AN EMPIRICAL COMPARISON OF ITEM RESPONSE THEORY AND CLASSICAL TEST THEORY: CASE STUDY SELECTED LOCAL GOVERNMENT AREA IN EDO STATE
CHAPTER ONE
INTRODUCTION
Background To The Study
Test is la method that determines a student’s ability to complete certain tasks or demonstrate mastery of a skill or knowledge of content. Some types would be multiple choice test, or a weekly spelling test. While it is commonly used interchangeable with assessment, or even evaluation,it can be distinguished by the fact that a test is one form of an assessment (Overton, 2012).In other words, testing consists of a set of uniform questions or tasks to which a student is to respond independently and the result of which can be treated in such a way as to provide a quantitative comparison of the performance in different students.  Omorogiuwa (2010) defines test as an item or set of items presented to an individual or set of individuals to which they are expected to respond under specific conditions, with the intent to determine the extent to which such traits are present or absent in the respondent(s).According to Anigbo (2006), test is any kind of device or procedure for measuring ability, achievement, interest and other traits. In essence, a test is supposed to measure student’s/examinees’ ability/performance or other traits irrespective of certain factors like gender, ethnicity, geographical locality, social status and others. More so testing is done to determine whether or not an objective or goal has been obtained. In other words, testing concerns specific achievement of a student in terms of a given objective.
By Item Response Theory (IRT) standards, test items should not depend on the characteristics of the sample. By the use of Item Response Theory (IRT) framework, in the analysis of test items, psychometricians have found that some items in a test may have functions different from what the test is meant for. It means that such items have interactions with the characteristics of the sample (examinees/students) taking the test. This describes such items as having differential functions.Item response theory assumes there is a mathematical function that relates the probability of a correct response on an item to an examinee’s ability (Osteen, 2010).
The practice of testing has become increasingly common and the reliance on information gained from test scores to make decision has made an indelible mark on our culture. The entire educational system in Nigeria today is highly concerned with the design and development of the tests, the procedures of testing, instruments for measuring data, and the methodology to understand and evaluate the results (Erguven, 2014). In theory of measurement in education and psychology there are two competing measurement frameworks, namely Classical Test Theory (CTT) and Item Response Theory (IRT). The techniques of the two frameworks are applied in assessment situations to improve test analysis and test refinement procedures.
          Assessment of students learning is very important in education. The assessment of students’ cognitive abilities, academic skills and intellectual development involves certain techniques employed to sample students’ performance on a particular learning outcome targeted by the instructional objectives one of that techniques is test, the test is expected to sample students’ behaviors. Thus creating quality tests is very important in assessing the students’ performance; many indices have been developed in order to construct valid and reliable items during test development. These indices developed mostly rely on the two popular statistical frameworks Classical Test Theory and Item Response Theory. The two frameworks are associated with the item development process in the field of educational and psychological test. These frameworks are widely been used in test development to ensure quality of measuring instruments and discuss in various literatures in the field of psychological and educational measurements on their suitability and effectiveness in test development process.
In the theories, the models associated with each have been described and compared, and the ways in which test development generally proceeds within each frameworks have be demonstrated (Fan, 2008)
Theoretically, IRT overcomes the major weakness of CTT, that is, the circular dependency of CTT’s item statistics (Fan, 2008).As a result, in theory, IRT models produce item statistics independent of examinee samples and person statistics independent of the particular set of items administered..
Statement of the Problem
Despite the number of empirical studies conducted to directly or indirectly provide empirical evidences of the relationship between CTT and IRT, there are not enough studies that provide evidence theoretical superiority of IRT over CTT. This inability of the studies to provide a clear distinction between the two measurement frameworks as theoretically been established leaves much to be ask as relate to the suitability of the tools used in the studies.
        A test is supposed to measure students/examinees ability/performance or other traits of interest irrespective of certain factors such as gender, ethnicity, geographical location, social status and others. In other words, a test item by IRT standards is supposed to be invariant in nature. This is not always the case for psychometricains have often found some test items to have interactions with the characteristics of the sample (examinee/students). This study sought to compare the item statistics of senior school certificates in Biology administered by the West African Examination Council (WAEC), using classical test theory and items response theory
Research Questions
Deriving from the stated problems, the following research questions have been formulated to guide the direction of this study:
(1)How comparable are CTT and IRT based item parameters?
(2)How invariant are CTT and IRT based item parameters across different item sets?
(3)How invariant are CTT and IRT based item parameters across different participant group?(4) Is Item Response Theory (IRT) more superior to the Classical Test Theory (CTT) as an important framework for test construction?
Hypotheses
The following research hypotheses stated in the null form would be tested:
1. There is no significant difference between CTT and IRT based item parameters.   
2. There is no significant invariant between CTT and IRT based item parameters across different item sets.
3. There is no significant invariant between CTT and IRT based item parameters across different participant group.
4. There is no significant statistical comparability in Item Response Theory (IRT) and Classical Test Theory (CTT) selected items.
Purpose of the Study
            The main objective of the study is to compare the item statistics of senior school certificates in Biology. The specific objectives of the study are to:
(1) ascertain the extent to which CTT and IRT based item parameters are comparable.   
(2) investigate the degree to which CTT and IRT based item parameters across different item sets are invariant
 (3) determine the extent to which CTT and IRT based item parameters across different participant group are invariant
(4) establish whether Item Response Theory (IRT) is more superior to the Classical Test Theory (CTT) as an important framework for test construction.
Significance of the Study
The results from this study will provide measurement specialists, test developers and the researchers with information regarding the suitability and comparability of the two frameworks from the practical point of view and provide basis for further research to improve measurement practice
Scope and Delimitation of the Study
This study describes the application of Classical Test Theory (CTT) and Item Response Theory (IRT) to compare the item statistics of senior school certificates in biology. The biology WAEC question for the year 2015 will be used. The choice of the sample period is dictated by the desire to take a short-term trend in item statistics of senior school certificates in biology comparison.
In this research work, the area of study is Edo State, Nigeria. Edo State is within the South-South zone of Nigeria. It is made up of 18 local government areas. The study will be delimited to the students in Edo State

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