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The study analyzed the psychometric properties of Basic education Certificate examination (BECE) multiple choice items in mathematics in Abia state specifically to determine the content validity, item difficulty, discrimination indices, effectiveness of distracters, internal consistencies and coefficient of stability of BECE mathematic items. The population comprises all upper basic (Junior Secondary III) students of private, state, Federal Secondary Schools in Abia State. The study adopted the survey design. The instrument used were past BECE questions, the validity of the instruments is part of what this research work addressed using content validity through expert judgment and table of specification while reliability was addressed using Pearson product moment correlation coefficient for coefficient of stability and Kuder Richardson 21 for internal consistency. The research used past questions of 2014, 2015, 2016 BECE multiple choice items in mathematics which were administered to the students. The result shows satisfactory content validity for the different years with room for improvement; 81.6% of the items across the three years had satisfactory items difficulty while 18.3% items across the three years had poor item difficulty. The discrimination parameters shows 81% of the items across the three years have moderate discrimination indices implying that they are satisfactory while 19% of the items across the three years indicated low discrimination indices and should be discarded. 82% of the distracter items was seen to be effective, while 8% of distracter items across the three years was ineffective and should be discarded. Among the recommendations is the need for those involved in constructing BECE items be conscious of distracter/options they include in multiple choice items. Test development experts should create awareness and train teachers on their efficiency in constructing tests with good psychometric properties. BECE Mathematics in 2014, 2015 and 2016 are moderately valid and reliable, and should be used by teachers in preparation for future BECE as mock examination.



TITLE PAGE                                                                                                             i

DECLARATION                                                                                                       ii

CERTIFICATION                                                                                                     iii

DEDICATION                                                                                                           iv

ACKNOWLEDGEMENTS                                                                                       v

TABLE OF CONTENTS                                                                                           vi

LIST OF TABLES                                                                                                     viii

ABSTRACT                                                                                                               ix


1.2        Background to the Study                                                                               1

1.2       Statement of the Problem                                                                               5

1.3        Purpose of the Study                                                                                      6

1.4       Research Questions.                                                                                        7

1.5       Significance of the Study                                                                               7

1.6       Scope of the Study                                                                                         9


2.1       Conceptual Framework                                                                                   10

2.1.1    Concept of Tests and Testing                                                                         10

2.1.2    Achievement Tests                                                                                          13      Objective and Essay Achievement Test                                                        14 Achievement test Development Procedures.                                                  18

2.1.3    Concept of Psychometric Properties                                                               23

2.1.4    Item Analysis                                                                                                  27

2.2       Theoretical Framework                                                                                   30

2.2.1    Classical Test Theory                                                                                      30

2.2.2    Item Response Theory                                                                                    32

2.2.3    Psychometrics: The technique of psychological measurement                       34

2.3       Empirical Studies                                                                                            34

2.4       Summary of Literature Review                                                                      39


3.1       Design of the Study                                                                                        40

3.2       Area of Study                                                                                                 40

3.3       Population of the Study                                                                                  41

3.4       Sample and Sampling Technique                                                                    42

3.5       Instrument for Data Collection                                                                       42

3.6       Validation of Instrument                                                                                43

3.7       Reliability of Instrument                                                                                 43

3.8       Method of Data Collection                                                                             44

3.9       Method of Data Analysis                                                                               44


4.1        Results                                                                                                            46

4.2       Summary of Findings                                                                                     66

4.3       Discussion of Findings                                                                                   67


5.1       Summary                                                                                                         71

5.2       Conclusion                                                                                                      74

5.3       Recommendations                                                                                          74

5.4       Educational Implications of the Study                                                           75

5.5       Limitations of the Study                                                                                 76

5.6       Suggestion for Further Studies                                                                       76

REFERENCES                                                                      78


2014 BECE Mathematics multiple choice questions

2015 BECE Mathematics multiple choice questions

Percentage of Testees who get the test right

Table of specification

Guidelines for Evaluating Discrimination Indices (DI)




Table 4:1:        Specification on Mathematics Multiple Choice Test

items in 2014 represent the content area in Basic Education

Certificate Examination (BECE) Mathematics.            46


Table 4:2:        Kendall co-efficient of concordance of the items from five

experts based on cognitive levels or objectives and content

areas of the Basic Education Certificate Examination

(BECE) Mathematics in 2014.                         47


Table 4:3:        Specification on Mathematics items in 2015 represents the

content area in Basic Education Certificate Examination

(BECE) Mathematics in 2015.                               48


Table 4:4:        Kendall co-efficient of concordance of the items from five

experts based on cognitive levels or objectives and content

areas of the Basic Education Certificate Examination

(BECE) Mathematics in 2015.                               49


Table 4:5:        Specification on Mathematics items in 2016 represents the

content area in Basic Education Certificate Examination

(BECE) Mathematics.                                             50


Table 4:6:        Kendall co-efficient of concordance of the items from five

Judges based on cognitive levels or objectives and content

areas of the Basic Education Certificate Examination

(BECE) Mathematics in 2016.                                 51


Table 4:7:        The item difficulty indices of the BECE Mathematics in 2014, 2015 and 2016                              53


Table 4:8:        The discrimination indices of the BECE mathematics in 2014, 2015, and 2016                               56


Table 4:9:        The effectiveness of distracters in 2014 BECE Mathematics

options of the test items.                              59


Table 4:10:      The effectiveness of distracters in 2015 BECE Mathematics

                        options of the test items                 61

Table 4.11:      The effectiveness of distracters in 2016 BECE Mathematics options of the test items.                             63

Table 4:12:      The coefficient of stability of the 2014, 2015, and 2016

BECE Mathematics tests items using the Pearson Product Moment Correlation Coefficient.                64


Table 4:13:      The Kudder Richardson 21 of the 2014, 2015, and

2016 BECE Mathematics tests items                               65





Basic Education spans through a 10 year period, comprising of 1year pre-primary, 6 years of primary education (3 years lower basic and 3 years of middle basic) and 3 years of junior secondary education (upper basic) (FRN, 2013). This is in line with the intention of achieving the sensitive targets of National Economic Empowerment and Development Strategies (NEEDS) of the Nigerian Government comprising value orientation, poverty eradication, job creation, wealth generation and empowerment of the citizens through education (Okafor & Anaduaka, 2013). Among other goals, Basic Education according to the 6th edition of the National Policy on Education of 2013, provides the child with diverse basic knowledge and skills for entrepreneurship, wealth generation and educational advancement as well as provide opportunities for the child in developing manipulative skills and enabling same, effectively function in the society in the limits of the child’s capabilities.

Furthermore, the National Policy on Education (FRN, 2013) emphasizes it to be free and compulsory. It also includes adult and non-formal education programmes at primary and junior secondary education levels for the adults and out-of-school youths. According to the National Policy on Education, Basic Education Certificate Examination (BECE) is sat for by the student at the completion of the 10 year formal schooling. The Basic Education Certificate is issued by the State governments and the Federal Capital Territory (FCT) administration and by NECO for federal schools. Efforts are put in place towards achieving equitable access to educational opportunities for all Nigerians in all parts of the country. On completion of  junior secondary school, students  shall be streamed into (i) senior secondary school, (ii) higher school (iii) continuing education given in Vocational Enterprise Institutions, The streaming shall be based on the result of tests’ to determine academic ability, aptitude and vocational interest; as much as possible to achieve a transition of 50:50. The Basic Education Certificate Examination (BECE) is based on continuous assessment and examination conducted by state and federal examination boards. The BECE is conducted and administered by 36 state Ministries of Education and the Federal Capital Territory (FCT) for all the private and public state secondary schools within the various states and FCT. The National Examination Council (NECO) also conducts BECE for federal unity schools, armed forces secondary schools and other federal institutions that operate secondary schools, inspite of the fact that the curriculum and the expectation across the federation is the same. Could it be possible the quality of NECO instruments may not be the same with the state ministries of education, where expertise in developing and administration of examinations may be a problem? Could there also be difference in the qualities of the different BECE as administered by the individual state ministries of Education?

At the junior secondary level, a maximum of 10 subjects are offered and Mathematics is among the subjects offered. By the completion of junior secondary school, a Nigerian student is expected to be proficient in number and numeration, basic (mathematics) operations, measurement, algebraic processes, elementary geometry and mensuration and everyday statistics. According to the National Educational Research and Developmental Council (NERDC), (2007), the revised National curriculum for mathematics curriculum for basic education programme in Nigeria has the objectives which include (i) to acquire mathematical literacy that is a necessary functionality in an information age. (ii) Cultivating the understanding as well as the application of mathematical skills and concepts necessary to drive the ever changing technological world. (iii) Developing the essential element of problem solving, communication and reasoning within the study of mathematics. (iv) Understanding the major ideas of mathematics with the mindset that the world has changed and is still changing.

The observation over the years in the outcome of public examinations both at the junior and senior secondary level of education in the country has not received favourable commendation by all stakeholders, becoming a source of concern to parents, educators, government and the general public (Okafor & Anaduaka, 2013).Most school children in Nigeria dread mathematics, with the perception of it as being difficult, complex and abstract. Students do not also seem to see the use or applicability of the subject in their everyday living and why being bothered with studying the subject. (Okafor and Anaduaka, 2013).

The use of test or testing is a fundamental part of teaching-learning process. It guides teaching and aids in the development of curriculum as well as assessment of needs, learning difficulties, level of mastery and differences among students. Tests can only perform this function when it is valid or have appropriate psychometric properties. Adebule (2009) infers that teaching and testing go together in schools. The preparation and writing of questions in our schools are the sole responsibilities of subject teachers. Nwana (2007) posits that majority of the teachers do not give adequate attention and due consideration to quality of the tests they set. Most of the test question items are not reliable while some items are either too difficult or too simple. Nwana also affirmed that most teacher-made tests have been found to be carelessly constructed without test blueprint or table of specification. This has prompted inquiry as to how this translates to a standardized test like BECE which is conducted at the level of Ministry of Education in the different states and FCT.

Psychometric characteristics of examinations refer to certain attributes inherent in tests. These characteristics include the facility or difficulty indices, the discrimination index, the effectiveness of distracters, validity and reliability indices. It’s perhaps worth mentioning that these attributes of a test are most often ignored. These indicators of the extent of quality of test items can be achieved through item analysis.

Oshkosh (2002) puts item analysis as a very important tool to increase the effectiveness of a test. Scientifically it improves test quality and test items as in an item bank and providing three important points about the quality of test items. (i) Item difficulty – a measure of whether an item is too easy or too hard, also called facility index. (ii) Item discrimination – which is a measure of whether an item discriminates between candidates who know the material well and candidates who do not. (iii) Effectiveness of distracters – determination of whether distracters (incorrect but plausible options) tend to be chosen by the less knowledgeable candidates and not by the more knowledgeable candidates.

With the acknowledgment of the fact that some expectations of teaching and learning are heaped on test outcomes, the seriousness of the role tests and examinations play, informs the drive in probing into the quality of tests given at different stages of academic growth. The basic education level has caught the researcher’s fancy due to its importance as a formative stage of academic development. How serious is this formative educational level handled by stakeholders? It is probable that some weaknesses exist in the tests developed and administered by the state ministries of education especially in Abia State. It is also not certain that some of the state ministries of education who develop and administer BECE examinations do not have measurement experts who should be involved in item development and validation. It becomes imperative in determining the extent to which Basic Education Certificate Examination for mathematics test items satisfy the psychometric properties of validity, reliability, item discrimination and item difficulty. Highlights of some of the related works carried out in this area include (i) The psychometric properties of mathematics in public examinations in Nigeria. Moyinoluwa,(2015). (ii) A study of the comparative analysis of psychometric properties of two Nigerian examining bodies for senior secondary schools mathematics. Kolawole,(2007). (iii) The study on the development and standardization of achievement test in senior secondary mathematics using item response theory. Enunwah and Akwa,(2014). This brings to importance, the need to establish the place of BECE mathematics in satisfying the psychometric properties.


The Basic Education Certificate Examination is of great importance to the educational development of the child. This is because it is at this stage that the child will start preparing himself/herself for future career prospects. The outcome prepares the mind of the pupil towards branching out to technical college and start towards skill acquisition or moving forward to senior secondary for the sciences or arts. One would ask if BECE is actually meeting up with the enormous responsibilities bestowed on it. If so then, being able to satisfy the psychometric properties of a standardized test will be an important factor in actualizing it.

Madu and Ihechu (2016) posit that tests and examinations at all stages of education have been considered an important tool for decision making in our competitive society, with people of all ages being evaluated with respect to their achievement, skills and abilities. Zola and Ben-chain (2009) have the opinion that the era in which we live is a test conscious age in which the lives of many people are not only greatly influenced, but are also determined by their test performance. This brings to the question of how valid and reliable BECE is as a tool in decision making. And also can BECE be said to be a quality tool or instrument to evaluate student achievement, skills and abilities? This question calls to mind the nature of administration of this examination, which is carried out by individual state government. How standardized are the BECE examinations conducted by Abia state with respect to satisfying the psychometric properties. Could there be areas of improvement on BECE as it is currently administered?

At present, no study seems to have been carried out to determine the psychometric properties of Basic Education Certificate Examination in mathematics in Abia State. The problem of this study therefore is: Can the psychometric properties of BECE mathematics in Abia State secondary schools be verified? Since the answer is in the affirmative, then how satisfactory are the psychometric properties of the test items?


The purpose of this study was to analyze the psychometric properties of Basic Education Certificate Examination multiple choice items in Mathematics in Abia State. Specifically the study sought to determine

1.      The content validity of BECE mathematics tests in Abia state.

2.      The item difficulty of BECE mathematics test items in Abia state.

3.      The discrimination indices of BECE mathematics test items in Abia state.

4.      The effectiveness of distracters of BECE mathematics the test items in Abia state

5.      The internal consistencies of the test instruments.

6.      The coefficient of stability of BECE mathematics in Abia state.



The following research questions guided this study.

1.     To what extent do mathematics test items in BECE represent content area in Basic mathematics?

2.      To what extent does BECE mathematics satisfy item difficulty?

3.      To what extent does BECE mathematics satisfy discrimination indices?

4.      What is the effectiveness of distracters of BECE mathematics options of the test items?

5.      What are the coefficient of stability of BECE mathematics multiple choice test items?

6.      What are the internal consistencies of the BECE mathematics multiple choice test items?


The analysis of Psychometric properties of BECE multiple choice items in mathematics in Abia State may impact on the general public, subject teachers, guidance counselors, Examination boards, Ministries of Education, Agencies associated with Education and Examinations,  Students, Abia state and the Nation at large.

This work is important because it will contribute to the efforts already being made in the improvement of tests and test outcomes. The implication of this work is that aside from its contributions towards good and quality instruments, humanity will hopefully be better for it. What with the importance attached to mathematics in scientific and technological development of any nation. Harnessing the results of the study will go a long way towards bringing teaching and learning of mathematics closer to the students and make them to start seeing its applicability and its importance towards better living as well as encouraging the students to want to do more in the area of mathematics. Abia state and Nigeria will be better for it in the area of teaching and learning of mathematics. With mathematics as a fulcrum of other subject areas, a good analysis on the administration of test items on the subject matter will go a long way to ease off some of the ‘myths’ associated in the teaching and learning of mathematics and mathematics test outcomes.

This work will certainly contribute in informing policy making in the right direction. This study will identify gaps and shortfalls and will hopefully be a wake-up call on stakeholders in correcting such and coming out with better outcomes and experiences. There is no gainsaying that the result of this study will showcase the overall quality of the BECE mathematics of Abia State Ministry of Education and the public confidence on the standard of the examinations to the different years. It will also enlighten the public on the interpretations of student results in the examinations.

The students who will be sitting for this examination in future will be the ultimate winners if the result of this study is put into use by the authorities. This is because it will contribute in the enrichment of subsequent BECE multiple choice items in mathematics in Abia state. Barriers which would have hampered in the student performance would have been eliminated, thereby enhancing the educational advancement of the students in the state and Nigeria in general. The crucial need to employ the hands of measurement and evaluation experts in preparing such examination and also before the release of the examination results will be put into consideration.

A new perspective to this study will bring to bear the need for more work to be done in the educational development of students at the basic education level, since most studies are done at the senior secondary school level. The analysis of the psychometric properties of BECE mathematics multiple choice items will help highlight the need for subject teachers in properly constructing their own test items for use during continuous assessment and terminal examinations. There is also the need for the result of this study be made known to Ministries of Education, examination boards, councellors and other agencies that have a role to play in academic advancement of the student. The outcome of this work will assist counselors in proper test utilization, especially in the area of interpreting and communicating student needs regarding the test.

This study is also linked to other knowledge since its outcome will have to be replicated in other subject areas as well as adoption of the proper procedure of testing where such is lacking. Other states of the federation are not left out in the expected outcome of this study where its outcome could be harnessed. So is with other areas of human endeavor outside Education.


This Study was focused on examining BECE multiple choice items in mathematics as administered by Abia State Ministry of Education. The study covered all the private, public and federal secondary schools in Abia state. It also examined the psychometric properties, reliability and validity of BECE mathematics test items used from 2014 to 2016.

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