This presentation covers the intricacies of the Item Response Theory. I made this presentation to explain the concepts of IRT to my lab research group at the University of Minnesota. I have taken the contents from various sources so apologies for the poor design of the presentation.
This is the first of a series of powerpoints presented at a CAT/IRT workshop at the University of Brasilia in 2012. It provides an introduction to item response theory (IRT), tying it to classical test theory and describing some of the major IRT models. Learn more at www.assess.com.
This presentation covers the intricacies of the Item Response Theory. I made this presentation to explain the concepts of IRT to my lab research group at the University of Minnesota. I have taken the contents from various sources so apologies for the poor design of the presentation.
This is the first of a series of powerpoints presented at a CAT/IRT workshop at the University of Brasilia in 2012. It provides an introduction to item response theory (IRT), tying it to classical test theory and describing some of the major IRT models. Learn more at www.assess.com.
Topic: Quantitative Item Analysis
Student Name: Hussain Shah
Class: M.Ed
Project Name: “Young Teachers' Professional Development (TPD)"
"Project Founder: Prof. Dr. Amjad Ali Arain
Faculty of Education, University of Sindh, Pakistan
Topic: Subjective and Objective Test
Student Name: Jeejal Samo
Class: B.Ed. Hons Elementary Part (II)
Project Name: “Young Teachers' Professional Development (TPD)"
"Project Founder: Prof. Dr. Amjad Ali Arain
Faculty of Education, University of Sindh, Pakistan
Topic: Validity
Student Name: Parkash Mal
Class: B.Ed. (Hons) Elementary
Project Name: “Young Teachers' Professional Development (TPD)"
"Project Founder: Prof. Dr. Amjad Ali Arain
Faculty of Education, University of Sindh, Pakistan
Using Item Response Theory to Improve AssessmentNathan Thompson
This is the second of a series of powerpoints presented at a CAT/IRT workshop at the University of Brasilia in 2012. It provides a discussion on how IRT is applied to developing better assessments, including item and test information functions, standard error of measurement, and use of Xcalibre. Learn more at www.assess.com.
This is the third of a series of powerpoints presented at a CAT/IRT workshop at the University of Brasilia in 2012. It provides an introduction to item response theory (IRT), discussing advanced topics like linking & equating, scaling, differential item functioning, polytomous models, and dimensionality. Learn more at www.assess.com.
Topic: Quantitative Item Analysis
Student Name: Hussain Shah
Class: M.Ed
Project Name: “Young Teachers' Professional Development (TPD)"
"Project Founder: Prof. Dr. Amjad Ali Arain
Faculty of Education, University of Sindh, Pakistan
Topic: Subjective and Objective Test
Student Name: Jeejal Samo
Class: B.Ed. Hons Elementary Part (II)
Project Name: “Young Teachers' Professional Development (TPD)"
"Project Founder: Prof. Dr. Amjad Ali Arain
Faculty of Education, University of Sindh, Pakistan
Topic: Validity
Student Name: Parkash Mal
Class: B.Ed. (Hons) Elementary
Project Name: “Young Teachers' Professional Development (TPD)"
"Project Founder: Prof. Dr. Amjad Ali Arain
Faculty of Education, University of Sindh, Pakistan
Using Item Response Theory to Improve AssessmentNathan Thompson
This is the second of a series of powerpoints presented at a CAT/IRT workshop at the University of Brasilia in 2012. It provides a discussion on how IRT is applied to developing better assessments, including item and test information functions, standard error of measurement, and use of Xcalibre. Learn more at www.assess.com.
This is the third of a series of powerpoints presented at a CAT/IRT workshop at the University of Brasilia in 2012. It provides an introduction to item response theory (IRT), discussing advanced topics like linking & equating, scaling, differential item functioning, polytomous models, and dimensionality. Learn more at www.assess.com.
Here is a simplified version of Item Analysis for Educational Assessments. Covered here are terminologies, formulas, and processes in conducting Item Discrimination and Difficulty. Thank you. Namaste!
THESIS - WIKANG FILIPINO, SA MAKABAGONG PANAHONMi L
I uploaded this thesis for the reference of the future researchers.
Entitled Wikang Filipino, sa Makabagong Panahon.
We tackled about the progress of Filipino language as time pass by. And the factors that affect it.
Enjoy and God bless! :)
Introduction to unidimensional item response modelSumit Das
Item response theory has become an important technique in the field of psychology and education. This slides gives a brief introduction to unidimensional item response models.
Top 100+ Google Data Science Interview Questions.pdfDatacademy.ai
Data science interviews can be particularly difficult due to the many proficiencies that you'll have to demonstrate (technical skills, problem solving, communication) and the generally high bar to entry for the industry.we Provide Top 100+ Google Data Science Interview Questions : All You Need to know to Crack it
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An Adaptive Evaluation System to Test Student Caliber using Item Response TheoryEditor IJMTER
Computational creativity research has produced many computational systems that are
described as creative [1]. A comprehensive literature survey reveals that although such systems are
labelled as creative, there is a distinct lack of evaluation of the Creativity of creative systems [1].
Nowadays, a number of online testing websites exist but the drawback of these tests is that every
student who gives a particular test will always be given the same set of questions irrespective of their
caliber. Thus, a student with a very high Intelligence Quotient (IQ) may be forced to answer basic
level questions and in the same way weaker students may be asked very challenging questions which
they cannot response. This method of testing results into a wastage of time for the high IQ students
and can be quite frustrating for the weaker students. This would never benefit a teacher to understand
a particular student’s caliber for the subject under Consideration. Each learner has different learning
status and therefore different test items should be used in their evaluation. This paper proposes an
Adaptive Evaluation System developed based on an Item Response Theory and would be created for
mobile end user keeping in mind the flexibility of students to attempt the test from anywhere. This
application would not only dynamically customize questions for students based on the previous
question he/she has answered but also by adjusting the degree of difficulty for test questions
depending on student ability, a teacher can acquire a valid & reliable measurement of student’s
competency.
Answer questions Minimum 100 words each and reference (questions.docxamrit47
Answer questions Minimum 100 words each and reference (questions #1-2) KEEP questions WITH ANSWER
1. A key point to get out of this topic is the idea that these errors are theoretical. You won't be sure as to whether one occurred or not. Why are they theoretical in nature? Hint: think about a study and knowing the "truth"
2. Pick a study of interest and identify the null and alternative hypothesis. How does this fit in with regards to the topic of a type I and type II error? Always keep this in mind when you are trying to identify what a type I and type II error are.
A minimum of 75 words each question and References (IF NEEDED)(Response #1 – 7) KEEP RESPONSE WITH ANSWER
Make sure the Responses includes the Following: (a) an understanding of the weekly content as supported by a scholarly resource, (b) the provision of a probing question. (c) stay on topic
1) According to the reading, we set the alpha which is the largest probability for type I error. To increase the power of a hypothesis researchers can use larger samples which provides more information and raise the significance level which increases the probability that the hypothesis will be rejected.
2) A Type 1 error occurs when individuals involved in research make the decision to reject the belief of truth when in actuality the hypothesis is true. Type 1 errors are errors in research when the researcher makes the wrong decision to reject a true null hypothesis. Type II errors are considered less of a problem than Type 1 errors, but can prove to be detrimental in the field of medicine. This type of error occurs when researchers decide to keep a false null hypothesis, when in fact the hypothesis is true. The method to avoid making Type 1 decisions is to test the null hypothesis at the highest level (Alpha Level). This will lessen the possibilities of making this type of error (Privitera, 2018).
3) According to Privitera (2018) a type 1 error is the probability of rejecting a null hypotheses that is actually true, researchers purposely make this error. A null hypotheses is a statement about a population parameter that is assumed to be true, this hypotheses is a starting point (Privitera, 2018). The type 2 error or beta error is the probability of retaining a null hypotheses that is actually false (Privitera, 2018). The type 1 error is committed when a researcher decides to reject previous notions of truth that are in fact true (Privitera, 2018). The best way to avoid these types of errors is to be open minded and not reject notions if there is fact to back the notions up. In my opinion a type 1 error is something committed with bias by the researcher. I say this because as a researcher it is their job to find all facts or at least most all facts and apply them to their study or research, especially if they commit a type one error knowingly. If a researcher does this error then they are not following through with basic research guidelines.
4) A one-tailed test is used in a hypothesi.
A case study that explains how quality of data is much better in case of online surveys, with guidelines on how sampling and non-sampling errors are eliminated.
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
Acetabularia Information For Class 9 .docxvaibhavrinwa19
Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
Honest Reviews of Tim Han LMA Course Program.pptxtimhan337
Personal development courses are widely available today, with each one promising life-changing outcomes. Tim Han’s Life Mastery Achievers (LMA) Course has drawn a lot of interest. In addition to offering my frank assessment of Success Insider’s LMA Course, this piece examines the course’s effects via a variety of Tim Han LMA course reviews and Success Insider comments.
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
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The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
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2. Different Measurement Theories
ClassicalTestTheory (CTT) or
ClassicalTrue Score (CTS)
GeneralizibilityTheory (G-Theory)
Item ResponseTheory (IRT)
3. Problems with CTT
True score and error score have
theoretical unobservable constructs
Sample dependence (test & testee)
Unified error variance
No account of interaction of error
variances
Single SEM across ability levels
4. Generalizibiliy Theory
(An Extension of CTT)
G-Theory advantages: Sources and
interaction of variances accounted
for
G-Theory problems: Sample
dependent and single SEM
5. IRT or Latent Trait Theory
Item response theory (IRT) is an approach
used to estimate how much of a latent
trait an individual possesses. The theory
aims to link individuals’ observed
performances to a location on an
underlying continuum of the unobservable
trait. Because the trait is unobservable, IRT
is also referred to as latent trait theory
IRT can be used to link observable performances
to various types of underlying traits.
6. Latent variables or construct
or underlying trait
second language listening ability
English reading ability
test anxiety
7. Four Advantages of IRT:
1. ability estimates are drawn from the population
of interest, they are group independent.This means
that ability estimates are not dependent on the
particular group of test takers that complete the
assessment.
2. it is used to aid in designing instruments that
target specific ability levels based on the TIF. Using
IRT item difficulty parameters makes it possible to
design items with difficulty levels near the desired
cut-score, which would increase the accuracy of
decisions at this crucial ability location.
8. Advantages of IRT:
3. IRT provides information about various
aspects of the assessment process, including
items, raters, and test takers, which can be
useful for test development. For instance,
raters can be identified that have inconsistent
rating patterns or are too lenient. These raters
can then be provided with specific feedback on
how to improve their rating behavior.
4. test takers do not need to take the same
items to be meaningfully compared on the
construct of interest (fairness)
9. lack of widespread use is likely due to
practical and technical disadvantages of
IRT when compared to CTT.
1. the necessary assumptions underlying IRT
may not hold with many language
assessment data sets.
2. lack of agreement on an appropriate
algorithm to represent IRT-based test scores
(to users) leads to distrust of IRTtechniques.
3. understanding of the somewhat technical
math which underlies IRT models is
intimidating to many.
10. lack of widespread use is likely due to
practical and technical disadvantages of IRT
when compared to CTT.
4. the relatively large samples sizes required for
parameter estimation are not available for many
assessment projects.
5. although IRT software packages continue to
become more user friendly, most have steep
learning curves which can discourage fledgling
test developers and researchers.
11. History:
ancient Babylon, to the Greek philosophers, to the
adventurers of the Renaissance”
Current IRT practices can betraced back to two
separate lines of development:
1) A method of scaling psychological and educational
tests, “intimations” of IRT for one line of
development.
Fredrick Lord (1952): provided the foundations of IRT
as a measurement theory by outlining assumptions
and providing detailed models.
12. History:
Lord and Novick’s (1968) monumental textbook,
Statistical theories of mental test scores, outlined
the principles of IRT
2) George Rasch (1960), a Danish mathematician with
focus on the use of probability to separate test taker
ability and item difficulty.
Wright and his graduate students are credited with
many of the developments of the family of Rasch
models.
13. The 2 development lines:
They have led to quite similar practices
one major difference:
Rasch models are prescriptive. If data do not fit
the model, the data must be edited or discarded
.The other approach (derived from Lord’s work)
promotes a descriptive philosophy. Under this
view, a model is built that best describes the
characteristics of the data. If the model does not fit
the data, the model is adapted until it can account
for the data.
14. History:
The first article in the journal LanguageTesting by Grant
Henning (1984)
“ advantages of latent trait measurement in language
testing,”
About a decade after IRT appeared in the journal
LanguageTesting, an influential book on the subject
was written byTim McNamara (1996), Measuring
Second Language Performance.
an introduction to many-facet Rasch model and FACETS
software used for estimating ability on performance-
based assessments.
studies which used MFRM began to appear in the
language testing literature soon after McNamara
publication
15. Assumptions underlying IRT
models
1. Local independence :
This means that each item should be assessed
independently of all other items.The assumption of local
independence could be
violated on a reading test when the question or answer
options for one item provide information that may be
helpful for correctly answering another item about the
same passage.
.
16. Assumptions underlying IRT
models
2. Unidimensionality:
In a unidimensional data set, a single ability
can account for the differences in scores. For
example, a second language listening test
would need to be constructed so that only
listening ability underlies test takers’
responses to the test items. A violation of this
assumption would be the inclusion of an item
that measured both the targeted ability of
listening as well as reading ability not
required for listening comprehension
17. Assumptions underlying IRT
models
3. it is , sometimes referred to as certainty of
response
test takers make an effort to demonstrate the level
of ability that they possess when they complete
the assessment (Osterlind, 2010). Test takers must
try to answer all questions correctly because the
probability of a correct response in IRT is directly
related to their ability. This assumption is often
violated when researchers recruit test takers for a
study, and there is little or no incentive for the test
takers to offer their best effort.
18. Assumptions underlying IRT
models
It is important to bear in mind that almost all
data will violate one or more of the IRT
assumptions to some extent. It is the degree
to which such violations occur that
determines how meaningful the resulting
analysis is (de Ayala, 2009).
19. How to assess assumptions:
Sample size:
In general, smaller samples provide less accurate
parameter estimates, and models with more
parameters require larger samples for accurate
estimates. A minimum of about 100 cases is
required for most testing contexts when the
simplest model, the 1PL Rasch model, is used
(McNamara, 1996). As a general rule, de Ayala
(2009) recommends that the starting point for
determining sample size should be a
few hundred.
20.
21. IRT Parameters
1. Item Parameters
Parameter is used in IRT to indicate a characteristic
about a test’s stimuli.
a) Item Characteristic Curve (ICC)
Difficulty (b)
Discrimination (a)
Guessing Factor (c)
b) Item Information Function (IIF)
2.Test Parameter
a)Test Information Function (TIF)
3. Ability Parameter (Ө)
22. A test taker with an ability of 0 logits would
have a 50% chance of correctly answering an item
with a difficulty level of 0 logits.
23. ICC
The probability of a test taker correctly
responding to an item is presented on the
vertical axis.This scale ranges from zero
probability at the bottom to absolute
probability at the top.
The horizontal axis displays the estimated
ability level of test takers in relation to item
difficulties, with least at the far left and most
at the far right.The measurement unit of the
scale is a logit, and it is set to have a center
point of 0.
24. ICC
ICCs express the relationship between the
probability of a test taker correctly
answering each item and a test taker’s
ability. As a test taker’s ability level
increases, moving from left to right along
the horizontal axis, the probability of
correctly answering each item increases,
moving from the bottom to the top of the
vertical axis.
25. ICC
the ICCs are somewhat S-shaped, meaning
the probability of a correct response changes
considerably over a small ability level range.
Test takers with abilities ranging from -3 to -1 have
less than a 0.2 probability of answering the item
correctly
test takers with abilities levels in the middle of the
scale, between roughly -1 and +1, the probability of
correctly responding to that item changes from
quite low, about 0.1 to quite high, about 0.9
26.
27. All ICC have the same level of difficulty
Different location index
Left ICC easy item
Right ICC hard item
Roughly half of the time the test takers respond
correctly, and the other half of the time, they
respond incorrectly. So these test takers have
about a 0.5 probability of answering these
items successfully. By capitalizing on these
probabilities, the test taker’s ability can be
defined by the items that are at this level of
difficulty for the test taker.
28.
29. Figure 3
All have same level of difficulty
Different level of discrimination
Upper curve: highest discrimination short
distance to the left or right will have much
different probability with dramatic change
(steep)
The middle one has moderate level of
discrimination
Lower one: very small slope and change
slightly as a result of movement to the left or
right point of 0.5
30. Some issues about ICC
When the a is less that moderate ICC is nearly
linear and flat
When the a is more than moderate, it is likely
to be steep in the middle section
A and b are independent of each other
Horizontal line in ICC : means no
discrimination and undefined difficulty
Probability of 0.5 corresponds to b in easy
items it occurs at low ability and in hard ones
it occurs at high ability level.
31. Some issues about ICC
When the item is hard most of the ICC has
the probability of correct response less than
0.5
When the item is easy most of the ICC has
the probability of correct response that is
larger than 0.5
32. Bear in mind
The figures show a range of ability is from -3
to + 3
The theoretical range of ability is from
negative infinity to positive infinity.
All ICC become asymptotic to a probaility of
zero at one tail and one at the other tail.
It is necessary to fit the curves on the
computer screen.
36. It is a vertical line along the ability scale.
It is ideal for distinguishing btw examinees
with abilities above and below 1.5
No discrimination of examinees below or
above 1.5
37. Different IRT Models
Model Item Format Features
1-Parameter Logistic
Model/
Rasch Model
Dichotomous Discrimination
power equal across
all items. Difficulty
varies across items
2-Parameter Logistic
Model
Dichotomous Discrimination and
difficulty parameters
vary across items
3-Parameter Logistic
Model
Dichotomous Also includes
pseudo-guessing
parameter
38. ICC models
A model is a mathematical equation in which
independent variables are combined to optimally
predict dependent variables
Each of these models has particular mathematical
equation and are used to estimate individuals’
underlying traits on language ability constructs.
The standard mathematical model for ICC is the
cumulative form of logistic function
It was first derived in 1844 and has been widely used in
biological sciences to model the growth of plants and
animals from birth to maturity
It was first used in ICC in the late 1950s because of its
simplicity.
39. Parameter a is multiplied by 1.70 to obtain
the corresponding logistic value
L=a (theta-b)
Discrimination parameter is proportional to
the slope of the ICC
40. The most fundamental IRT model,
the Rasch or 1-parameter (1PL)
logistic model
Relating test taker ability to the difficulty of items
makes it possible to mathematically model the
probability that a test taker will respond correctly to
an item.
43. It was first published by Danish mathematician:
Georg Rasch
Under this model, the discrimination parameter of
the two-parameter logistic model is fixed at a value
of a = 1.0 for all items;
only the difficulty parameter can take on different
values. Because of this, the Rasch model is often
referred to as the one parameter logistic model.
45. the probability of correct response includes a small
component that is due to guessing.
Neither of the two previous item characteristic curve models
took the guessing phenomenon into consideration.
Birnbaum (1968) modified the two-parameter logistic model
to include a parameter that represents the contribution of
guessing to the probability of correct response.
Unfortunately, in so doing, some of the nice mathematical
properties of the logistic function were lost.
Nevertheless the resulting model has become known as the
three-parameter logistic model, even though it technically is
no longer a logistic model.The equation for the three-
parameter model is:
48. Range of parameters:
-3<a<+3
-2.80<b<+2.80
0<c<1 values above 0.35 are not acceptable
Item parameters are not dependent upon the
ability level of examinees or they are group
invariant-parameters are the value of items
not the group
50. Positive and Negative Discrimination
Positive: the probability of correct response
increases as the ability level increases
Negative: the probability of correct response
decreases as the ability level increases from
low to high.
51. Items with negative
discrimination occur in two
ways:
. First, the incorrect response to a two-choice
item will always have a negative
discrimination parameter if the correct
response has a positive value.
Second when something is wrong with the
item: Either it is poorly written or there is
some misinformation prevalent among the
high-ability students.
52. AN ITEM INFORMATION FUNCTION (IIF)
GIVING MAXIMUM INFORMATION FOR
AVERAGE ABILITY LEVEL
55. TIF
Information about all of the items on a test
are often combined and presented in test
information function (TIF) plots.
TheTIF indicates the average item
information at each ability level.TheTIF can
be used to help test developers locate areas
on the ability continuum where there are few
items. Items can then be written that target
these ability levels.
56. Steps in running IRT analysis
Data entry
Model selection through scale and fit
analyses
Estimating and inspecting
1. ICC
2. IIF
3. DIF (If needed)
4.TIF
57. Many-facet Rasch measurement
model
The many-facet Rasch measurement (MFRM)
model has been used in the language testing
field to model and adjust for various assessment
characteristics on performance-based tests.
Facets such as:
1. test taker ability
2. item difficulty
3. Raters
4. Scales
58. Many-facet Rasch measurement
model
The scores may be affected by factors like
rater severity, the difficulty of the prompt, or
the time of day that the test is administered.
MFRM can be used to identify such effects
and adjust the scores to compensate for
them.
59. The difference between this MFRM and the
1PL Rasch model for items scored as correct
or incorrect is that
The severity of the rater :
Rater severity denotes how strict a rater is in
assigning scores to test takers
The rating step difficulty:
rating step difficulty refers to how much of the ability
is required to move from one step on a rating scale
to another
For example, on a five-point writing scale with 1
indicating least proficient and 5 most proficient, the
level of ability required to move from a rating of 1 to 2,
or between any two scales would be difficulty of
rating step.
60. A test taker with an ability level of 0 would
have virtually no probability of a rating of 1
or 5, a little above a 0.2 probability of a
rating of 2, and about a 0.7 probability of a
rating of 3.
61. CRC
CRCs are analogous to ICCs.The probability of
assignment of a rating on the scale, the five-
point scale
It indicates that a score of 2 is the most
commonly assigned since it extends the furthest
along the horizontal axis.
Ideally, rating categories should be highly
peaked and equivalent in size and shape to each
other.
Test developers can use the information in the
CRCs to revise rating scales.
62. Use of MFRM:
investigating task characteristics and their effects
on various types of performance-based
assessments.
investigate the effects of rater bias, rater severity,
Rater training, rater feedback ,task difficulty and
rating scale reliability
63. IRT Applications
Item banking and calibration
AdaptiveTests (CAT/IBAT)
Differential Item Functioning
(DIF) studies
Test equating
64. CAT
Applications of IRT to computer adaptive testing (CAT)
are not commonly reported in the language
assessment literature, likely because of the large
number of items and test takers required for its
feasibility. However, it is used in some large-scale
language assessments and is considered one of the
most promising applications of IRT.
A computer is programmed to deliver items
increasingly closer to the test takers’ ability levels. In its
simplest form, if a test taker answers an item correctly,
the IRT-based algorithm assigns the test taker a more
difficult item, whereas, if the test taker answers an
item incorrectly, the next item will be easier. The test is
complete when a predetermined level of precision of
locating the test taker’s ability level has been achieved.
65. Differential Item Functioning
(DIF)
Differential Item Functioning is said
to occur when the probability of
answering an item correctly is not
the same for examinees who are on
the same ability level but belong to
different groups.
66. Differential Item Functioning
(DIF)
Language testers also use IRT techniques to
identify and understand possible differences in
the way items function for different groups of
test takers. Differential item functioning (DIF),
which can be an indicator of biased test items,
exists if test takers from different groups with
equal ability do not have the same chance of
answering an item correctly. IRT DIF methods
compare ICCs for the same item in the two
groups of interest.
67. Differential Item Functioning
(DIF)
DIF is an extremely useful and rigorous method
for studying groups differences:
Sex Differences
Race/Ethnic Differences
Academic background differences
Socioeconomic status differences
Cross-cultural and Cross-national studies
Determine whether differences are an artifact of
measurement or something different about the
construct and population.
68. Bias & DIF
The logical first step in detecting bias is to find
items where one group performs much better
than the other group: such items function
differently for the two groups and this is known
as Differential Item Functioning (DIF).
DIF is a necessary but not sufficient condition for
bias: bias only exists if the difference is
illegitimate, i.e., if both groups should be
performing equally well on the item.
69. Bias & DIF (Continued)
An item may show DIF but not be biased if the
difference is due to actual differences in the groups'
ability needed to answer the item, e.g., if one group
is high proficiency and the other low proficiency: the
low proficiency group would necessarily score much
lower.
Only where the difference is caused by construct-
irrelevant factors can DIF be viewed as bias. In such
cases, the item measures another construct, in
addition to the one it is supposed to measure.
Bias is usually a characteristic of a whole test,
whereas DIF is a characteristic of an individual item.
70. An example of an item that displays
uniform DIF
The item favors all males regardless of ability.
Only difficulty parameters differ across groups.
71. Comparison of CTT and IRT
(Embreston & Reise, 2000)
CTT
1. Single SEM across
2. Longer test more
reliable
3. Score comparison across
parallel forms are
optimal
4. Unbiased estimates
requires representative
sample
IRT
1.Various SEM across
2. Shorter test can be
equally or even more
reliable (TIF)
3. Optimal when test
difficulty varies between
persons
4. OK with
unrepresentative sample
72. Continued…
CTT
5. Scores are meaningful
against norm
6. Interval scales properties
achieved through
normal distribution
7. Mixed item formats
leads to unbalance
8. Change score not
comparable when initial
score differ
IRT
5.Test scores against distance
from items
6. Interval scales properties
achieved by applying
justifiable measurement
model
7. No problem
8. No problem
73. Continued…
CTT
9. Factor analysis produces
artifacts
10. Item stimulus features are
not important compared to
psychometric properties
11. No graphic displays of item
and test parameters
* All in all, better and more
practical for class based
low-stake tests.
IRT
9. Factor analysis produces full
information FA
10. Item stimulus features are
directly related to
psychometric properties
11. Graphic displays of item and
test parameters
* Much more advantageous
and preferable for high-
stake, large-sample tests.
*THE ONLY CHOICE FOR
ADAPTIVETESTS.
74. future research:
Techniques, such as item bundling (to meet
the assumption of local independence)
The development of techniques which require
fewer cases for accurate parameter
estimation
Guidance on using IRT (written resources
specific to the needs of language testers)
computer-friendly programs so that the use
of IRT techniques will become more prevalent
in the field
76. References:
Bachman, L. F. (1990). Fundamental
considerations in language testing. Oxford:
Oxford University Press.
Baker, F. B. (2001). The basics of item response
theory. ERIC Clearing House on Assessment and
Evaluation.
Embreston, S. E. & Reise, S. P. (2000). Item
response theory for psychologists. Mahwah, New
Jersey: Lawrence Erlbaum Associates.
Fulcher, G. & Davidson, F. (2007). Language
testing and assessment: An advanced resource
book. NewYork: Routledge
Fulcher, G. & Davidson, F. (2012).The Routledge
Handbook of LanguageTesting. NewYork:
Routledge