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Development and Validation of Diagnostic Economics Test for Secondary Schools

A diagnostic test in economics to aid the teachers determine student’s specific weak content areas was developed and validated. Five research questions guided the study. Preliminary validation was done by two experienced teachers in the content area of secondary economics and two experts in test construction. The pilot testing was conducted for grammatical checking and compatibility bench marking while the test was try-out tested for item analysis. The overall number of test items was 83. The test difficulty indices ranged from 0.24 to 0.79 and discrimination indices were within 0.22 to 0.65. The content validity index for the 83 items was 0.76 and the Kappa statistic reliability value of the test was 0.83. The test was found to be of good quality, valid and highly reliable. The test is therefore recommended for identifying specific mastered and least learned content areas in economics in Nigeria, South Africa and other countries with emerging economies.


Introduction
Economics, a science concerned with how individuals, businessmen and governments make use of limited resources at their disposal (Chudi, 2013), plays a key role in the future progress of human kind. The contributions of economics have in no small measure been of immense benefit to the world in general. According to Chudi (2013), economics puts both leaders and citizens in a better position to understand economic problems and consequently proffer solutions to them. Economics as a subject is part of the senior secondary school (SSS) curriculum and it covers the basic aspects of human lives. The benefits of economics can only be realized if the students who are taught economics understand the basic concepts.
Despite the advantages of economics, there exist incessant failure of students in economics' examinations (Adu, Ojelabi & Hammed, 2009). For example in Nigeria, available statistics from West African Examination Council (WAEC) Chief Examiners' reports (1999, 2001, 2003, 2004, 2006, 2007, 2008, 2011 and 2012) on senior secondary school students' achievement in economics revealed poor performance. In the report sheet, the chief examiners identified some problems that cause students' poor performance in economics including poor coverage of the syllabus, poor understanding of concepts taught, inability to draw and label demand curves properly, inaccurate measurement of diagram outlines and poor manipulations of demand equations. In 2010 and 2012, the chief examiners' reports also showed that students' weaknesses were generally observed to fall into two content areastheory of demand and theory of cost. Specifically the students' weaknesses were categorized as: a) Calculations-majority of the students/candidates were unable to calculate total cost, marginal cost, price elasticity and quantity. A question in price elasticity of demand was attempted by very few candidates, in which they could not adequately calculate the price elasticity of demand.
The first sample for the test try-out consisted of 600 randomly selected students from 15 Nigerian' schools in different education zones. The schools were selected through disproportionate stratified random sampling while the students were selected through proportionate stratified random sampling. The second sample for establishing the reliability consisted of 100 students from 4 schools in Nigeria. These four schools volunteered to participate in the test re-tests study. Then from each of the four schools twenty five students were selected.
The content area of a diagnostic test, according to Alderson (2005), needed to be more specific and focused than that of a proficiency test. This was necessary, because a diagnostic test requires a detailed exhaustive analysis of the content area. The content area of this study covered theory of demand, theory of cost/revenue and market structure. These three topics were also the topics pointed out by the WAEC Chief Examiners' reports in 2010 and 2012 as the weak areas of students.
The table of specifications of the test consisted of 34, 25 and 24 items of theory of demand, theory of cost/revenue and market structure respectively. Various units of the test content were listed along the rows while different educational objectives to be tested were listed along the columns. during the pilot testing, the test was subsequently arranged in three parts of content area to help the students concentrate on a single area of content at a time. This was an improvement/enhancement to the preliminary (pilot) version of the test, where the items were grouped according to objective levels.
The test try-out: The test try-out occurred during first term of 2014/2015 academic session when subject teachers and the students had completed the teaching and learning of the test content. Before the administration of the test try-out, the researcher made personal visits to secure permission from the concerned principals and economics subject teachers. The test was administered to 600 SS3 economics students of the sampled schools. The test try-out was for the purpose of item analysis. That is, to distinguish the difficulty, discrimination and distracter indices of the test items.
The researcher, with the help of the economics teachers of the participating schools, administered the test to the students.
Item analysis: Item analysis was conducted on the test items mainly to ensure the quality of the items. It involved seven (7) main steps.
Step 1-Identify the higher and lower achievers. The total number of scripts collected and marked was (600). The students' marked scripts were arranged in the order of magnitude with respect to their scores. Then 33% of the scripts from the top and the same number of scripts from bottom were taken as the higher and lower achievers respectively (Author and Collaborator, 2010). The two groups were used in processing test responses.
Step 2-Process test responses. The researcher for each item, counted the number of students in each group who chose each alternative or omitted the item completely.
Step 3-Calculate item difficulty index. The difficulty index of each item was calculated using the formula.

H L 2N
Where, H is the number of students in the higher achiever group who answered the item correctly.
L is the number of students in the lower group who answered the item correctly.
N is the total number of students in both the higher and lower groups.
Step 4-Calculate item discrimination index. The discrimination index of each item was calculated using the formula.

H L N
Where, H, L and N retain their meanings.
Step 5-Calculate the distracter indices. The distracter indices of each item were calculated using the formula.

L H N
Where, H represents those who failed the item in the higher group, L are those who failed the item in the lower group, and N is the total number of students in higher and lower group.
Step 6-Selection of good items. An item was considered good for inclusion in the final output of the test if it had difficulty index of 0.30 to 0.70, discrimination index greater than 0.20 and a positive distracter index. However, items with appropriate difficulty indices but with discrimination indices of less than 0.20 were not accepted as good. Also items with appropriate discrimination index but have difficulty index of less than 0.20 or more than 0.80 were rejected (insert Table 2 around here). This according to Author and Collaborator (2010) is to ensure the content validity of the test.
Step 7-Revising and retesting of rejected items. To preserve the validity of the entire test and to maintain the total number of items all items that were rejected were revised or replaced. Revised or replaced items were re-administered to the target examinees (SS3 economics students), and its test responses were used to re-check the items' difficulty and discrimination indices for final verification of whether these items are to be retained or not.
Retesting of the revised and replaced items was necessary in preparation for the final version of the diagnostic test in order not to omit any learning point (Ceniza & Cereno 2012;Izard 2005). The item difficulty and discrimination indices of the revised and retested items met the criteria for accepting item as good (see Table 3).
Determining the cut off score: In order to determine the bases of the cut-off score, the DET was given to three experienced teachers in economics to critically examine and determine the minimum number of items in the test a typical student should answer correctly before being classified as a master of the content. The first teacher suggested 60 items; the second teacher suggested 58 items while the third teacher suggested 56 items out of 83 items of the test. The average of 60, 58 and 56 is 58. The percentage of 58 out of 83 is 70 percent. Therefore, students who scored 70 percent of the DET correctly were classified as having mastered the content of the test. That is, 58 items out of the 83 items of the DET. Seventy percent (70%) each of 34 items of theory of demand, 25 items of theory of cost/revenue and 24 items of market structure gave 24,17 and17 items respectively. Classification of students as masters or non-masters of the DET was necessary for the estimation of DET reliability (Onunkwo, 2002;Rivera, 2007).

Assembly of final test:
The DET was arranged in three parts of content areas. The first part contains 34 items constructed from the content area of theory of demand. The second part contains 25 items from the content area of theory of cost/revenue, while the third part covers content area of market structure with 24 items.

Validity of the test
The test validity was ensured by computing the content validity index (CVI) of the DET. The final version of the DET was given to two content specialists on request to independently rate the relevance of each item to the type of content and behavior it purported to measure. The ratings were done in a four-point rating scale of Not Relevant = 1, Somewhat Relevant = 2, Quite Relevant = 3, Very Relevant = 4. The data yielded from these two raters were used to compute the inter-rater agreement statistics (i.e. Po, Pc and K). The higher the value of CVI the more valid the test was.

Test reliability
Test-retest reliability measurements were employed in this study to ensure the temporal stability of the DET.
The final version of the test was administered twice to 100 SS3 economics students from four secondary schools in Anambra State that willingly volunteered to participate in the test re-test study (see Figure 1). Three weeks after the first administration of the test, a second administration with the same items was administered to the same 100 SS3 economics students for the purpose of comparing the proportions of the students who showed mastery of the content area being measured in the first and second administrations. A student was classified as a master of the content area of the test, when their score was equal to or above the cut off score (70%). From the data obtained, po, pc, and k statistics were computed. The higher the value of k, the more reliable the test was.
Proportion of observed agreement (po) = a+b.
Proportion of agreement uncontaminated by chance (K) = Po -Pc

Results
The results of the study were presented and analyzed below.

Research question 1 and 2
The difficulty and discrimination indices of the DET gotten after the item analysis of the test try-out are shown in Table 2. The difficulty and discrimination indices for each item suggested that sixty eight (68) items be retained while item numbers 8, 10,15,24,31,33,37,43,65,66,70,76,77,81 and 83 be rejected. The rejected items were either revised or replaced and re-tested. Table 3 shows the item difficulty and discrimination results after retesting of the revised and replaced items.

Research question 3
The distracter indices of the DET obtained after item analysis are presented in Table 4.

Research question 4
Content validity index (CVI) of the DET was computed to determine the validity of the DET. The inter-rater agreement and content validity index of the DET were computed and presented in Table 5.  Table 5, CVI of DET is 0.7590. This is the content validity index (CVI).

Research question 5
The reliability value for the three topics (Theory of Demand, Theory of Cost/Revenue and Market Structure) were computed separately and presented in Table 6. As observed in the summary results in Table 6, the reliability value for section A (theory of demand) of the test was 0.72, the reliability for section B (theory of cost/revenue) was 0.60 and the reliability for section C (market structure) was 0.76. The single K value for the DET was 0.83. This was the Kappa statistics (k) reliability value.

Discussion
The economic events and economic issues remain a significant burden worldwide. This is because the leading economies are facing debt crises, recessions and downturns in the growth of the economies. The exchange rate for foreign exchange are constantly fluctuating. Consumers are confronted on a daily basis with the rising food prices and fluctuating oil prices. But despite the attention that has been given to economics in the recent years, the overwhelming findings remain that students are unfamiliar with economics and basic economic concepts (Fourie & Krugell, 2015). Fourie and Krugell (2015) and Chudi (2013) posit that if the students are familiar with the basic concepts of economics, it may directly affect positively in improving the economy. A dire challenge faced by Nigeria, South Africa and many other countries with emerging economies is the economics teachers' lack of diagnostic test to aid the teacher in identifying students' specific least learned content areas of economic concepts. The discourse about the potential solution to this issue revolve around diagnostic test.

Item Difficulty and Discrimination Indices of the DET
As observed in Table 2, 68 item were found to be good with appropriate difficulty and discrimination indices. Items numbers 24, 31, 37, 70, 76 and 77 had difficulty indices that were less than 0.20. This means that they were very difficult items. No item in the current study was found to be very easy.
Table 2 also shows that, three (10, 66, 83) items had negative discrimination indices. This indicated that low ability students performed better on those items than high ability students as previously described by Author and collaborator (2010). Such items discriminated but in the negative (wrong) direction. Item number 24 had a zero (0.0) discrimination index. This implied that equal number of students in the high ability group and low ability group correctly answered the items. Such items did not discriminate. On the other hand, 11 items (8,15,31,33,37,43,65,70,76,77 and 81) as seen in a study by Onunkwo (2002). This study in Nigeria, had low but positive discrimination values (0.0 ≤ 0.20). This implied that students who incorrectly answered these items also scored high on the test overall, while students who correctly answered the items scored low on the test overall as suggestions.
Similarly in South Africa, the quality of candidates' performance in economics is disappointing when compared to previous years. It does appear that the 2015 NSC diagnostic report for economics was considered to help the candidates in general and the weaker learners especially to take advantage of the low difficulty questions that comprised of about 30% of the questions (South African National Senior Certificate Examination 2015).
Items that had poor difficulty and discrimination indices were retested. This retesting process was to ensure that no learning points were omitted in the final version of DET as suggested by Ceniza and Cereno (2012).

Distracter Indices of the DET
The distracters of the items after the test try-out revealed that 59 items have 3 positive distracter values, 19 items had 2 positive distracter values and 5 items had only one positive distractibility index. The positive value indicated that the distracters are good. It also implied that more of the students in the low ability group chose the distracter than those in the high ability group. It was also observed in Table 4 that some distracter indices were either negative or zero. The negative value of the indices indicated that the distracters were bad or poor. This showed that they were chosen by more of the students in the high ability group than those in the low ability group. The zero distracter indices revealed that these distracters did not distract or confuse any student. This means that, the distracters with zero values made no differentiation in the amount of confusion it posed to student in the two ability groups. The distracters with negative or zero values were reviewed then replaced for improvement and ease of the test takers.
Other items were also improved by restructuring the manner of questioning to lesson confusions in answering.

Validity of the DET
Validity of the test was done by matching the test items from the objectives and presenting the whole test to two experts in the test construction and two experienced teachers in the content areas of secondary economics for item review. These experts guaranteed that the instrument had strong content validity in which each item represented the content area being investigated, rather than asking unrelated questions.
According to findings of this study, in Table 5, the values of Po and K were 0.8193 and 0.3361 respectively. This indicated that the type of content and component behaviors of the test were clearly stated, there was no need for refinement and the raters understood the rating scale. Also from Table 5, the content validity index of test was 0.7590. This implied that 75.90% of the test items were rated Quite Relevant or Very Relevant (i.e. 3 or 4) to the type of content and behaviors being measured, by the two content specialists. This implied that the test was valid.

Reliability of the DET
As observed in the summary results in Table 6, the proportion of agreement uncontaminated by chance (k) for theory of demand, theory of cost/revenue and market structure were 0.63, 0.60 and 0.76 respectively. The single/general k value was 0.83. This implied that 83% of the observed agreements in the decisions made by the two administrations of the test were uncontaminated by chance. That is, there was 83% certainty of the consistency of the test in classifying students into mastery states. This implied that the test was very reliable. A previous study on reliability by Ceniza and Cereno (2012), came to a similar conclusion. According to Ceniza and Cereno (2012), the reliability coefficient within the range of 0.81 to 1.0 indicated high reliability, 0.61 to 0.80 signified a moderate reliability, 0.41 to 0.60 signified fair reliability, 0.10 to 0.40 signified slight reliability, and less than 0.10 signified no reliability. Therefore, the test reliability was high.
This study provides valuable useful findings in the field of economics education, since it is the first conceptual diagnostic test in economics in Africa, to the best of our knowledge. However, some limitations are attributed to this study. First, the level of performance of the students was low, and it was possible that more studious students would have performed differently. Second, the study did not have any control group, because the researcher could not access group with similar characteristics.

Conclusions
The results of this study reflect that the diagnostic test being developed is valid. The final output of the test showed that the overall test difficulty was within the range of 0.24 to 0.79. As demonstrated from findings in this study and according to Ceniza and Cereno (2012), the diagnostic test therefore has a moderate level of difficulty. The discrimination indices were within the range of 0.22 to 0.65. This according to Winarni (2002) implies a moderately discriminating instrument. With the CVI at 0.7590, the developed diagnostic economics test (DET) shows good validity. Also, the K values at 0.63, 0.60, 0.76 and a general reliability of 0.83, indicate that the currently developed diagnostic economics test (DET) indicates high reliability. Thus, it could be concluded that the diagnostic test developed in this study is valid, highly reliable and fair. Hence, this test is of good quality, validated, reliable and can now be used in assessing students' specific learning strengths and weaknesses in secondary economics. It is an instrument that can measure the desired trait of secondary school economics in Nigeria, South Africa and other countries.

Recommendations
Based on the findings of this study, the researchers' recommend that the diagnostic economics test (DET) be used by the students to reinforce and improve their learning. Teachers should also be encouraged to use DET for identifying the least learned content areas of their students and to effect remediation promptly. School heads should use the DET as an evaluative tool for preparing the students for both internal and external examinations. School authorities should use the DET to monitor the teachers and their mastery of the subject as well as their coverage of syllabus. The DET should be adopted by government and used in all secondary schools as a tool to identify students' specific mastered and least learned content areas in (theory of demand, theory of cost/revenue and market structure) economics while teaching the students. The researchers finally recommend the instrument for use by future researchers interested in developing diagnostic tests. Similar test needs to be developed in other African countries including other countries of the world using specific country-based content areas.

1.
An effective demand is defined as a) need backed up with the necessary ability but without the willingness to pay b) desire that is not backed up by the required money to pay for it c) want backed up with the desire and willingness to pay at a particular time. d) goods required at a price and with the willingness to pay at a particular time.

2.
A demand schedule is described as a table containing a) the price and quantity of a commodity at a time b) the relationship between price and quantity demanded of a commodity c) the relationship between price and quantity supplied of a commodity d) the quantity of goods the consumer is willing to buy.

3.
The type of demand that exist between torch light and battery is known as _________ demand. The demand for beans is given by the function Q= 36 + 0.4P. When P is price in naira and Q is quantity. Use the above equation to answer question 16 and 17.