A norm-referenced test (NRT) is a type of
test
Test(s), testing, or TEST may refer to:
* Test (assessment), an educational assessment intended to measure the respondents' knowledge or other abilities
Arts and entertainment
* ''Test'' (2013 film), an American film
* ''Test'' (2014 film), ...
,
assessment, or
evaluation
Evaluation is a
systematic determination and assessment of a subject's merit, worth and significance, using criteria governed by a set of standards. It can assist an organization, program, design, project or any other intervention or initiative ...
which yields an estimate of the position of the tested individual in a predefined population, with respect to the trait being measured. Assigning scores on such tests may be described as relative grading, marking on a curve (
BrE
British English (BrE, en-GB, or BE) is, according to Oxford Dictionaries, "English as used in Great Britain, as distinct from that used elsewhere". More narrowly, it can refer specifically to the English language in England, or, more broadly, ...
) or grading on a curve (
AmE #REDIRECT AME
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,
CanE
Cane or caning may refer to:
*Walking stick or walking cane, a device used primarily to aid walking
*Assistive cane, a walking stick used as a mobility aid for better balance
*White cane, a mobility or safety device used by many people who are b ...
) (also referred to as curved grading, bell curving, or using grading curves). It is a method of assigning grades to the students in a class in such a way as to obtain or approach a pre-specified
distribution Distribution may refer to:
Mathematics
*Distribution (mathematics), generalized functions used to formulate solutions of partial differential equations
* Probability distribution, the probability of a particular value or value range of a vari ...
of these grades having a specific mean and derivation properties, such as a
normal distribution
In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is
:
f(x) = \frac e^
The parameter \mu ...
(also called
Gaussian
Carl Friedrich Gauss (1777–1855) is the eponym of all of the topics listed below.
There are over 100 topics all named after this German mathematician and scientist, all in the fields of mathematics, physics, and astronomy. The English eponymo ...
distribution).
The term "curve" refers to the
bell curve, the graphical representation of the probability density of the normal distribution, but this method can be used to achieve any desired distribution of the grades – for example, a
uniform distribution. The estimate is derived from the analysis of test scores and possibly other relevant data from a
sample
Sample or samples may refer to:
Base meaning
* Sample (statistics), a subset of a population – complete data set
* Sample (signal), a digital discrete sample of a continuous analog signal
* Sample (material), a specimen or small quantity of s ...
drawn from the population. That is, this type of test identifies whether the test taker performed better or worse than other test takers, not whether the test taker knows either more or less material than is necessary for a given purpose. The term ''normative assessment'' is used when the reference population are the peers of the test taker.
Norm-referenced assessment can be contrasted with
criterion-referenced assessment
A criterion-referenced test is a style of test which uses test scores to generate a statement about the behavior that can be expected of a person with that score. Most tests and quizzes that are written by school teachers can be considered criteri ...
and
ipsative assessment In psychology, ipsative questionnaires (; from Latin: ''ipse'', 'of the self') are those where the sum of scale scores from each respondent adds to a constant value. Sometimes called a forced-choice scale, this measure contrasts Likert-type scales ...
. In a criterion-referenced assessment, the score shows whether or not test takers performed well or poorly on a given task, not how that compares to other test takers; in an ipsative system, test takers are compared to previous performance. Each method can be used to grade the same test paper.
[Cronbach, L. J. (1970). ''Essentials of psychological testing'' (3rd ed.). New York: Harper & Row.]
Robert Glaser Robert Glaser (January 18, 1921 – February 4, 2012) was an American educational psychologist, who has made significant contributions to theories of learning and instruction. The key areas of his research focused on the nature of aptitudes and in ...
originally coined the terms ''norm-referenced test'' and ''criterion-referenced test''.
Common uses
Many college entrance exams and nationally used school tests use norm-referenced tests. The
SAT
The SAT ( ) is a standardized test widely used for college admissions in the United States. Since its debut in 1926, its name and scoring have changed several times; originally called the Scholastic Aptitude Test, it was later called the Schol ...
,
Graduate Record Examination
The Graduate Record Examinations (GRE) is a standardized test that is an admissions requirement for many graduate schools in the United States and Canada and a few other countries. The GRE is owned and administered by Educational Testing Serv ...
(GRE), and
Wechsler Intelligence Scale for Children
The Wechsler Intelligence Scale for Children (WISC) is an individually administered intelligence test for children between the ages of 6 and 16. The Fifth Edition (WISC-V; Wechsler, 2014) is the most recent version.
The WISC-V takes 45 to 65 minut ...
(WISC) compare individual student performance to the performance of a normative sample. Test takers cannot "fail" a norm-referenced test, as each test taker receives a score that compares the individual to others that have taken the test, usually given by a percentile. This is useful when there is a wide range of acceptable scores, and the goal is to find out who performs better.
IQ test
An intelligence quotient (IQ) is a total score derived from a set of standardized tests or subtests designed to assess human intelligence. The abbreviation "IQ" was coined by the psychologist William Stern (psychologist), William Stern for th ...
s are norm-referenced tests, because their goal is to rank test takers' intelligence. The median IQ is set to 100, and all test takers are ranked up or down in comparison to that level.
Other types
As alternatives to normative testing, tests can be ipsative assessments or criterion-referenced assessments.
Ipsative
In an
ipsative In psychology, ipsative questionnaires (; from Latin: ''ipse'', 'of the self') are those where the sum of scale scores from each respondent adds to a constant value. Sometimes called a forced-choice scale, this measure contrasts Likert-type scales ...
assessment, the individuals' performance is compared only to their previous performances.
[Assessment](_blank)
/ref> For example, a person on a weight-loss diet is judged by how his current weight compares to his own previous weight, rather than how his weight compares to an ideal or how it compares to another person.
Criterion-referenced
A test is criterion-referenced when the performance is judged according to the expected or desired behavior. Tests that judge the test taker based on a set standard (e.g., everyone should be able to run one kilometre in less than five minutes) are criterion-referenced tests. The goal of a criterion-referenced test is to find out whether the individual can run as fast as the test giver wants, not to find out whether the individual is faster or slower than the other runners. Standards-based education reform focuses on criterion-referenced testing. Most everyday tests and quizzes taken in school, as well as most state achievement tests and high school graduation examination
An exit examination is a test that students must pass to receive a diploma and graduate from school. Such examinations have been used in a variety of countries; this article focuses on their use within the United States. These are usually criteri ...
s, are criterion-referenced. In this model, it is possible for all test takers to pass or for all test takers to fail.
Methods
One method of grading on a curve uses three steps:
# Numeric scores (or possibly scores on a sufficiently fine-grained ordinal scale
Ordinal data is a categorical, statistical data type where the variables have natural, ordered categories and the distances between the categories are not known. These data exist on an ordinal scale, one of four levels of measurement described b ...
) are assigned to the students. The absolute values are less relevant, provided that the order of the scores corresponds to the relative performance of each student within the course.
# These scores are converted to percentiles
In statistics, a ''k''-th percentile (percentile score or centile) is a score ''below which'' a given percentage ''k'' of scores in its frequency distribution falls (exclusive definition) or a score ''at or below which'' a given percentage falls ...
(or some other system of quantiles).
# The percentile values are transformed to grades according to a division of the percentile scale into intervals, where the interval width of each grade indicates the desired relative frequency for that grade.
For example, if there are five grades in a particular university course, A, B, C, D, and F, where A is reserved for the top 20 % of students, B for the next 30 %, C for the next 30–40 %, and D or F for the remaining 10–20 %, then scores in the percentile interval from 0 % to 10–20 % will receive a grade of D or F, scores from 11–21 % to 50 % will receive a grade of C, scores from 51 % to 80 % receive a grade of B, and scores from 81 % to 100 % will achieve a grade of A.
Consistent with the example illustrated above, a grading curve allows academic institutions to ensure the distribution of students across certain grade point average
Grading in education is the process of applying standardized measurements for varying levels of achievements in a course. Grades can be assigned as letters (usually A through F), as a range (for example, 1 to 6), as a percentage, or as a numbe ...
(GPA) thresholds. As many professors establish the curve to target a course average of a C, the corresponding grade point average equivalent would be a 2.0 on a standard 4.0 scale employed at most North American universities. Similarly, a grade point average of 3.0 on a 4.0 scale would indicate that the student is within the top 20 % of the class. Grading curves serve to attach additional significance to these figures, and the specific distribution employed may vary between academic institutions.
Advantages and limitations
The primary advantage of norm-reference tests is that they can provide information on how an individual's performance on the test compares to others in the reference group.
A serious limitation of norm-reference tests is that the reference group may not represent the current population of interest. As noted by the Oregon Research Institute
The Oregon Research Institute is an American psychology research institute in Eugene, Oregon. It manages the International Personality Item Pool The International Personality Item Pool (IPIP) is a public domain collection of items for use in pers ...
's International Personality Item Pool The International Personality Item Pool (IPIP) is a public domain collection of items for use in personality tests. It is managed by the Oregon Research Institute.
The pool contains 3,329 items. These items make up more than 250 inventories that m ...
website, "One should be very wary of using canned 'norms' because it isn't obvious that one could ever find a population of which one's present sample is a representative subset. Most 'norms' are misleading, and therefore they should not be used. Far more defensible are local norms, which one develops oneself. For example, if one wants to give feedback to members of a class of students, one should relate the score of each individual to the means and standard deviations derived from the class itself. To maximize informativeness, one can provide the students with the frequency distribution for each scale, based on these local norms, and the individuals can then find (and circle) their own scores on these relevant distributions."
Norm-referencing does not ensure that a test is valid (i.e. that it measures the construct it is intended to measure).
Another disadvantage of norm-referenced tests is that they cannot measure progress of the population as a whole, only where individuals fall within the whole. Rather, one must measure against a fixed goal, for instance, to measure the success of an educational reform program that seeks to raise the achievement of all students.
With a norm-referenced test, grade level was traditionally set at the level set by the middle 50 percent of scores. By contrast, the National Children's Reading Foundation believes that it is essential to assure that virtually all children read at or above grade level by third grade, a goal which cannot be achieved with a norm-referenced definition of grade level.
Norms do not automatically imply a standard. A norm-referenced test does not seek to enforce any expectation of what test takers should know or be able to do. It measures the test takers' current level by comparing the test takers to their peers. A rank-based system produces only data that tell which students perform at an average level, which students do better, and which students do worse. It does not identify which test takers are able to correctly perform the tasks at a level that would be acceptable for employment or further education.
The ultimate objective of grading curves is to minimize or eliminate the influence of variation between different instructors of the same course, ensuring that the students in any given class are assessed relative to their peers. This also circumvents problems associated with utilizing multiple versions of a particular examination, a method often employed where test administration dates vary between class sections. Regardless of any difference in the level of difficulty, real or perceived, the grading curve ensures a balanced distribution of academic results.
However, curved grading can increase competitiveness between students and affect their sense of faculty fairness in a class. Students are generally most upset in the case that the curve lowered their grade compared to what they would have received if a curve was not used. To ensure that this does not happen, teachers usually put forth effort to ensure that the test itself is hard enough when they intend to use a grading curve, such that they would expect the average student to get a lower raw score than the score intended to be used at the average in the curve, thus ensuring that all students benefit from the curve. Thus, curved grades cannot be blindly used and must be carefully considered and pondered compared to alternatives such as criterion-referenced grading. Furthermore, constant misuse of curved grading can adjust grades on poorly designed tests, whereas assessments should be designed to accurately reflect the learning objectives set by the instructor.
See also
* Concept inventory
A concept inventory is a criterion-referenced test designed to help determine whether a student has an accurate working knowledge of a specific set of concepts. Historically, concept inventories have been in the form of multiple-choice tests in ord ...
* Educational assessment
Educational assessment or educational evaluation is the systematic process of documenting and using empirical data on the knowledge, skill, attitudes, aptitude and beliefs to refine programs and improve student learning. Assessment data can be o ...
* Equating
Test equating traditionally refers to the statistical process of determining comparable scores on different forms of an exam.Kolen, M.J., & Brennan, R.L. (1995). Test Equating. New York: Spring. It can be accomplished using either classical test ...
* Grading in education
Grading in education is the process of applying standardized measurements for varying levels of achievements in a course. Grades can be assigned as letters (usually A through F), as a range (for example, 1 to 6), as a percentage, or as a numbe ...
* List of law school GPA curves
Many, or perhaps most, law schools in the United States grade on a norm-referenced grading curve. The process generally works within each class, where the instructor grades each exam, and then ranks the exams against each other, adding to and sub ...
* Macabre constant
* Psychometrics
Psychometrics is a field of study within psychology concerned with the theory and technique of measurement. Psychometrics generally refers to specialized fields within psychology and education devoted to testing, measurement, assessment, and ...
* Standardized test
A standardized test is a test that is administered and scored in a consistent, or "standard", manner. Standardized tests are designed in such a way that the questions and interpretations are consistent and are administered and scored in a predete ...
—all individuals are given the same test under the same conditions; used for both norm-referenced and criterion-referenced tests
References
{{reflist
External links
A Comprehensive Look at Types of Curves
* ttp://support.microsoft.com/kb/213930 How to Create a Bell Curve in Excel
Psychological testing
Standardized tests
Educational psychology
Educational evaluation methods