IJOLAE | p-ISSN 2655-920x, e-ISSN 2656-2804 Vol. 2 (1) (2020) 1-9 

1 

 
Rasch Modeling: A Multiple Choice Chemistry Test 

 

 

 

Rasch Modeling: A Multiple Choice Chemistry Test  

 

Atiek Winarti1, Al Mubarak2 
1,2Faculty of Teacher Training Education, Universitas Lambung Mangkurat, Indonesia 

 
DOI: 10.23917/ijolae.v2i1.8985 

Received: October 6th, 2019. Revised: October 23rd, 2019. Accepted: October 25th, 2019. 

Available Online: October 26th, 2019. Published Regulary: January 1st, 2020. 

Abstract 

The study aimed to reveal the difficulty level of items and the suitability of items of Chemistry test with the 

Rasch model. In addition to detecting this item quality, the Rasch model shows the student's answer pattern 

as well, so that the assessment can imply the quality of the instrument as an assessment of chemical learn-

ing. As many as 20 numbers of multiple-choice questions in chemical bonding material were analyzed by 

using WINSTEPS 3.73. The samples consisted of 200 senior high school students in Banjarmasin Indonesia. 

The results revealed that the average item measure was 0.00 with items (Measure Order = 4.64) which has 

the highest difficulty level. The Q10 was the item that has a level of conformity with the model, and outliers 

or misfit in Rasch were MNSQ=+0.97, ZSTD=-0.2, Pt Mean Corr=+0.58. In other words, assessment of 

learning with test techniques such as multiple choice based on Rasch model analysis was an effective way 

for teachers to review the progress of students in the learning process, guidelines for designing chemical 

learning strategies, and identifying students' understanding of chemical material. 

 

Keywords: rasch model, multiple choices, chemical bonding  

Corresponding Author:  

Atiek Winarti, Faculty of Teacher Training Education, Universitas Lambung Mangkurat, Indonesia 

e-mail: atiekwin_kimia@ulm.ac.id 

 

1. Introduction 

Learning assessment is an important 

point that must be conducted by the teacher 

(Potgieter & Davidowitz, 2011). The as-

sessment of learning provided contains a lot 

of essential information such as evaluating 

student learning progress, the extent of stu-

dents' cognitive depth on learning that has 

been passed, and the accuracy of test instru-

ments in measuring their mental models 

(Potgieter &. Davidowitz, 2011; Brannon et 

al, 2018). The learning process that is as-

sessed by the instructor without using as-

sessment will be difficult to know cognitive 

development, behavior, depth of understand-

ing, and the impact of the designed teaching 

(Potgieter &. Davidowitz, 2011).  

During the learning process, the instruc-

tor will not only transform knowledge in the 

classroom but also provide other treatments 

to develop students' potential such as as-

signments, practice cognitive skills, forma-

tive or summative tests, and direct communi-

cation between the teacher and students sci-

entifically (Sprague et. Al, 2018). Indirectly, 

that learning assessment is an illustration of 

how the teacher reflects on the learning pro-

cess that has been experienced (Izci et al., 

2018). Associated with the teaching of chem-

istry, that the main target of learning is not 

only to bring students at a high cognitive 

level but also how students interpret and in-

ternalize experiences that have been experi-

enced while learning to become valuable 

individuals (Hindal, 2013).  

A written test as an assessment tech-

nique is often used to review the progress of 

student learning and the effectiveness of 

learning undertaken (Herrmann-Abell & 

DeBoer, 2011). Written tests that can be used 

are multiple choice with the aim of analyzing 

Indonesian Journal on Learning and Advanced Education 

http://journals.ums.ac.id/index.php/ijolae 



 

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Rasch Modeling: A Multiple Choice Chemistry Test 

the cognitive processes of students, empha-

sizing whether students experience miscon-

ceptions or not on chemical material, and 

evaluating learning concepts, so that assess-

ment results are used as references in updat-

ing the learning process, and identifying the 

nature of the items distributed (Brandriet & 

Bretz, 2014; Cheung, 2011; Treagust, et al, 

2011; Milenković, et al, 2016; Yasin, et al, 

2015). Experts also emphasized that the use 

of a distractor for multiple choice instru-

ments could be used as an advantage in mak-

ing multiple choice items (Herrmann-Abell 

& DeBoer, 2011; Villafañe, 2011). Multiple 

choice questions with distractors can diag-

nose students' ability to understand material 

and this becomes a strategy in preventing 

potential student misconceptions (Herrmann-

Abell & DeBoer, 2011). In addition, the in-

structor also made the results of cognitive 

chemical analysis in this format as a guide in 

evaluating the learning process (Rauch & 

Hartig, 2010).  

Measurements with the multiple choice 

question format are closely related to the 

ability of the instrument to measure students' 

cognitive structure and item quality (de la 

Torre, 2009; Zamri, 2015). That is, the 

aspects of validity and reliability are part of 

the interpretation of data, especially the 

quality of the items (Zamri, 2015; Brandriet 

et.al, 2015). The Rasch model is a data 

analysis technique where it is very effective, 

precise, and systematic in justifying items 

with a logarithmic approach (Yasin et. al, 

2015; Park et al. 2017; Lee et al., 2011). The 

concept of the Rasch model is not just a 

technique that shows the level of difficulty 

and feasibility of the question assessment 

instrument, but it is also able to show the 

pattern of student answers in responding to 

the problem (Sumintono, 2018; Chiang, 

2015). In other words, the use of the Rasch 

model confirms that each student has the 

same opportunity to answer questions 

correctly, not just about items (Park et al. 

2017; Chan et al, 2014). Rasch not only 

assesses the ability of students through the 

distribution of data, but also shows the level 

of difficulty of the problem, the suitability of 

the items with the sample used, and the 

symptoms of misconception, so that the 

Rasch model is an appropriate analysis 

technique used to identify the things 

mentioned (Zamri, 2015). The conclusion is 

that the Rasch model provides a more 

comprehensive and concrete picture in the 

measurement aspects of the test because the 

Rasch model involves two basic aspects as 

parameters namely (a) students' abilities, and 

(b) the difficulty level of the question or 

ability of the question (Zamri, 2015; Amin et 

al, 2012; Runnels, 2012).  

 

2. Method 

The quantitative approach was used. It 

was used because the instructor needed to 

ascertain and confirm what and how the 

assessment process is carried out so that it 

required a quantitative and in-depth 

interpretation of the research conducted 

(Potgieter & Davidowitz, 2011). The 

selected samples are 200 students of 

chemistry education department from 

semester 1 to semester 5. These samples 

were considered important to identify their 

potential as prospective teachers.  

The assessment instrument of Chemical 

bonding material consisted of 20 number of 

multiple choice questions were analyzed by 

using WINSTEPS 3.73 Rasch model.  The 

questions analyzed would represent the level 

of students' understanding of the material 

and also determined the measurement of the 

questions. Rasch modeling with multiple 

choice formats uses and combines an 

algorithm that states the results of 

probabilistic expectations of items "i" and 

respondents "n", which are mathematically 

expressed as (Chan, 2014; Runnels, 2012): 

 

Pni (Xni = 1ǀ bn, di) =  

Where Pni (Xni = 1ǀ bn, di)  is the 

probability of respondent n in item i to 

produce a correct answer (x = 1); with the 

respondent's ability, βn and the difficulty 

level of the item δi. The equation above by 

Rasch can be further simplified by entering 

the logarithmic function and making it: 



 
 

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Rasch Modeling: A Multiple Choice Chemistry Test 

 
Log Pni (Xni = 1ǀ βn, δi) = βn - δi 

 

So the probability will be a success that 

can be written as: 

Probability to succeed = respondent's ability - 

item difficulty level 

The Rasch model emphasizes that each 

student has the same opportunity to answer 

questions correctly and at the same time the 

problem has different levels of difficulty. 

This is termed Rasch as a person logit and 

logit item. 

Person logit = ln[p/(1-p)] 

Item logit = ln [p-value] = ln [p-value/(1-p-

value)] 

3. Result and Discussion 

a.  Item Measure 

The item measure in Rasch is an 

analysis of the difficulty level of the item. 

The rightmost column (item) is the code of 

the 20 items distributed. This table provides 

a lot of information about the items 

distributed such as the "measure" column, 

where the column visualizes the difficulty 

level of each item with the term “logit 

value”. From top to bottom is the range from 

the difficulty level of the highest item to the 

lowest level. It means item with code Q15 is 

the item with the highest difficulty level 

(logit = 4.64) and Q7 is the item with the 

lowest difficulty level (-3.45 logit). Evidence 

that Q15 is the most difficult question, 

namely in the "total score" column, where 

Q15 has a total score of 7. This score 

indicates that overall only 7 samples 

answered questions Q15 correctly. 

Conversely, item Q7 has a total score of 192, 

meaning that 192 samples are able to answer 

Q7 questions correctly. In other words, Q7 is 

a question that is easily answered by 

students. 

Then, the table can also explain the 

specifications of the items in another 

perspective because Rasch produces the 

same scale distance. If you pay attention to 

the "logit value" of the question, they 

(questions) have different logit values 

between one another. For example, the Q19 

(logit value = 1.93) when compared to the 

Q17 (logit value = .53) and the Q5 (logit 

value = 14), it can be said that the Q19 has a 

difficulty level 3 times compared to the Q17 

and more than 10 times the Q5. Besides the 

distance of logit values differed significantly, 

the total score value also looks much 

different, where only 57 samples answered 

correctly for item Q19, 107 samples 

answered correctly for item Q17, and Q5 as 

many as 121 samples answered correctly. 

Overall, the item measure table has 

provided concrete information about the 

condition of each item so that this can be the 

evaluation for the teacher and the students. 

Teacher can use this data as a guideline and 

reference in making the appropriate learning 

assessment (written test assessment), 

knowing the characters of each question, 

analyzing the extent of students' 

understanding of the chemical bonding 

material, and how each item is assessed as a 

learning assessment.  

b. Item Fit 

The “misfit order” in Rasch is an 

analysis of the suitability of the item. If we 

previously discussed the difficulty level of 

the item, then "order misfit" represents the 

item's suitability level. Item fit (misfit order) 

explains whether an item is functioning 

normally or not in making measurements. If 

the detected items are not fit, then the 

question indicates that there is a 

misconception between students and the 

items they are working on (Herrmann-Abell 

& DeBoer, 2011). The indicated items are 

not fit, it needs more in-depth discussion. It 

means the teacher needs to further analyze 

the problem structure and student answer 

patterns so that they can find a point of the 

problem. Information based on this table is 

very valuable for teachers to be a reference 

for improving the quality of teaching. In 

addition, this information is also able to 

prevent and deal with attacks of 

misconceptions that will arise next.



 

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Rasch Modeling: A Multiple Choice Chemistry Test 

Table 1. Item measure 

 
 

Table 2. Item Fit/Misfit Order 

 
 

Boone et al (2014) explained that checking 

the suitability of the items can be identified 

based on the Mean Square Outfit (MNSQ) value 

with a range of values of 0.5 <MNSQ <1.5, Z-

standard (ZSTD) outfit values for the range -2.0 

<ZSTD <+2.0, and 0.4 <Pt Mean Corr <0.85 for 

the value of Point Measure Correlation outfit (Pt 

Mean Corr). The value of ZSTD is strongly 

influenced by the number of samples used. When 

the sample size is large, then the ZSTD outfit 

value will always be above 3 so that the ZSTD 

value by experts does not recommend this value 

when the sample size in calibration is large (N = 

500). 

Table 1 shows that Q15 item is on the first 

order of all items analyzed. This indicates that 

based on the "item measure" table, the Q15 is the 

item that has the highest difficulty level among 

the other items (logit value = + 4.64). Then, fit 

items are the basis for assessing whether or not 

the item is maintained as a measuring instrument. 

This is indicated by their outfit value, where the 

Q15 has an MNSQ outfit value of 3.73, ZSTD 

outfit value is 3.0, and -0.07 for the Pt Mean Corr 

outfit value. If we look back at the standard 

criteria for item suitability, the outfit value of 

Q15 is an item that is not fit. It means the Q15 is 

not statistically recommended to be used as a 

measurement tool because it is not representative 

in measuring students' understanding of chemical 

bonding material. The reason that Q15 is the 

hardest question is because of from 200 samples, 

only 7 samples answered the Q15 correctly (see 

"total score" in the item fit / item measure table).  
Another proof to support the argument 

above is through the suitability of the items that 

can be seen from the graph, namely the 

"expected ICC score" chart. Look at the graph of 

the specific item's suitability for items for the 

Q15, where there is a response beyond the Rasch 

point threshold.



 
 

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Rasch Modeling: A Multiple Choice Chemistry Test 

                                         

Figure 1. Graph of item adjustment level for Q15 

Based of this finding, it can be 

concluded that Q15 is not recommended to 

be used as a measuring instrument. Whereas, 

number 15 is content as a basic material in 

understanding the concept of chemical 

bonds. The following is question number 15. 
 

The amount of covalent bonds in H2SO4 

molecules is ... (answer B). 

a. 1 

b. 4 

c. 2 

d. 0 (none 

e. 3 

The basic theory in answering the above 

questions is, first: students must have the 

knowledge aspect at level C1 (remembering), 

where they have to recall how to write shell 

and subshell electrons configuration for each 

chemical element. Then, they have to write 

the configuration precisely and based on 

scientific principles of the electron 

configuration theory in question. The second, 
they are able to analyze the symptoms and 

nature of a molecule based on configuration, 

this will stimulate cognitively and construct 

their mind so that the role of valence 

electrons is very much needed. In addition, 

they must know the concept of "formal 

charge" and how to implement the concept. 

If they know and understand the points 

mentioned, students are able to analyze and 

identify the tendency of each chemical 

element/molecule to bond.  

Based on the item structure, actually the 

Q15 can be considered as the easiest item for 

university students because they have a more 

mature mental model of thinking. But, only 

the small number of students who answer 

this item corectly. Student’s cognitive 

abilities in analyzing the Q15 question are 

not fully optimal even though these 

questions are considered as the most basic 

scientific questions to understand in the 

material of chemical bonds. Representative 

interpretation especially sub-microscopic and 

symbolic levels (Eliyawati et al, 2018; 

Serobatse, et al, 2014) can help students 

answer Q15 correctly. When viewed in a 

matter structure, Q15 is an easy question to 

be answered by college students where they 

already have a more mature mental model of 

thinking. That is, their cognitive abilities in 

analyzing Q15 questions are not fully 

optimal even though these questions are 

considered as the most basic scientific 

questions to understand in the material of 

chemical bonds. 

Another analysis is the Q10, where this 

item is in the fit criteria, misfit criteria, 

which has MNSQ outfit values of 0.97, 

ZSTD -0.2, and Pt Mean Corr 0.58. The Q10 

can be used as a measurement tool in 

analyzing students’ cognitive. Overall, 

Rasch-based statistical results, measuring 

student understanding, have provided a lot of 

information.  

Consider the following table! 

No Compound Pairs 

1 NH4+ and NH3BF3 

2 H2O and HCl 

3 HF and H2O 

4 NH3 and HBr 

5 NH3 and H2S 

 



 

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Rasch Modeling: A Multiple Choice Chemistry Test 

The group of compounds that have co-

ordination covalent bonds is 

a. 1 
b. 4 
c. 2 

d. 0 (None) 
e. 3 

Overall the statistical results shown that 

the Rasch model analysis provide a lot of 

information about the feasibility of an item 

in measuring the level of student 

understanding. This is because, if we 

examine more deeply the results of the 

analysis of the Rasch model, then we not 

only find the size of the instruments made 

but also the patterns of student answers. As a 

result, teachers obtain a lot of information as 

a basis for improving the quality of teaching 

and as an evaluation of chemistry learning. 

This is reinforced by research (Cheung, 

2011) that it is necessary to carry out a 

process of diagnosis of students and the 

learning process carried out as a strategy to 

design effective teaching and improve the 

quality of students' understanding in learning 

chemistry. In addition, (Zamri bin Khairani 

& Bin Abd. Razak, 2015) added that the 

Rasch model is able to provide more 

interpretation of the results of the statistical 

data presented so that teachers are easier in 

the diagnosis process. 

4. Conclusion 

Overall it can be concluded that the 

distributed dichotomy items are worthed to 

be used as the assessment tool of cognitive 

ability by viewing the item fit value. The 

item fit data showed that 90% of the 

questions are worthed to be used as the 

assessment tool.  From 20 numbers of 

analyzed questions the item of Q15, Q16, 

and Q17 are not suitable with Rasch model 

criteria. Even though ZSTD value is affected 

by the number of sample, MNSQ and Pt 

Mean Corr values become the other 

references in  assessing the quality of the 

questions. 

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