Assessing Item Difficulty, Discrimination, Guessing and Carelessness Parameters of the NABTEB 2022 Economics in South-South States of Nigeria

VillageMath Educational Review, 7(1) https://ngsme.villagemath.net/journals/ver 158 Volume 7, Issue 1 October, 2025 CODEN: VERIAU Assessing Item Difficulty, Discrimination, Guessing and Carelessness Parameters of the NABTEB 2022 Economics in South-South States of Nigeria Kennedy Imasuen 1 and Iyabo Ayodeji Ukanah 2 1 Institute of Education, University of Benin, Benin City, Nigeria 2 Adekunle Ajasin University, Akungba Akoko, Nigeria DOI: https://doi.org/10.5281/zenodo.17268474 Article History: Received 23rd July, 2025; Revised 4th October, 2025; Published 5th October, 2025. Copyright © 2025 by Author(s) and The VillageMath Network This work is licensed under Creative Commons Attribution 4.0 International (CC BY 4.0) https://creativecommons.org/licenses/by/4.0/ How to Cite this Article: Imasuen, K. & Ukanah, I. A. (2025). Assessing Item Difficulty, Discrimination, Guessing and Carelessness Parameters of the NABTEB 2022 Economics in South-South States of Nigeria. VillageMath Educational Review (VER), 7(1), 158-169. https://ngsme.villagemath.net/journals/ver/v7i1/imasuen-ukanah-1 Abstract The study examined the item parameters of the National Business and Technical Education Board 2022 May/June Economics examination in the South-South States of Nigeria using the four-parameter item response theory model. The study was a descriptive survey, which adopted the ex post facto design. The population of the study consists of 2909 students who took the National Business and Technical Education Board 2022 May/June Economics multiple choice Examinations in Akwa-Ibom, Bayelsa, Cross River, Delta, Edo, and Rivers States. This also serves as the sample of the study. The research instrument for the study was the Economics multiple choice test items for the National Business and Technical Education Board 2022 May/June Examinations. The National Business and Technical VillageMath Educational Review An International/Multidisciplinary Journal of Network for Grassroots Science and Mathematics Education (The VillageMath Network) A publication of VillageMath Educational Services (CAC RC: 4097888) VillageMath Educational Review, 7(1) https://ngsme.villagemath.net/journals/ver 159 Imasuen & Ukanah Certificate Examinations (NABTCE) May/June 2022 Economics multiple-choice items were already validated and standardized. However, the reliability of the scores was ascertained using the Cronbach alpha and it gave an index of 0.89. In analyzing the data, the item calibration was done using Jmetrik IRT software. Thereafter, the research questions were answered using frequency counts. The findings that emerged showed that the items of the National Business and Technical Education Board 2022 May/June Economics discriminated effectively among the low and higher achievers, was of medium difficulty, and the guessing and carelessness parameters performed well which suggested that the items were good. It was therefore recommended that examination bodies should use the fourparameter item response theory because there is always the possibility that students with low or high abilities may give an aberrant response. Keywords: Carelessness Parameter, Item Difficulty, Item Discrimination, Guessing Parameter, Measurement and Evaluation Introduction In measurement theory, the Classical Test Theory (CTT) approach is the first and the most highly used. It is a linear model which shows the relationship between the observed score, the true score and the error component in the score obtained by a testee. More importantly, it has also been used extensively in identifying test item characteristics as well as the test itself. Another reason for its usage is the ease and simplicity of the calculation (Santoso et al., 2022). However, it has been observed that it has a major drawback as it is sample and examinee group dependent (Hambleton et al. cited in Pardede et al., 2023; Zanon et al., 2016). This suggests that a test item can be easy when the examinee has a high ability. However, when these test items are administered to the examinee with low ability, the test items may become difficult. Another issue with CTT is that it is difficult to identify the extent of the students’ or examinees’ abilities because the students’ or examinees’ ability depends on the difficulty level of the test items. This suggests that with the CTT approach, it may be difficult to identify the characteristics of a test and the test items because, as the context of the examinee changes, the characteristics of the examinee will also change (Pardede et al., 2023). Secondly, these characteristics will change within the context of the administered test (Hambleton et al. cited in Pardede et al., 2023). In an attempt to provide solutions to these problems inherent in CTT, the modern trait test theory, also known as Item Response Theory (IRT) or latent trait theory, was introduced. IRT is a model system that determines the relationship between latent variables and their manifestations (Gyamfi & Wren, 2022; Butakor, 2022). According to Bichi et al. (2016), the determination of what to answer in a test or the response pattern or the way an examinee responds to an item, IRT does not explain. Rather, it behaves like the statistical estimation theory where latent characteristics of the examinees and items are used as predictors of observed scores (Gyamfi, 2023). Before IRT is used in any test, its assumptions must be considered. According to Bulut (2015), IRT has two basic assumptions which underpin IRT for polytomous items, which are unidimensionality and local independence. However, there is a third assumption of item and person invariance for monotonous items. The most popular assumption of IRT VillageMath Educational Review, 7(1) https://ngsme.villagemath.net/journals/ver 160 is the unidimensionality assumption (DeMar, 2012). According to Annan-Brew (2020), unidimensionality is a special Item Response Function (IRF) form that can be checked empirically. Unidimensionality implies that the test measures the same latent trait. The unidimensionality makes it possible to estimate the ability of the examinee on the same ability scale from any pool of items in the universe of items. The unidimensionality can be checked using various statistical techniques such as the principal component analysis in factor theory and parallel analysis. The scree plot (elbow) can also be utilized in checking for unidimensionality. In checking for unidimensionality, the dominant factor usually takes a larger portion of the total variance. The local independence assumption states that the response to an item of a test is not statistically independent of the ability level of the examinee 𝜃 (Annan-Brew, 2020). This implies that the examinees’ performance on one item must not have a positive or negative impact on their responses to subsequent test items. The assumption of local independence requires that the examinees’ performance in responding to one test item is not related to or not affected by the examinees’ performance in responding to other test items. Parameter invariance includes item parameter invariance and person parameter invariance. Item invariance requires that when a group of examinees is divided into two subgroups based on certain conditions, the values of the item parameter estimate of the two groups must be similar or tend to be similar. In the same vein, the person parameter suggests that when the test items are divided into two subgroups based on certain conditions, the estimation of the person parameter (ability) using the item responses from the two groups must be similar or tend to be similar. In any test, other possibilities could be investigated. These are the item difficulty, how the item discriminates among examinees, the effect of guessing to answer an item and missing an easy item due to carelessness. These four possibilities, known as parameters, make up what is known in the IRT paradigm as difficulty parameters (𝑏𝑖), discrimination parameter (𝑎𝑖), the pseudo-guessing parameter (𝑐𝑖). and the carelessness parameter (𝑑𝑖). According to Annan-Brew (2020), the parameters of IRT are the characteristics that are estimated. In IRT, item difficulty means the percentage of students who answer correctly each test item (Hussain et al., 2012). It is an indication of the proportion of examinees who responded to the item correctly. The lower the proportion, the more difficult the item is. It is also known as the location parameter. It is the ability level needed to respond to a specific threshold with a 50% probability. Item difficulty is an indication of how likely an individual with low proficiency is to answer the item correctly. It has been suggested that when the ability distribution is at a mean of 0 and a standard deviation of 1, the estimated parameter difficulty of an item should vary and be in the range of -2.00 to 2.00 (DeMars, 2010). If it is close to -2.00, it means the item is getting easier, while if the estimated value is close to 2.00, it means the item is getting harder. Adedoyin and Mokobi (2013) proposed criteria for the categorization of item difficulty on a logit scale under the IRT framework. According to them, for items with medium difficulty, the estimated difficulty parameter should lie in the range of -1.00 and 1.00. However, VillageMath Educational Review, 7(1) https://ngsme.villagemath.net/journals/ver 161 Imasuen & Ukanah Georgiev (2008) proposed that the categorization of the item difficulty parameter should be more than medium but should be categorized as very easy (𝑏 < −2.00), easy easy ( -2.00≤ 𝑏 < −1.00), hard (1.00< 𝑏 ≤ 2.00), and very hard (𝑏 > 2.00). DeMars (2010) suggested that for items to be used in large numbers on a test, they must exhibit a medium difficulty. Item discrimination, according to Niko in Gyamfi and Acquaye (2023), is the difference between the upper achievers and the lower achievers in responding to an item. Its importance lies in the fact that it can indicate both the absolute and relative achievements of the students. The criteria for grouping the discrimination parameter, as proposed by Baker and Kim (2017) is 0 ≤ 𝑎 < 0.34 very low, 0.35 ≤ 𝑎 ≤ 0.64 low, 0.65 ≤ 𝑎 ≤ 1.34 is regarded as moderate, 1.35 ≤ 𝑎 ≤ 1.69 is seen as high, and 𝑎 ≥ 1.70 very high. The guessing parameter is the likelihood of the examinee correctly getting an item by guessing. This parameter does not change with the level of ability; it is the same regardless of the skill level. Examinees with high ability and those with low ability have the same chance of guessing correctly an item (Amam-Brew, 2020). The criterium for grouping the guessing parameter is   where, k is the number of options in the test. In this study, the test used has 4 options; therefore, the guessing parameter c is grouped as 0 ≤ 𝑐 ≤ 0.25 and 𝑐 > 0.25. The carelessness parameter (di) is a situation where a high-ability examinee gets an item incorrect due to carelessness. It has other names such as upper asymptote, response time, and slowness parameter. A very high-ability examinee may, on some occasions, answer an easy item incorrectly. The criteria for grouping the carelessness parameter d as proposed by Guyer and Thompson (2011) is 0 ≤ 𝑑 < 1. Barnard-Brack et al. (2018) suggested that the estimated carelessness parameter should remain high, at least 0.90. If the interest is only in ascertaining the difficulty level of the items, we have the one-parameter logistic model (1PLM). The 1PLM assumes that all items have the same slope and only differ in threshold (item difficulty). If the interest is to also look at how the items discriminate between the high and low abilities of the examinees, in addition to the difficulty level of the items, it becomes the two-parameter logistic model (2PLM). The 2PLM allows items to have different slopes and is consistent with evidence that not all items are equally discriminating (Grey-Little et al. cited in Pardede et al., 2023). If the possibility of the examinee guessing to get the correct response is included, we have the three-parameter logistic model (3PLM). The 3PLM introduces a lower asymptote and is often used in multiple-choice items in educational testing or for instruments where even low-ability respondents have a finite probability of a correct response. The addition of the carelessness parameter makes it the four-parameter logistic model (4PLM). The first empirical investigation of 4PLM was done by Barton and Lord in 1981. The rationale was to see if adding an upper asymptote of less than 1 would improve the ability estimation on standardized tests. To them, the 3PLM might be excessively punitive to high-ability examinees who get an easy item incorrectly. The 3PLM can only accommodate a low-ability examinee who correctly guesses a difficult item, but the upper asymptote of 1 in the 3PLM assigns effectively a probability of zero that higher-ability VillageMath Educational Review, 7(1) https://ngsme.villagemath.net/journals/ver 162 students incorrectly answer an easy item. Barton and Lord proposed the following response model P(𝑋 = 1/ 𝜃, 𝑎, 𝑏, 𝑐, 𝑑) = 𝑐+ (𝑑 − 𝑐).() .() IRT analysis has been used severally in large-scale assessments by various scholars. For example, Dogruoz and Aikan (2020) observed that the 2PLM and the 3PLM models were the most used in estimating item parameters and the ability of the examinee. The 4PLM has not been given much attention due to the theoretical and practical obstacles; one of which is related to the setting of the upper asymptote parameter value to be not equal to 1. Secondly, there is the issue of software that can accommodate the 4PLM. Hence, the emphasis has been on the second and third logistic parameter models. Some studies have arisen due to advancements in technology. For example, Dogruoz and Arikan (2020), Kalkan (2022), Liao et al. (2012), Loken and Rulison (2010), Ogasuwar (2017), Primi et al. (2018), Robitzsch (2022), and Pardede et al. (2023) have carried out studies to further explore the 4PLM. The studies revealed the promising potential of the 4PLM in practice, especially in the computerized adaptive testing (CAT) in estimating the abilities of examinees efficiently and with precision when there is a high-ability examinee exhibiting aberrant responses due to careless behaviour. However, only a few studies (Pardede et al., 2023) have examined the careless behaviour among examinees in paper-and-pencil testing. Therefore, this study examines the item parameters of the National Business and Technical Education Board 2022 May/June Economics examination in the South-South geographical zone in Nigeria. Research Questions The following research question was asked to guide the study: i. What are the item properties of the National Business and Technical Education Board 2022 May/June Economics based on the discrimination, difficulty, guessing, and carelessness parameters? Methodology The study was a descriptive survey, which adopted the ex post facto design. The population of the study consist of the scores of 2909 students of Technical and Vocational Colleges in the 2022 May/June National Business Certificate (NBC) and National Technical Certificate (NTC) Economics multiple choice Examinations in the South-South geo-political zone of Nigeria, comprising Akwa-Ibom, Bayelsa, Cross River, Delta, Edo, and Rivers States. This also serves as a sample of the study. The research instrument for the study was the Economics multiple-choice test questions (items) paper for the National Business Certificate (NBC) and National Technical Certificate (NTC), 2022 May/June Examinations. The instrument consists of 50 items with four (4) options lettered A-D. The candidates were required to select one correct answer from the four options. The response to each item was coded as 1 for a correct response and 0 for an incorrect response. The National Business and Technical Certificate Examinations (NABTCE) May/June 2022 Economics multiplechoice items were already subjected to the process of validation and standardization; hence VillageMath Educational Review, 7(1) https://ngsme.villagemath.net/journals/ver 163 Imasuen & Ukanah they are presumed to be valid. However, the reliability of the scores was ascertained using the Cronbach Alpha, and it gave an index of 0.89. In analyzing the data, the principal component analysis was used to determine the unidimensionality of the data for the 2022 Economics multiple-choice test items, using the Statistical Package for Social Sciences (SPSS). Thereafter, item calibration was done using Jmetrik IRT software, which can handle the four-parameter model. The criteria for grouping the difficulty parameter, as proposed by Georgiev (2008) is 𝑏 < −2 very easy, −2 ≤ 𝑏 < −1 easy, 1 ≤ 𝑏 < 2 hard, and 𝑏 > 2 very hard. The criteria for grouping the discrimination parameter as proposed by Baker and Kim (2017) is 0 ≤ 𝑎 < 0.34 very low, 0.35 ≤ 𝑎 ≤ 0.64 low, 0.65 ≤ 𝑎 ≤ 1.34 is regarded as moderate, 1.35 ≤ 𝑎 ≤ 1.69 is seen as high, and 𝑎 ≥ 1.70 very high. The criterium for grouping the guessing parameter is   where k is the number of options in the test. In this study, the test used has 4 options, therefore the guessing parameter c is grouped as 0 ≤ 𝑐 ≤ 0.25 and 𝑐 > 0.25. The criteria for grouping the carelessness parameter d as proposed by Guyer and Thompson (2011) is 0 ≤ 𝑑 < 1. The research question was answered using frequency counts. Results The results of this study are presented according to the research question. Research Question One What are the item properties of the National Business and Technical Education Board 2022 May/June Economics based on the discrimination, difficulty, guessing, and carelessness parameters? Before checking for the assumption of unidimensionality using factor analysis, we needed to ensure the suitability of the responses of the examinees for factor analysis and principal components. This was achieved by considering the correlation matrix and sample adequacy. Bartlett’s test of sphericity (𝜒(703) = 34294.874, p<0.05) suggests that there is sufficient evidence not to accept that the correlation matrix formed is an identity matrix. The Kaiser-Meyer Olkin (KMO) factor adequacy (overall MSA = 0.887) demonstrated that the sample of responses on the test items was sufficient for each variable in the model and complete model. Based on the two results, we proceeded with the analysis to check for the assumption of unidimensionality through the factor theory analysis and principal components using the Statistical Package for Social Science (SPSS) version 27. This was to ascertain if the NABTEB 2022 May/June Economics multiple-choice test items measure only one dominant factor or latent trait. Unidimensionality was established in the NABTEB 2022 May/June Economics multiplechoice test items. There was a presence of a dominant factor of the first Eigenvalue of 7.943 which accounted for 20.90% and is larger than the second eigenvalue of 3.99 which accounted for 10.51. The spree plot also shows that the instrument is unidimensional, hence necessitating the analysis to be done using the IRT model. VillageMath Educational Review, 7(1) https://ngsme.villagemath.net/journals/ver 164 Figure 1: Spree Plot of the National Business and Technical Education Board 2022 May/June Economics Table 1: The Item Response Theory 4 Item Parameters of the NABTEB 2022 May/June Economics Multiple-Choice Test Items Items a (Discrimination) b (Difficulty) c (Guessing) d (Carelessness) 1. 2.74 -1.58 0.14 0.97 2. 2.23 -2.16 0.19 0.98 3. 2.82 -0.61 0.27 0.93 4. 2.91 0.49 0.72 0.60 5. 0.82 2.16 0.20 0.91 6. 2.94 0.44 0.53 1.00 7. 2.15 -2.09 0.15 0.97 8. 1.14 - 1.23 0.13 0.98 9. 1.64 -1.72 0.14 0.96 10. 1.93 -2.50 0.21 0.95 11. 0.82 1.00 0.33 0.60 12. 2.93 0.54 0.68 0.60 13. 0.82 2.56 0.21 0.91 14. 2.18 -1.61 0.11 0.88 15. 2.09 -1.23 0.15 0.95 16. 2.95 0.16 0.26 0.96 17. 2.56 -0.69 0.21 0.98 18. 2.34 -1.39 0.13 0.95 19. 2.02 -1.91 0.15 0.96 20. 2.64 -1.56 0.20 0.99 VillageMath Educational Review, 7(1) https://ngsme.villagemath.net/journals/ver 165 Imasuen & Ukanah 21. 2.71 -1.57 0.18 0.98 22. 2.76 -1.43 0.22 0.97 23. 2.76 -1.74 0.07 0.97 24. 2.78 -0.74 0.42 0.98 25. 2.71 -1.92 0.08 0.98 26. 2.82 -0.64 0.13 0.98 27. 1.55 -0.33 0.24 0.98 28. 2.45 -1.89 0.12 0.98 29. 1.07 -2.18 0.25 0.99 30. 2.77 -0.78 0.32 0.97 31. 9.23 0.35 0.70 0.60 32. 0.82 2.32 0.06 0.91 33. 1.23 -1.19 0.14 0.99 34. 2.62 -1.51 0.21 0.92 35. 1.49 -1.81 0.11 0.98 36. 1.32 - 0.69 0.21 0.99 37. 0.82 2.27 0.16 0.91 38. 2.93 0.40 0.52 0.92 39. 0.82 2.54 0.02 0.91 40. 2.93 0.22 0.50 0.92 41. 2.92 0.23 0.47 0.92 42. 2.90 0.40 0.50 0.92 43. 0.82 2.35 0.06 0.91 44. 0.82 3.99 0.03 0.91 45. 0.82 2.88 0.04 0.91 46. 2.22 -1.89 0.18 0.98 47. 2.40 -1.61 0.12 0.98 48. 1.70 -1.88 0.16 0.98 49. 2.62 -1.76 0.09 0.97 50. 1.05 -2.20 0.16 0.98 From the data in Table 1, none of the items exhibited very low, and low discrimination. 14 items representing 28% discriminated moderately, 3 items representing 6% exhibited high discrimination, and 33 (66%) discriminated very highly. The difficulty parameter also revealed that 4(8%) of the items were very easy, 27 (54%) were easy, 11 (22%) were hard, and 7 (14%) of the items were very hard. Concerning the guessing parameter, only 13 (26%) were above 0.25, and 37(74%) were at most 0.25. The carelessness parameter shows that only 4 (8%) were below the 0.90 benchmark. VillageMath Educational Review, 7(1) https://ngsme.villagemath.net/journals/ver 166 Table 2: Mean and standard deviation of the item parameters of the National Business and Technical Education Board 2022 May/June Economics Parameter Mean SD SEM Remarks Discrimination 2.191 1.29 0.18 Very high Difficulty -0.455 1.64 0.23 Easy Guessing 0.232 0.17 0.02 Performed well Carelessness 0.926 0.10 0.01 Performed well Table 2 shows that the discrimination parameter had a mean of 2.19 and a standard deviation of 1.29 which implies that the item discrimination level was very high. The mean and standard deviation for the difficulty parameter was -0.45 and 1.64 which suggested that the items exhibited medium difficulty. The guessing parameter had mean and standard deviation of 0.23 and 0.17 suggesting that the items were good, and the mean and standard deviation values of 0.93 and 0.01 for carelessness indicate that items performed well. Discussion The findings of the study revealed that the items of the National Business and Technical Education Board 2022 May/June Economics discriminated very highly among the lower and higher ability examinees, using the 4-parameter item response parameter model. This supports the findings of Pardede et al. (2023). The findings from the study also showed that the items of the National Business and Technical Education Board 2022 May/June Economics were not too hard for the examinees. This suggests that the items were of medium difficulty. These findings aligned with DeMars (2010) who suggested that items of medium difficulty should be used in large numbers in a test. Another revelation from the study was that both the guessing and carelessness parameters performed well in the test. This corroborated the views of Barnard-Brak et al. (2018), who suggested that the guessing and carelessness parameters, which have values of 0.25 and at least 0.90, can descriptively be said to be good. It also aligned with the findings by Pardede et al. (2023). The findings indicate that the NABTEB Economics examination successfully distinguished between high-ability and low-ability students while remaining accessible to most candidates. This outcome carries several important implications. For examination bodies, this validates the reliability of the test but also calls for continued refinement of item construction to minimize guessing and reduce careless errors, even among top-performing students. For teachers and learners, the results highlight the need to balance subject mastery with effective test-taking skills such as accuracy, time management, and concentration. The medium difficulty of the items suggests alignment between classroom teaching and assessment in the South-South, yet the occurrence of careless responses signals the importance of strengthening metacognitive and self-regulation strategies. Policymakers should integrate critical thinking and problem-solving into the curriculum while providing extra support for disadvantaged learners, and researchers are encouraged to adopt the 4PLM as it offers a more holistic assessment of test quality than Classical Test Theory. Taken together, the parameters of discrimination, difficulty, guessing, and carelessness not only