Inter national J our nal of Ev aluation and Resear ch in Education (IJERE) V ol. 5, No. 3, September 2016, pp. 235 245 ISSN: 2252-8822 235       I ns t it u t e  o f  A d v a nce d  Eng ine e r i ng  a nd  S cie nce   w     w     w       i                       l       c       m     Design and Implementation of P erf ormance Metrics f or Ev aluation of Assessments Data Irfan Ahmed * and Arif Bhatti * * Colle ge of Computers and Information T echnology , T aif Uni v ersity , Saudi Arabia Article Inf o Article history: Recei v ed July 21, 2016 Re vised August 10, 2016 Accepted August 16, 2016 K eyw ord: assessment e v aluation higher education student outcomes ABSTRA CT Ev ocati v e e v aluation of assessment data is essential to quantify the achie v ements at course and program le v els. The objecti v e of this paper is to design performance metrics and respecti v e formulas to quantitati v ely e v aluate the achie v ement of set objecti v es and e x- pected outcomes at the course le v els for program accreditation. Ev en though assessment processes for accreditation are well docum ented b ut e xistence of an e v aluation process is assumed. This w ork pro vides performance metrics such as attainment, student achie v e- ment, and x-th percentile for the e v aluation of assessment data at course and program le v el. Then, a sample course data and uniformly distrib uted synthetic data are used to an- alyze the results from designed metrics. The primary findings of this w ork are tw ofold: (i) analysis with sample course assessment data re v eals that qual itati v e mapping between marks obtained in assessments to the defined outc omes is essential for meaningful re- sults, (ii) analysis with synthetic data sho ws that higher v alues of one metric does not imply higher v alues of the other metrics and the y depend upon the obtained marks dis- trib ution. In particular , for uniformly distrib uted marks, achiev ement < attainment for meanO f U nif or mD istr : < av er ag eM ar k s < passing T hr e s ho l d ( ) . Authors hope that the articulated description of e v aluation formulas will help con v er gence to high quality standard in e v aluation process. Copyright c 2016 Institute of Advanced Engineering and Science . All rights r eserved. Corresponding A uthor: Irf an Ahmed Colle ge of Computers and Information T echnology , T aif Uni v ersity , T aif-21974, Saudi Arabia i.ahmed@tu.edu.sa 1. INTR ODUCTION An y educational program starts with a mission statement, objecti v es, and the program or student outcomes. Mission st atement describes t h e broad goals of the program. Program educational objecti v es (PEO) are statements re g arding the e xpected positions that students may attain within a f e w years of graduation, whereas Student outcomes (SO) are the e xpected skills at the time of graduation. SOs are directly ti ed with the course learning outcomes (CLO) which are the e xpected skills of a student at the end of the course in a program; more formal d e finitions can be found at [1]. Assessment and e v aluation are inte gral parts of the quality assurance, continuous impro v ement, and the accreditation. Assessment is defined as one or more processes that identify , collect, and prepare the data necessary for e v aluation. Ev aluation is defined as one or more processes for interpreting t he data acquired through the assessment processes in order to determine ho w well SOs are being attained [1]. Man y authors ha v e published their w ork on continuous impro v ement, data collection and assessment strate- gies b ut there is no w ork in the literature that focuses on the e v aluation of the assessment data at course and program le v els. A complete procedure for ABET accreditat ion for Engineering programs at Qassim Uni v ersity has been pre- sented in [2]. It gi v es the detail ed implementation of the continuous impro v ement process, ef fecting major changes in the educational plan, curricular content, f acilities, acti vities, teaching methodologies, and assessment practices. But this paper does not go into the details of e v aluation process. Olds et al. [3] e xamine man y possible assessment methods in comply with ABET cr iteria. The y cate gorize assessment methodologies into descripti v e and e xperimental studies, J ournal Homepage: http://iaesjournal.com/online/inde x.php/IJERE       I ns t it u t e  o f  A d v a nce d  Eng ine e r i ng  a nd  S cie nce   w     w     w       i                       l       c       m     Evaluation Warning : The document was created with Spire.PDF for Python.
236 ISSN: 2252-8822 and pro vide v arious ef fecti v e types of assessme n t s for engineering education without the insights of e v aluation strate- gies. An o v ervie w of program le v el assessment for continuous impro v ement is gi v en in [4]. It e xplains assessment process in v e steps: from the identification of educational objecti v es to the measurement of assessment data b ut none of these step pro vides the e v aluation methodology . A complete assessment process from writing good learning out- comes, mapping between course le v el outcomes and program le v el outcomes, and data collection using v arious direct and indirect assessment methods is illustrated in [5] and [6]. In [7] authors present an assessment plan and continuous impro v ement process at James Madison Uni v ersity . The y ha v e introduced course assessment and continuous impro v e- ment (CA CI) reports at course-le v el and student outcomes summary report (SOSR) at program-le v el. This paper sho ws some sample reports and assessment templates b ut does not discuss the e v aluation process. A web-based tool has been introduced in [8] for outcome-based open-ended and recursi v e hierarchical quantitati v e assessment. This quantitati v e assessment is used to structure outcomes and measures into a le v eled hierarch y , with course outcomes at the bottom and more general objecti v es at the top. A general curriculum outcome (GCO) layer has been added between course’ s outcomes and program or student’ s outcomes. In [9] both direct and indirect measures are used to collect and analyze data to assess the attainments of the student outcomes. T o ensure data inte grity , a set of rubrics with benchmarks and performance indicators at both the program and curriculum le v els are de v eloped. Each outcome has been assessed for dif ferent le v els (introductory , be ginning, de v eloping, proficient, e x emplary) and from dif fere n t sources. The article [10] presents discussions on writing learning outcomes a nd to assess soft skills in engineering education. The paper [11] describes the assessment techniques and the mapping of CLO to SO without the insight of e v aluation process. A case study [12] describes the features that contrib ute to assessment qualit y at the programme, course and task le v el. This case study has a particular focus on the technical such as task analysis and task relationship patterns. Another case study [13] presents a health science program reform and e v aluation. It discusses potential for e v aluation to es- tablish responsi v e communication between students, teaching staf f and programme administrators, ensuring a match between the intended, implemented and attained curriculum. A web-based Instrumental Module De v elopment System (IMODS) for outcome-based course design has been presented in [14]. It defines the learning outcomes, mapping, and assessment process b ut the e v aluation of assessment data is not e xplained. Ibrahim et al. [15] w ork is close to our proposed design. It consists of a web-based tool to measure the mean, standard de viation, and the achie v ement through course assessments’ data. The y formulate these e v aluation metrics by assuming normally distrib uted dataset only . These formulas cannot be applied to other distrib utions that may occur in real practice. None of these w orks ho we v er , pro vide the detail of general e v aluation metrics and their use in course and program assessment. The rest of the article is or g anized as follo ws: the ne xt section describes the performance metrics formulation, course le v el e v aluation based on performance metrics are e xplained in section III, analysis and interpretations are discussed in section IV and conclusions are dra wn in section V . 2. PERFORMANCE METRICS FORMULA TION Let A i;j ;m be the marks obtained by student m in question j of assessment i (home w ork, assignment, quiz, midterm, or final etc). Here i can tak e the v alues, i = 1 ; 2 ; :::; I , j can tak e the v alues j i = 1 ; 2 ; :::; J i , and m can tak e the v alues m = 1 ; 2 ; :::; M . I ; J i ; M are the total number of assessments, questions in assessment i , and the students, respecti v ely . F or quantitati v e analysis, question is a basic unit of computation for assessment. A v erage score of question j in assessment i that has M students is gi v en by B i;j = 1 M M X m =1 A i;j ;m (1) B i;j can be written in v ector form as ~ B = B 1 B 2 : : B I 1 L (2) P assing threshold (PT) could be absolute, relati v e or composite [8], such that the PT of question j in assessment i is gi v en by one of the follo wing: P T i;j = Q tot i;j (3) P T i;j = B i;j (4) P T i;j = min f B i;j ; Q tot i;j g (5) IJERE V ol. 5, No. 3, September 2016: 235 245 Evaluation Warning : The document was created with Spire.PDF for Python.
IJERE ISSN: 2252-8822 237 where Q tot i;j is the maximum or total marks of question j in assessment i and 0 < < 1 . The maximum, minimum, standard de viation, and x-th percentile of question j in assessment i are calculated as A i;j ;max = max m A i;j ; : A i;j ;min = min m A i;j ; : A i;j ;std = stdev A i;j ;m A i;j ;per = per centil e ( A i;j ; : ; x ) Course learning outcomes describe what students are e xpected to learn in a course. A mapping between CLO and assessment questions is required to compute the attainment of the course CLOs. If a course co v ers N number of CLOs then n th CLO is written as C LO n ; n = 1 ; 2 ; :::N . The three dimensional matrix A is con v erted into a tw o dimension matrix ~ A as ~ A = A T 1 A T 2 : : A T I (6) where A T i is the transpose matrix of i th assessment matrix A J M . Matrix ~ A has the dimension M L , where M is the total number of students and L = P I i =1 J i is a total number of questions in all assessments. CLO to SO mapping matrix is by CS = 2 6 6 6 6 4 C S 1 ;a C S 1 ;b C S 1 ;k C S 2 ;a C S 2 ;b . . . . . . . . . . . . . . . C S N 1 ;k C S N ;a C S N ;j C S N ;k 3 7 7 7 7 5 (7) The matrix element C S n;a is a v ariable. C S n;a > 0 if C LO n maps to SO a , otherwise C S n;a = 0 . A non-zero v alue is a rele v ance of the CLO to compute the SO. It can tak e v alues 1,2,3, for low , moder ate , and high rele v ance, respecti v ely . Similarly , the CLO to question mapping is gi v en by the follo wing matrix CQ = 2 6 6 6 6 4 C Q 1 ; 1 C Q 1 ; 2 C Q 1 ;L C Q 2 ; 1 C Q 2 ; 2 . . . . . . . . . . . . . . . C Q N 1 ;L C Q N ; 1 C Q N ;L 1 C Q N ;L 3 7 7 7 7 5 (8) Ro ws of abo v e matrix contain binary v ariables C Q n;l that represent the m apping of n th CLO with question l , where l maps to j th question of an assessment i . C Q n;l = 1 if C LO n maps to question l . Student marks in assessment questions are used to compute ho w well the students ha v e done and what per - centage of students ha v e met a certain criteria. Ev ery question contrib utes to one or more CLOs and e v ery CLO contrib utes to one or more student outcomes (SO) as sho wn in (8) and (7) respecti v ely . 2.1. CLO Attainment This metric is about ho w well the students ha v e done, in percentage, for each CLO. Attainment of a CLO is deri v ed from the a v erage marks obtained di vided by total marks for all questions that maps to the CLO. Let Q tot i;j be the maximum or total marks of question j in assessment i . In general, for assessment i , Q tot i = Q tot i; 1 Q tot i; 2 : : Q tot i;J (9) and ~ Q tot = Q tot 1 Q tot 2 : : Q tot I 1 L (10) Then, the percentage of CLO attainment for n th CLO is gi v en by attainmentC LO n [%] = P L l =1 ~ B l C Q n;l P L l =1 ~ Q tot l C Q n;l 100 (11) The operator is used for element-wise multiplication. Design and Implementation of P erformance Metrics for Evaluation ... (Irfan Ahmed) Evaluation Warning : The document was created with Spire.PDF for Python.
238 ISSN: 2252-8822 2.2. CLO W eightage Inf ormation In order to get meaningful results, one should design the CLOs such that there is a uniform distrib ution of the marks o v er CLOs in questions to CLO mapping. F or e xample, if a course contains four CLOs then, ideally , each CLO should get 25% weightage. The ideal case of uniform distrib ution of marks o v er the CLOs is seldom realized. In these situations, the CLO weightage information renders a f air picture of % CLO attainment. The percentage weightage of n th CLO is gi v en by W eig htag eC LO n = X i P J i j w ( C Q n;j ) Q tot i;j A tot i w ( A i ) (12) where w ( C Q n;j ) is the weight of C LO n in question j , w ( A i ) is the weight of assessment i , and A tot i is the total marks of assessment i . 2.3. Student Achie v ement per CLO Student Achie v ement per CLO is defined as the percentage of student s who are abo v e the e xpected le v el as sho wn in (5). Expectation or tar get is a design parameter , one choice of the tar get could be min( B i;j ; 0 : 7 Q tot i;j ) , i.e., the minimum of the a v erage obtained marks and the 70% of the total marks [8]. It counts the number of students who met the criteria by comparing each student marks in a question j of an assessment i . If the marks obtained A i;j ;m are greater than the passing threshold P T i;j , then it increments the counting v ariable C P S (count pass student) by 1 . Finally , C P S i;j or C P S l 1 contains number of passed students for each question j in assessment i . Therefore, the a v erage student achie v ement per CLO is gi v en by S A C L O n = P I i =1 1 M i P J i j =1 C P S i;j C Q n;i;j Q tot i;j P I i =1 P J i j =1 Q tot i;j C Q n;i;j (13) where M i is the number of students that participated in the assessment i . 2.4. Student P er ception of CLO Attainment A course surv e y is conducted at the end of each semester to g auge students’ perception of ho w well the CLOs were co v ered in the course. It is the a v erage of CLO perception from the students. F or each CLO, students pro vide their i nput on the scale of 1 5 where 1 means CLO is not achie v ed and 5 means CLO is achie v ed completely . Summary of responses is gi v en in follo wing matrix. SC = 2 6 6 6 6 4 S C 1 ; 1 S C 1 ; 2 S C 1 ;N S C 2 ; 1 S C 2 ; 2 . . . . . . . . . . . . S C M 1 ;N S C M ; 1 S C M ;N 1 S C M ;N 3 7 7 7 7 5 (14) Student’ s perception of n th CLO attainment is gi v en by S E C L O n = 1 M M X m =1 S C m;n (15) 2.5. x-th P er centile Marks per CLO x-th Percentile Marks per CLO is defined as the weighted a v erage of x th percentile marks di vided by total marks of the questions that map to particular CLO. Let xP i;j be the x-th percentile marks of question j in assessment i . In general, for assessment i we ha v e xP i = xP i; 1 xP i; 2 : : xP i;J (16) and ~ xP = xP 1 xP 2 : : xP I 1 L (17) 1 C P S l is a ro w v ector form of C P S i;j , similar to (6) or (2) IJERE V ol. 5, No. 3, September 2016: 235 245 Evaluation Warning : The document was created with Spire.PDF for Python.
IJERE ISSN: 2252-8822 239 T able 1. Basic V ariables to compute e v aluations metrics for a sample course. CLOs and questions mapping (8) is sho wn in first tw o ro ws midterm Quiz1 Quiz4 Quiz3 HW1 Qui z2 Final Class partici pation CLOs Co v er ed 1,2,3 1 2 3,4 1 6 5 2 2 3 3 3 2 5 5 5 6 6 1-6 Question No. 1 2 3 4 1 1 1 1 2 3 4 5 1 1 2 3 4 5 1 Question Marks 8 8 8 8 4 4 4 0.4 0.4 0.4 0.4 0.4 4 5 10 10 10 10 5 Actual A v erage 5.22 6.6 6.99 6.69 3.25 3.664 3.12 0.4 0.4 0.4 0.352 0.128 3.68 1.9 8.3 7.2 6.1 9.3 4.7 P assing Threshold (PT) 5.22 5.6 5.6 5.6 2.8 2.8 2.8 0.28 0.28 0.28 0.28 0.128 2.8 1.9 7 7 6.1 7 3.5 No. of Students Abo v e PT 6 9 10 9 9 10 6 10 10 10 8 4 9 7 6 4 4 10 10 Minimum Marks 1.2 4.2 6 4.5 1.3 3.04 2.4 0.4 0.4 0.4 0.16 0 2.4 0 5 5 1 8 4.27 Maximum Marks 7.35 7.5 7.5 7.5 4 3.84 3.84 0.4 0.4 0.4 0.4 0.32 4 4 10 10 10 10 4.9 Standard De viation 1.78 0.95 0.62 0.92 0.78 0.25 0.47 0.00 0.00 0.00 0.10 0.12 0.44 1.37 1.95 1.60 2.91 0.64 0.21 50th Percentile Marks 5.85 6.75 7.35 6.9 3.3 3.76 3.2 0.4 0.4 0.4 0.4 0.08 3.84 2 9.5 6.5 5.5 9 4.79 Then, the a v erage percentage x-th percentile marks per CLO is gi v en by xP er centil eC LO n = P L l =1 xP l C Q n;l P L l =1 Q tot l C Q n;l (18) 2.6. SO Attainment By using CLO-SO mapping in (7), cours e le v el SO assessment can be achie v ed. SO attainment for an SO is computed from the CLO attainment of all CLOs that map to t he SO. SO attainment is defined as the weighted a v erage of CLOs attainment (in %). attainmentS O n = P i 2C n attainmentC LO i w i P i 2C n w i (19) where C n is the set of CLOs that map to S O n and w i is the weight (or rel e v ance) of i th mapping between CLO and SO. 2.7. Student Achie v ement per SO It is defined as weighted a v erage of student achie v ement of CLOs (in %) that map to a particular SO. S A S O n = P i 2C n S A C LO i w i P i 2C n w i (20) 2.8. Student P er ception of SOs Attainment Student perception of SOs attainment gi v es an indirect measurement of SO attainment. Thi s metric is deri v ed from student perception of CLOs attainment in (15) and the CLO-SO mapping in (7). S E S O n = P i 2C n S E C L O i w i P i 2C n w i (21) 2.9. x-th P er centile per SO x-th Percentile per SO uses CLO-A v erage x-th Percentile % marks with CLO-SO mapping in (7). xP er centil eS O n = P i 2C n xP er centil eC LO i w i P i 2C n w i (22) 3. COURSE LEVEL PERFORMANCE EV ALU A TION Direct assessment of an academic program is performed by e v aluation of courses in the study plan. If not all, at least a selected subset of the courses is required to find out program’ s success le v el. Pre vious section presented formal formulations of the performance metrics that can be used in course e v aluation. This section discusses an implementation of thes e metrics in e v aluation of a sample course. The section starts with setup required for e v aluation follo wed by e v aluation results and concludes by discussing issues and concerns. Design and Implementation of P erformance Metrics for Evaluation ... (Irfan Ahmed) Evaluation Warning : The document was created with Spire.PDF for Python.
240 ISSN: 2252-8822 T able 2. Mapping of Course Learning Outcomes (CLOs) to Student Outcomes (SOs) (7) as Course Assessment Matrix CLO a b c d e f g h i j k 1 2 2 2 1 1 3 3 4 2 1 5 3 2 2 6 3 3 2 T able 3. Computation of SO attainment from CLO attainment using table 2 CLO-SO mapping CLO a b c d e f g h i j k 1 79.08 2 82.91 82.91 82.91 3 78.78 4 87.62 87.62 5 74.18 74.18 74.18 6 81.94 81.94 81.94 SO attainment 79.68 79.68 79.94 87.62 82.91 87.62 74.18 W eighted SO attainment 79.27 79.52 79.77 87.62 82.91 87.62 74.18 Rele v ance 3 2 3 2 1 1 2 3.1. Course Setup f or Ev aluation Course e v aluation is computation of performance metrics from basic v ariable of the course and perform analysis. T o compute metrics defined in section II from collected data, each course must ha v e well defined CLOs, CLO to SO mapping as in (7), CLO to question mapping in each assessment as in (8), and passing threshold as defined in (5). T able 1 sho ws basic v ariables of a sample course. First tw o ro ws sho w mapping between CLOs and questions for all assessments conducted in t he course. T able 2 sho ws mapping between CLOs and SOs defined by the course designer . A numeric v alue in a cell represents a relationship be tween a CLO and an SO. A v alue of 1, 2, or 3 indicates that a CLO addresses an SO slightly , moder ately , or substantively . P assing threshold is set to min( av g ; 70%) , which is used in computation of student achie v ement per CLO (13) and student achie v ement per SO (20). 3.2. P erf ormance Ev aluation This section presents computed v alues of metrics defined in section II for the sample course. 3.2.1. CLO Attainment CLO attainment for the sample single section course is sho wn in Figure 1. CLO attainment quantifies the student attainment le v el of particular CLO through the perc entage marks allocated to that CLO. Since this is a per - centage v alue of a v erage marks obtained in the questions maps to a particular CLO, therefore, it is necessary to either distrib ute the marks uniformly o v er the CLOs or gi v e an e xplicit e vidence of CLO to marks ratio. 9 5 1 0 0 C L O   8 5 9 0 9 5 A t t a i n m e n t   [ % ] S t u d e n t   7 5 8 0 a c h i e v e m e n t   [ % ] 50th Ͳ t i l % 6 5 7 0 p e r c e n t i l e   %   m a r k s S t u d e n t   perception 6 0 C L O 1 C L O 2 C L O 3 C L O 4 C L O 5 C L O 6 perception   o f   C L O   [ % ] Figure 1. CLO Performance Ev aluation IJERE V ol. 5, No. 3, September 2016: 235 245 Evaluation Warning : The document was created with Spire.PDF for Python.
IJERE ISSN: 2252-8822 241 3.2.2. CLO W eightage The CLO weightage for a sample single section course is assumed as CLO1 15% , CLO2 16% , CLO3 9% , CLO4 5% , CLO5 30% , and CLO6 25% . The CLO attainment and student achie v ement of CLO are based on these weightages. 3.2.3. Student Achie v ement per CLO Student achie v ement per CLO for the sample single section course is sho wn in Figure 1. It is the percentage number of students that meet or e xceed the tar get or e xpectations. There i s an upper limit for the tar get ( 70% ) b ut there is no lo wer limit and it depends upon the a v erage marks. W e can get absolute student achie v ement by fixing the tar get, for e xample, with tar get v alue of 60% . 3.2.4. 50-th P er centile per CLO The 50-th percentile for the sample course is sho wn in Figure 1. It sho ws the percentage median marks for each CLO. 3.2.5. Student P er ception of CLOs Attainment F or each CLO, student perception of CLO attainment can be on the scale of 1 to 5 , 1 mean str ongly disa gr ee to 5 for str ongly a gr ee . Student perception of CLO attainment for the sample course is sho wn in Figure 1. There were 10 students b ut 8 participated in the course surv e y . 3.2.6. SO Attainment Bar graphs for SO attainment are sho wn in Figure 2. These le v els are a v erages of CLO attainments that map to particular SO, therefore, the health of CLO attainments and CLO-SO mapping is critical. 9 5 0 0 1 0 0 . 0 0 8 0 0 0 8 5 . 0 0 9 0 . 0 0 9 5 . 0 0 A v e r a g e   %   S O   a t t a i n m e n t S t u d e n t   7 0 . 0 0 7 5 . 0 0 8 0 . 0 0 a c h i e v e m e n t   o f   S O   [ % ] 5 0 t h Ͳ percentile   % m a r k s 5 5 . 0 0 6 0 . 0 0 6 5 . 0 0 %   m a r k s S t u d e n t   p e r c e p t i o n   o f   S O   a t t a i n m e n t [ % ] 5 0 . 0 0 a b c e h i k a t t a i n m e n t   [ % ] Figure 2. SO Performance Ev aluation 3.2.7. Student Achie v ement per SO Student achie v ement for the sample course is gi v en in Figure 2. This is a deri v ed v alue from CLO achie v e- ments and depicts the percentage number of students achie v ed the set tar get a v eraged o v er the CLOs mapped to that SO. 3.2.8. 50-th P er centile per SO The 50-th percentile per SO v alues are deri v ed from 50-th percentile per CLO. Figure 2 depicts the 50-th percentile or median marks for each mapped SO. 3.2.9. Student P er ception of SOs Attainment The student perception of SOs attainment is sho wn in Figure 2. It is an indirect measurement obtained from the course e xit surv e y where students pro vide their feedback about the CLOs attainment. Design and Implementation of P erformance Metrics for Evaluation ... (Irfan Ahmed) Evaluation Warning : The document was created with Spire.PDF for Python.
242 ISSN: 2252-8822 3.3. Issues and Guidelines Course designer is responsible to establish quality mapping between CLOs and SOs. Course instructor is responsible for CLOs to questions mapping for all assessments. Quality of these mappings ha v e direct impact on the e v aluation results as discussed in rest of this section. 3.3.1. Relationship of Questions, Marks distrib ution and CLOs It has been observ ed that questions to CLO mapping requires uniform marks distrib ution o v er the CLOs. The quantitati v e measurement of CLOs pro vides the baseline data for direct assessment, therefore, questions to CLOs mapping is critical in direct assessment. CLOs should be designed in such a w ay that the y co v er all the core topics (qualitati v e equality) and course assessments should co v er all CLOs with uniform marks distrib ution o v er the CLOs (quantitati v e equality). Similar measures are required in capstone project rubrics’ design. Capstone project is an important entity of program in which students apply the kno wledge g ained during the course of the program to solv e the engineering problems. The capstone project rubrics map to CLOs and these CLOs usually co v er all the SOs. Since the sample size in this assessment is not as lar ge as of direct assessment therefore results may dif fer in these assessments. 3.3.2. Questions to CLOs Mapping A ppr oaches Due to the man y-to-man y mapping between questions and CLOs, a common ques tion arises about the weights of a question that maps to multiple CLOs. There are three possibilities: One-to-man y mapping with equal weights One-to-man y mapping with proportional weights One-to-one mapping between questions and CLOs. In this manuscript, equal weights ha v e been used in questions to CLOs mapping. The proportional weights add one more le v el of comple xity for the f aculty and hence more chances of errors. One- to-one mapping is another attracti v e solution which eliminates the weight problem because in this case one question can be mapped to one CLO at most. In this technique man y questions can be mapped t o one CLO b ut con v erse is not possible. Proportional weights and one-to-one schemes require a proper design of CLOs and the mapping table between questions and CLOs. 3.3.3. CLOs to SOs Mapping within a Course There are three choices: One CLO can be mapped to an y number of SOs without weights (one-to-man y mapping without weights) One CLO can be mapped to an y number of SOs with weights (one-to-man y mapping with weights) One CLO can be mapped to one SO only (one-to-one mapping) [16] In this manuscript, one-to-man y mapping with weights has been used as sho wn in T able 2. One-to-man y mapping without weights assumes equal weights across all S Os mapped to a particular CLO. A straight forw ard w ay of mapping is one-to-one mapping which does not require weights b ut ag ain the design of CLOs is important in this case. 4. AN AL YSIS AND INTERPRET A TIONS This section pro vides a detail analysis of course le v el e v aluations based on the formulated e v aluation metrics using synthetic data. The implementation of these metrics ha v e re v ealed se v eral ne w directions and interpretations. Course e v aluation produces quantitati v e v alues of attainment, achie v ement, and x th percentile metrics for CLOs and SOs. F or a course, relati v e v alues of these metrics pro vide insight into what happened in the course and zero v alue for a metri c indicates that topics related to the corresponding CLO or SO are either not co v ered in the course or data w as not collected for e v aluation. F or a multi-section course, these metrics can point to lack of coordination among course instructors, and dif ference in teaching and e v aluation standards, If a course instructor does not co v er some CLOs then corresponding metrics v alues will be zero as sho wn in Figure 3. F or the sample course, CLO 4 and 5 are not co v ered and since these tw o CLOs maps to SO ”a”, so the SO IJERE V ol. 5, No. 3, September 2016: 235 245 Evaluation Warning : The document was created with Spire.PDF for Python.
IJERE ISSN: 2252-8822 243 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90 100 Average marks Percentage values     Attainment Achievement absolute Achievement relative Achievement composite 50−th percentile Figure 3. Comparison of CLO attainment, student achie v ement, and 50-th percentile is also not co v ered in the course. F or multi-section courses, a zero v alue for an y of the defined metrics in some of the section indicates lack of coordination among course instructors. In order to e xplain the relationship, CLO attainment, student achie v ement, and 50-th ha v e been plotted ag ainst the students’ a v erage marks in Fig. 3. These graphs sho w the three e v aluation metrics’ v alues for a range of a v erage marks associated with a particular CLO. In this figure, the a v erage marks are obtained from normal distrib ution mean (a v erage) with standard de viation 5 . Number of students is 30 and the results are a v eraged o v er 1000 iterations. From this figure, i t can be seen that CLO attainment is a linear function of questions’ a v erage marks mapped to that CLO. The at tainment is equal to the 50-th percentile because the mean and median of normal distrib ution are equal. The composite student achie v ement remains al most constant up to 70% a v erage marks due to the passing threshold min( av er ag e M ar k s; 70% T otal M ar k s ) . F or normally dis trib uted marks, there are al w ays 50% students belo w the a v erage v alue and 50% students are abo v e the a v erage v alue, hence, student achie v ement remains constant at 50% v alue. When the a v erage marks go abo v e 70% , the passing threshold shifts from a v erage v alue to 70% and all the students with marks greater than 70% contrib ute to the student achi e v em ent. At about 80% a v erage marks, the student achie v ement reaches to 100% v alue because all the students e v en with the standard de viation of 5 no w lie abo v e 70% threshold. The relat i v e achie v ement (passing threshold=a v erage marks) al w ays remains around 50% . The absol ute achie v ement (passing threhold=0.7T otal marks) for = 0 : 7 crosses the 50% v alue at a v erage marks equal to 70 . The designed e v aluation metrics gi v e comprehensi v e results when considered collecti v ely . 1. Attainment and Ac hie vement : The relationship between attainment and student achie v ement ( absolute, com- posite) is linear for a v erage marks greater than set tar get, i.e., for suf ficiently lar ge population size and normal distrib ution of obtained marks, high v alues of attainment corresponds to high v alues of achie v ements and the lo w attainment e xpects lo w achie v ement. Attainment and achie v ement are independent for achie v ement le v el belo w the threshold. If the distrib ution is not normal then linearity is not guaranteed. F or e xample, if there are 10 students and 9 students secure 50 marks (out of 100 ) and one student get 10 marks then the composite achie v ement is 90% b ut the attainment is 46% 2. Attainment and P er centile : The 50-th percentile (or median) gi v es an additional information about the health of attainment. It is also called location parameter . Median close to attainment indicates normal distrib ution of marks. 3. Ac hie vement and P er centile : If 50-th percentile (median) is equal to the tar get v alue of achie v ement then the achie v ement is equal to 50% . Median v alues abo v e the the achie v ement tar get sho ws that more students ha v e met the e xpectation and v alue of achie v ement will be high. Media n v alues less than the achie v ement tar get results in the achie v ement le v el less than 50% . 4. Attainment, Ac hie vement, and P er centile : Attainment and 50-th percentile (median) ha v e the same units, i.e., a v erage and median marks in a particular CLO, whereas, student achie v ement gi v es the number of students. If attainment and median are sim ilar (normal distrib ution) and ha v e high v alues, then, the absolute and composite achie v ements will also be high because more number of students w ould ha v e marks greater than the set tar get, whereas, the relati v e achie v ement will remain flat at 50% because of normally distrib uted marks. Con v ersely , if attainment and median ha v e lo w le v els, then, the composite achie v ement becomes 50% . Note that the absolute achie v ement is proportional to the attainment and median near the tar get and becomes independent for the a v erage marks suf ficiently less or greater than the tar get v alue. Design and Implementation of P erformance Metrics for Evaluation ... (Irfan Ahmed) Evaluation Warning : The document was created with Spire.PDF for Python.
244 ISSN: 2252-8822 5. CONCLUSION AND FUTURE W ORK This w ork qualitati v ely e v aluates the course assessment data using designed perf ormance metrics (attainment, student achie v ement, x-th percentile). The main contrib ution of this w ork is to design and implement the performance metrics for the e v aluation of assessment data. There are man y publis hed papers on the outcome-based assessment of course and program b ut none of those e xplicitly depicts the formulation of the e v aluation metrics. Using the designed metrics, the first finding obtained is that meaningful results from e v aluation metrics depend upon the qualitati v e mapping between marks obtained in assessments to the CLOs. CLOs definitions from the course core topics require qualitati v e equality , and the marks distrib ution o v er the CLOs requires quantitati v e equality . 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Dalrymple, “Outcome-based Education Model for Computer Science Education, IJERE V ol. 5, No. 3, September 2016: 235 245 Evaluation Warning : The document was created with Spire.PDF for Python.