in the Spring.
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Norm Groups
To whom are my students being compared . . .
 Look for detailed description in test manual to
ascertain the norming group. Might one or a
combination of the following:






Users (all previous test takers, e.g. ACT)
Subgroup (ACT scores achieved by men)
Local (students in the district)
Institutional (State)
National
International
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Example: National vs. Local Norms
Sally’s score (the x below) is at the 55th percentile when compared to National
tests takers, but her score is at the 45th percentile compared to Local test takers
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Usefulness of Standardization Group
 To what extent do the norms provide a meaningful framework?
Two issues:
 Stability
 Usually not a problem because the norms are developed
based on so many cases.
 Representativeness
 Compare data on norm group with data on the target
group
 Typical variables for comparison:
 Age, gender, ability, education, geographic region,
size city, racial/ethnic group, socioeconomic status
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Criterion-referenced
 “Criterion-referenced” refers to the nature of the
interpretation, not the nature of the test.
 Requires well-defined content domain.
 Often more complicated than it first sounds.
 Often uses “rubrics” – guides for defining
performance levels.
 Ohio likes to use the term Performance Standards
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Performance Standards
 Outgrowths of standards-based education
 Common terms: advanced, proficient, basic
 Each division requires a cut-score
 Cut-scores determined



By groups of people
Using one of several different methods
Determined basically by judgments
 Ohio uses the term benchmark

the specific component of the knowledge or skill identified by
an academic content, performance or operational standard.
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Self-Referencing on Repeated Measures
. . . some call this dynamic assessment . . .
. . . has elements of both norm & criterion
 Dynamic assessment is an interactive approach that embeds
intervention within the assessment procedure. Dynamic assessment is
a product of research by developmental psychologist Lev Vygotsky.
 Main features:
 Improved task performance becomes the criterion for the
student; Her/His own past performance constitutes the norm
 Simple counts, brief tasks, repeated frequently, results graphed
 Has many potential uses:
Documenting Special Education student progress
Assessing Basic Skill progress
Monitoring School Attitude changes
 Also known as CBA "The term curriculum-based assessment means
simply measurement that uses direct observation and recording of a
student's performance in the local curriculum as a basis for gathering
information to make instructional decisions" (Deno, 1987).
 And also known as CBM (see next slide)
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Curriculum-Based Measurement
Student Progress Monitoring . . .
 Curriculum-Based Measurement (CBM) is a method teachers use to
find out how students are progressing in basic academic areas while
there is still time to intervene.
 CBM can be helpful to teachers and students because it provides
current, week-by-week information on academic progress. The teacher
using CBM finds out how well a child is progressing in learning the
content for the academic year in time to modify his/her instructional
strategies. If a student’s performance is not meeting expectations, the
teacher then changes the way of teaching to try to find the type and
amount of instruction this particular student needs to make sufficient
progress toward meeting the academic goals. This assessment
approach allows the student to see immediate progress and may be
more motivational than “punitive” tests and quizzes. This powerful
assessment approach can also be shared with parents to document
their child’s progress.
 See next slide for an example progress chart.
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Kim's Progress in Words Read per Minute
40
35
25
20
15
10
28
25
22
19
16
13
10
7
4
5
0
1
Words/Min
30
Day
Intervention
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Closing Thoughts on . . .
Dynamic Assessment & Vygotsky
If we accept Vygotsky’s view of intellectual development, we might
conclude that it is, in fact, learning that leads to intellectual
development (as opposed to the other way around).
In Vygotsky’s view, the standard IQ test only indicates what a child can
achieve on his/her own. He calls this the ‘level of actual development.’
While such a measure is undoubtedly important, it is also incomplete.
Given appropriate help from an adult, children can increase their thinking
ability. What the child can achieve with this outside help is referred to as
the ‘level of potential development.’ (Vasta, R., Haith, M.M., Miller, S.A.,
1995)
As educators, are we not interested in increasing this potential rather than
labelling and sorting children based on IQ scores?
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Practical Advice
1.
Understand relations among types of norms.
2.
Be cautious about IQ scores & grade equivalents.
3.
Know the nature of the norm group(s).
4.
Know what process was used to develop the
performance standards (e.g., benchmarks) in a
criterion-referenced test.
5.
Consider using dynamic assessment as part of
your assessment repertoire.
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