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2012. Vol.3, Supplement, 162-164
Published Online December 2012 in SciRes (http://www.SciRP.org/journal/ce) DOI:10.4236/ce.2012.37B042
Copyright © 2012 SciRes.
The Statistical Analysis and Evaluation of Examination
Results of Materials Research Methods Course
Wenjie Yuan, Chengji Deng , Hongxi Zhu, Jun Li
The State Key Laboratory Breeding Base of Refractories and Ceramics, Wuhan University of Science and
Technology, Wuhan 430081, P.R . China
The statistical analysis and evaluation of examination results provide the theoretical basis for teaching
quality and management. Materials research methods course is the key course for the undergraduates ma-
jor in materials science and engineering. Based on the examination results of inorganic nonmetal mate-
rials engineering specialty students in the first term of 2011-2012 school year of Wuhan University of
Science and Technology, the quantitative analysis for several parameters including difficulty, discrimina-
tion and reliability were investigated. The results indicate that the distribution of examination scores ap-
proximate to normal distribution. Difficulty of the exam paper belongs to median level, and discrimina-
tion of this is qualified as well as reliability. Thus it was concluded that the design of the examination pa-
per was good and dependable.
Keywords: Statistical Analys is; E xamina tion Results; Difficul ty; Discrimination; Reliability
The statistical analysis of examination results is an important
work for the management of examination. Its conclusions are
the theoretical basis for teaching evaluation, research and
reform. By analyzing examination results, in one hand, the
teachers can get to know how much knowledge students have
obtained. For the other hand, it can be a feedback that the
quality of examination papers, which is benefit to modify the
questions and make the test more standard. Therefore statistical
analysis of the examination results has been suggested for
identifying the problems in the examination system as well as
in the teaching process of a university.
Materials research methods course is a required course for
inorganic nonmetal materials engineering specialty students. In
this course, it is introduced that basic principles of materials
research, characterization methods and their application in
analysis of different materials and measurement of their proper-
ties. After completing the study module, the student knows the
most important research methods and techniques used in mate-
rials science. The student understands the basic operating prin-
ciples, applicability and limitations of these methods and tech-
niques. The student can work successfully in the various fields
of industry and research requiring good knowledge on materials
research methods and techniques and on their capabilities,
which has magnificent significance. But the fundamentals of
modern techniques for characterizing materials are too abstract
to understand. There are some problems in the teaching and
examination of this course. In this paper, the analysis of ex-
amination results of materials research methods course was
investigated in order to clarify problems existed in the teaching
The procedure for the analysis was as follows. Firstly
examination results of inorganic nonmetal materials engineering
specialty students in the first term of 2011-2012 school year of
Wuhan University of Science and Technology were extracted
from the scripts. Subsequently relative parameters including
difficulty, discrimination and reliability were calculated. Third,
the values of above parameters have been compared and
discussed in order to identify possible sources of problems.
To achieve the objective, the parameters will be first
described according to specialized technical literature
1) Difficulty. The difficulty of an item is understood as the
proportion of the persons who answer a test item correctly.
When this proportion is higher, the difficulty is lower. Usually
this proportion is indicated by the letter P, which indicates the
difficulty of the item . It is calculated by the following for-
where: Pi= Difficulty index of item i, Ai =Average scores to
item i, Ni = Full scores of item i
For the whole script, the average difficulty index P can be
calculated by the formula as below:
Generally the average difficulty index P should be controlled
near 0.7. If P is more than 0.75, it indicates that the exam is
quite easy. While P is less than 0.45, it indicates the exam is
rather difficult .
2) Discrimination. If the test and an item measure the same
ability or competence, it would be expected that those having a
high overall test score would have a high probability of being
able to answer the item. Thus, a good item should discriminate
between those who score high on the test and those who score
low. The discrimination index D can be calculated by using
W. J. YUAN ET AL.
Copyright © 2012 SciRes.
where: PH= Average score for the 27% of those with highest
test scores, PL= Average score for the 27% of those with lowest
R.L. Ebel gave us the following rule for determining the
quality of the items, in terms of the discrimination index . If
D>0.39, the quality of the exam paper is excellent. When D is
in the 0.30-0.39 range, the exam paper is qualified. If
0.20<D<0.29, it indicates that the quality of the exam paper is
passable and has possibility for improvement. The exam paper
should be discarded if D is less than 0.20.
3) Reliability. Estimates of reliability (Cronbach’s alpha) are
at the heart of the quality control process of the examination
system. For the majority of the examinations propounded by
teachers these indices tend to be somewhere in the 0.60-0.8
range . Cronbach’s alpha can be calculated by following
where: k = Total of item, 2
S = Variance of scores for item i,
S = Variance of scores for script
Results and Discu ssion
Based on the data of examination results, frequency
distribution of scores for overall students is shown in Figure 1.
The results indicate that the distribution of examination scores
approximate to normal distribution. The number of students
with scores between 70-79 is dominant. But the situation of
various classes is different as shown in Figures 2(a)-(d).
Compared with other class, the proportion of students in class
No.01 with scores between 70-79 is relatively most. The
frequency distribution of scores for class No.02 is more
uniform, furthermore there is no student with scores more than
90 or less than 40. For class No.03, the score of majority of
students is less than 70. While all of students in class No.04
have the score more than 50. The above differences demonstrate
the levels of various classes are unbalanced though overall
students listen to this course in the same classroom.
Frequency distribution of scores for overall students.
Frequency distribution of scores for individual class: a) No.01; b)
No.02; c) No.03 and d) No.04
W. J. YUAN ET AL.
Copyright © 2012 SciRes.
Difficulty index (P) analysis of exam paper and results.
of terms S
Score 30 20 30 20 100
Difficulty 0.83 0.70 0.59 0.59 0.69
Quality easy median median median median
Discrimination index (D) analysis of examination results for different
Class No. 01 02 03 04 Total
Average score 71.5 65.5 64.0 73.0 68.7
Standard deviation 14.5 13.2 12.5 9.65 13.1
Discrimination 0.32 0.34 0.28 0.24 0.31
Quality qualified qualified passable passable qualified
By comparing the different type questions of t he e xa mination,
it can be seen that its difficulty index P ranges from 0.59 to
0.83 (Table 1). The easiest part is multiple choices those re-
lated with basic concepts, which can be understand well by
students. Short answer questions, as well as general questions,
are the most difficult parts. It is evidenced that the ability of
students for mastering knowledge and handle problems is defi-
cient. The difficulty index P of exam paper is moderate, there-
fore it is not difficult for students to pass this examination.
Analysis of the discrimination index D of four classes for the
examination results shows that these range from 0.24 to 0.34
(Table 2). According to Ebel’s rule, the exam paper is qualified
in general. The discrimination index of scores is much less for
relatively concentrated distribution such as the situation of class
No.03 and 04 (seen in Figure 2). All standard deviation of
scores are less than 15, and the changes of those have the same
trend with the discrimination index. The discrete degree of
examination results is suitable combined with discrimination
index and standard deviation . The average scores for
individual class also show that there is a big gap among four
classes, which may be related with the ethos of study. However,
it is clear that not all the students answered the same question
about theme areas, so that although this comparison is not exact,
it is closely approximate.
The exam paper of materials research methods course in-
cludes twenty-three items. Reliability (Cronbach’s alpha) was
estimated according to equation (4). The quality of the exam
paper is proved to be good by the result of α = 0.75.
The statistical analysis of the examination results of materials
research methods course was carried out. Several parameters
for the exam paper including difficulty P, discrimination D and
reliability were calculated. The values are 0.69, 0.31 and 0.75,
respectively. The results indicate that the distribution of ex-
amination scores approximate to normal distribution. It is noted
that there is a big gap among four classes. Difficulty of the
exam paper belongs to median level, and discrimination of this
is qualified as well as reliability. Thus it was concluded that the
design of the examination paper was good and dependable.
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