fullpaper icrem5 adisetiawan
Determine Teaching Quality of Lecturer
Based on Student Questioner Using T Statistics
Adi Setiawan and Hanna Arini Parhusip
Department of Mathematics, Faculty of Science and Mathematics,
Satya Wacana Christian University Jl. Diponegoro 52-60 Salatiga 50711
adi setia 03@yahoo.com
Abstract
This paper proposes a method to measure teaching quality based on student questioner. The T statistics is proposed as a measurement of teaching quality. Based
on the real questioner data, the statistical T value can be determined for every
item and course. Using the proposed statistics, the course which has highest quality among 15 courses can be determined.
Keywords : teaching quality, T statistics
Introduction
Several recent papers explained methods to model teaching quality. For example paper by Ahmed et al. (2010) and Barone et al. (2010). In this paper we
propose the method to measure teaching quality based on student questioner by
using T statistics. The explained method will be described by using real data to
find which courses have highest quality.
Theory
Every end of semester, students fill a questioner to measure student satisfy of
teaching. The questioner consist of 16 items of question (e.g. utilizes content scope
and sequence planning, clearness of assignments and evaluations, etc). The score
of every item in a questioner for n student can be expressed as
Xi = (X1i , X2i , ....., Xpi )
(1)
where Xk i = 0, 1, 2 or 3 for k = 1, 2, , p and i = 1, 2, , n which means very
bad, enough, satisfactory and good. In this case, p is the number of items in the
questioner that is used to measure the teaching quality and n is the number of
students. The teaching quality for every item and course can be determined by
using the proposed T statistics :
Ti =
Xi
√
Si / n
(2)
Pn
where Xi = k=1 Xik /n is the arithmetic mean and Si standard deviation of the
i-th item of course. If Si = 0 then it can be changed by the smallest Si and Si = 0
1
for i = 1, 2, ..., p. This following example gives description of the method by using
data that contains 3 items and 2 courses. A good quality of teaching is determined
by the average of statistical T value for every items. Teaching quality is called good
if the average of score of questioner is big and the standard deviation is small. Base
¯ = (8.58, 9.05, 9.05) with the
on the data, the statistical T value of course 1 : X
¯ = (6.24, 5.80, 5.72) with
average 8.90 and the statistical T value of course 2 : X
the average is 5.93. We can conclude that the teaching quality of Course 1 is better
than Course 2.
Table 1. Example of data (15 students for Course 1 and 7 students Course 2)
C1
C2
.
1
2
2
2
1
2
2
2
2
2
2
2
2
2
2
2
3
2
2
2
3
2
3
3
4
2
2
2
4
3
3
2
5
2
2
2
5
3
3
3
6
2
3
3
6
3
3
2
7
3
3
3
7
3
3
2
8
2
3
3
9
3
3
3
10
3
3
3
11
3
3
3
12
3
3
3
13
3
3
3
14
3
3
3
15
3
3
3
Result and Analysis
The used data are taken from student questioners. The data come from 15
courses and 203 questioner sheets. Every course has different the number of students who filled questioner sheets. Every course can be determined the statistical
T value for every item and the teaching quality is determined by average of T
value. The results are presented in Table 2. Based on Table 2, we can conclude
that the third item has the highest average of T value that means student is very
satisfy with ’Systematical in Lecturing’. In other side, the twelfth item has the
lowest average of T value that means students does not satisfy with the twelfth
item.
Table 3 presents the number of student for every course, the average (arith¯ and
metic mean), the T statistics. The correlation between arithmetic mean X
the proposed statistics T is 0.446 (with p-value equals to 0.095 that is not significant for α = 0.05) means that the T value does not depend on the average
statistically. In other side, the correlation between the number of students n that
attends the course and the T statistics is 0.936 with p-value tends to 0 that means
the T value depend on the number of students. Based on statistics T in Table 3,
we can conclude that Course 6 becomes the highest teaching quality (this can be
caused by the number of students and the small value of standard deviation) and
Course 9 becomes the lowest teaching quality. These results can be different from
the teaching quality based on the average score of questioner.
2
Table 2. The statistical T value for every item and course
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Mean
S
9
9
9
10
8
9
11
9
9
9
9
5
9
10
9
10
6
6
6
6
6
6
6
6
6
6
6
7
7
6
5
6
5
4
6
4
4
4
4
4
4
4
6
5
6
4
6
5
10
9
13
10
10
13
10
10
8
10
9
6
10
9
8
10
5
4
6
4
4
6
4
4
4
4
4
5
6
4
5
5
15
13
15
13
14
16
14
12
11
12
13
11
12
12
13
14
11
10
11
8
9
7
11
8
9
8
9
7
10
10
10
11
8
8
8
8
8
8
8
8
8
8
8
8
8
9
8
8
4
4
5
4
4
5
5
4
5
4
5
5
4
5
4
5
9
8
7
8
9
8
6
7
8
8
7
7
8
8
7
8
7
6
6
6
5
6
7
6
7
6
6
4
7
7
7
5
7
5
5
5
6
6
5
6
7
5
5
4
5
7
7
7
9
9
9
10
8
9
11
9
9
9
9
5
9
10
9
10
7
7
10
12
8
8
7
7
6
7
6
8
8
8
8
8
4
5
4
5
5
4
4
3
5
4
4
5
6
4
5
5
7.73
7.13
8.00
7.53
7.20
7.67
7.53
6.87
7.07
6.93
7.07
6.13
7.67
7.53
7.40
7.80
2.94
2.61
3.16
2.97
2.76
3.24
3.16
2.53
2.05
2.49
2.43
1.88
2.13
2.53
2.32
2.76
Table 3. Table of courses and the teaching quality (the average of T statistics)
.
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Course Name
Course 1
Course 2
Course 3
Course 4
Course 5
Course 6
Course 7
Course 8
Course 9
Course 10
Course 11
Course 12
Course 13
Course 14
Course 15
The number of students n
15
7
6
19
6
39
21
12
4
20
11
10
15
13
5
¯
X
2.67
2.49
2.17
2.44
2.20
2.48
2.44
2.50
2.66
1.98
2.20
1.84
2.67
2.41
2.01
T =
¯
(n)X/S
9.05
6.05
4.74
9.56
4.70
13.06
9.22
7.68
4.51
7.59
6.28
5.69
9.05
7.78
4.33
p
Simulation Study
Simulation study is done by sample (size N1 ) from the old sample. New sample
is made by selection one by one score observation for every item with replacement
until N1 times. The statistical T value is calculated based on the new sample.
The procedure is done until a big number B times such that we have B new
statistical T values T1∗ , T2∗ , ...., TB∗ . The histogram of B new statistical T values
can be presented.
Table 4 present the mean of statistical T value based on new sample for every
courses and percentile 95 % confidence interval of mean are presented. Based on
Table 4, we can conclude that there exist strong correlation between statistical T ∗
value and mean of observation score (with correlation 0.87 and p-value tends to
zero). Thus, we conclude that the standard deviation only gives a small influence
to the statistical T ∗ value.
3
Table 4. The measure of teaching quality based on simulated sample
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Course Name
Course 1
Course 2
Course 3
Course 4
Course 5
Course 6
Course 7
Course 8
Course 9
Course 10
Course 11
Course 12
Course 13
Course 14
Course 15
¯
Mean X
2.67
2.49
2.17
2.44
2.20
2.48
2.44
2.50
2.66
1.98
2.20
1.84
2.67
2.41
2.01
Mean T ∗
23.85
23.85
20.30
22.30
21.47
21.12
20.39
22.68
24.60
17.26
19.42
18.51
23.85
22.13
20.74
Percentile 95% confidence interval for mean T ∗
(23.40, 24.34)
(23.44, 24.32)
(20.01, 20.62)
(20.67, 21.56)
(21.76, 23.04)
(20.81, 22.36)
(20.67, 21.56)
(22.51, 22.89)
(24.06, 25.34)
(16.93, 17.62)
(19.12, 19.75)
(18.14, 18.91)
(23.40, 24.34)
(21.63, 22.81)
(20.19, 21.49)
Conclusion
This paper proposes a measurement method of teaching quality by using T statistics. Statistics T is used to measure the teaching quality. Using the proposed
statistics, the course which is has highest quality among 15 courses can be determined.
Acknowledgement
This research is funded by Satya Wacana Christian University.
References
[1] Ahmed, I, M. M. Nawaz, Z. Ahmad, Zafar Ahmad, M. Z, Shaukat, A. Usman,
Wasim-ul-Rehman, N. Ahmed, (2010), Does service quality affect student’s
performance? Evidence from institutes of higher learing, Af rican Journal of
Bussiness M anagement Vol. 4 (12)
[2] Barone, S and E. L. Franco, 2010, TESF Methodology for Statistics Education
Improvement, Journal of Statistics Education, Vol. 18 (3)
[3] Johnson ,R.A., and Wichern, D.W., 2007. Applied M ultivariate Statistical
Analysis, 6th ed., Prentice Hall, New York.
[4] Tabachnick, B. G. and L. S. Fidell., 2007. U sing M ultivariate Statistics 5th
edition, Pearson Education, Boston.
.
Appendix
Question for students observation to measure the teaching quality :
1. Utilize content scope and sequence planning.
2. Clearness of assignment and evaluations.
4
3. Systematical in Lecturing
4. Encourages Students attendance
5. Demonstrate accurate and current knowledge in subject field.
6. Creates and maintains an environment that supports learning.
7. Clearness of purpose on each assignment.
8. Attractiveness of the lecture.
9. Clearness of purpose on each assignment.
10. Lecture’s competence on stimulating students excitement.
11. Lecture’s competence on delivering idea.
12. Does teacher have available time to help students for the related topic outside
the class ?
13. Effectiveness of time used in the class.
14. Provides relevant examples and demonstrations to illustrate concepts.
15. The quality of lecturer’s feedback due to the given assignment.
16. Score the overall the lecturer’s performance.
5
Based on Student Questioner Using T Statistics
Adi Setiawan and Hanna Arini Parhusip
Department of Mathematics, Faculty of Science and Mathematics,
Satya Wacana Christian University Jl. Diponegoro 52-60 Salatiga 50711
adi setia 03@yahoo.com
Abstract
This paper proposes a method to measure teaching quality based on student questioner. The T statistics is proposed as a measurement of teaching quality. Based
on the real questioner data, the statistical T value can be determined for every
item and course. Using the proposed statistics, the course which has highest quality among 15 courses can be determined.
Keywords : teaching quality, T statistics
Introduction
Several recent papers explained methods to model teaching quality. For example paper by Ahmed et al. (2010) and Barone et al. (2010). In this paper we
propose the method to measure teaching quality based on student questioner by
using T statistics. The explained method will be described by using real data to
find which courses have highest quality.
Theory
Every end of semester, students fill a questioner to measure student satisfy of
teaching. The questioner consist of 16 items of question (e.g. utilizes content scope
and sequence planning, clearness of assignments and evaluations, etc). The score
of every item in a questioner for n student can be expressed as
Xi = (X1i , X2i , ....., Xpi )
(1)
where Xk i = 0, 1, 2 or 3 for k = 1, 2, , p and i = 1, 2, , n which means very
bad, enough, satisfactory and good. In this case, p is the number of items in the
questioner that is used to measure the teaching quality and n is the number of
students. The teaching quality for every item and course can be determined by
using the proposed T statistics :
Ti =
Xi
√
Si / n
(2)
Pn
where Xi = k=1 Xik /n is the arithmetic mean and Si standard deviation of the
i-th item of course. If Si = 0 then it can be changed by the smallest Si and Si = 0
1
for i = 1, 2, ..., p. This following example gives description of the method by using
data that contains 3 items and 2 courses. A good quality of teaching is determined
by the average of statistical T value for every items. Teaching quality is called good
if the average of score of questioner is big and the standard deviation is small. Base
¯ = (8.58, 9.05, 9.05) with the
on the data, the statistical T value of course 1 : X
¯ = (6.24, 5.80, 5.72) with
average 8.90 and the statistical T value of course 2 : X
the average is 5.93. We can conclude that the teaching quality of Course 1 is better
than Course 2.
Table 1. Example of data (15 students for Course 1 and 7 students Course 2)
C1
C2
.
1
2
2
2
1
2
2
2
2
2
2
2
2
2
2
2
3
2
2
2
3
2
3
3
4
2
2
2
4
3
3
2
5
2
2
2
5
3
3
3
6
2
3
3
6
3
3
2
7
3
3
3
7
3
3
2
8
2
3
3
9
3
3
3
10
3
3
3
11
3
3
3
12
3
3
3
13
3
3
3
14
3
3
3
15
3
3
3
Result and Analysis
The used data are taken from student questioners. The data come from 15
courses and 203 questioner sheets. Every course has different the number of students who filled questioner sheets. Every course can be determined the statistical
T value for every item and the teaching quality is determined by average of T
value. The results are presented in Table 2. Based on Table 2, we can conclude
that the third item has the highest average of T value that means student is very
satisfy with ’Systematical in Lecturing’. In other side, the twelfth item has the
lowest average of T value that means students does not satisfy with the twelfth
item.
Table 3 presents the number of student for every course, the average (arith¯ and
metic mean), the T statistics. The correlation between arithmetic mean X
the proposed statistics T is 0.446 (with p-value equals to 0.095 that is not significant for α = 0.05) means that the T value does not depend on the average
statistically. In other side, the correlation between the number of students n that
attends the course and the T statistics is 0.936 with p-value tends to 0 that means
the T value depend on the number of students. Based on statistics T in Table 3,
we can conclude that Course 6 becomes the highest teaching quality (this can be
caused by the number of students and the small value of standard deviation) and
Course 9 becomes the lowest teaching quality. These results can be different from
the teaching quality based on the average score of questioner.
2
Table 2. The statistical T value for every item and course
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Mean
S
9
9
9
10
8
9
11
9
9
9
9
5
9
10
9
10
6
6
6
6
6
6
6
6
6
6
6
7
7
6
5
6
5
4
6
4
4
4
4
4
4
4
6
5
6
4
6
5
10
9
13
10
10
13
10
10
8
10
9
6
10
9
8
10
5
4
6
4
4
6
4
4
4
4
4
5
6
4
5
5
15
13
15
13
14
16
14
12
11
12
13
11
12
12
13
14
11
10
11
8
9
7
11
8
9
8
9
7
10
10
10
11
8
8
8
8
8
8
8
8
8
8
8
8
8
9
8
8
4
4
5
4
4
5
5
4
5
4
5
5
4
5
4
5
9
8
7
8
9
8
6
7
8
8
7
7
8
8
7
8
7
6
6
6
5
6
7
6
7
6
6
4
7
7
7
5
7
5
5
5
6
6
5
6
7
5
5
4
5
7
7
7
9
9
9
10
8
9
11
9
9
9
9
5
9
10
9
10
7
7
10
12
8
8
7
7
6
7
6
8
8
8
8
8
4
5
4
5
5
4
4
3
5
4
4
5
6
4
5
5
7.73
7.13
8.00
7.53
7.20
7.67
7.53
6.87
7.07
6.93
7.07
6.13
7.67
7.53
7.40
7.80
2.94
2.61
3.16
2.97
2.76
3.24
3.16
2.53
2.05
2.49
2.43
1.88
2.13
2.53
2.32
2.76
Table 3. Table of courses and the teaching quality (the average of T statistics)
.
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Course Name
Course 1
Course 2
Course 3
Course 4
Course 5
Course 6
Course 7
Course 8
Course 9
Course 10
Course 11
Course 12
Course 13
Course 14
Course 15
The number of students n
15
7
6
19
6
39
21
12
4
20
11
10
15
13
5
¯
X
2.67
2.49
2.17
2.44
2.20
2.48
2.44
2.50
2.66
1.98
2.20
1.84
2.67
2.41
2.01
T =
¯
(n)X/S
9.05
6.05
4.74
9.56
4.70
13.06
9.22
7.68
4.51
7.59
6.28
5.69
9.05
7.78
4.33
p
Simulation Study
Simulation study is done by sample (size N1 ) from the old sample. New sample
is made by selection one by one score observation for every item with replacement
until N1 times. The statistical T value is calculated based on the new sample.
The procedure is done until a big number B times such that we have B new
statistical T values T1∗ , T2∗ , ...., TB∗ . The histogram of B new statistical T values
can be presented.
Table 4 present the mean of statistical T value based on new sample for every
courses and percentile 95 % confidence interval of mean are presented. Based on
Table 4, we can conclude that there exist strong correlation between statistical T ∗
value and mean of observation score (with correlation 0.87 and p-value tends to
zero). Thus, we conclude that the standard deviation only gives a small influence
to the statistical T ∗ value.
3
Table 4. The measure of teaching quality based on simulated sample
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Course Name
Course 1
Course 2
Course 3
Course 4
Course 5
Course 6
Course 7
Course 8
Course 9
Course 10
Course 11
Course 12
Course 13
Course 14
Course 15
¯
Mean X
2.67
2.49
2.17
2.44
2.20
2.48
2.44
2.50
2.66
1.98
2.20
1.84
2.67
2.41
2.01
Mean T ∗
23.85
23.85
20.30
22.30
21.47
21.12
20.39
22.68
24.60
17.26
19.42
18.51
23.85
22.13
20.74
Percentile 95% confidence interval for mean T ∗
(23.40, 24.34)
(23.44, 24.32)
(20.01, 20.62)
(20.67, 21.56)
(21.76, 23.04)
(20.81, 22.36)
(20.67, 21.56)
(22.51, 22.89)
(24.06, 25.34)
(16.93, 17.62)
(19.12, 19.75)
(18.14, 18.91)
(23.40, 24.34)
(21.63, 22.81)
(20.19, 21.49)
Conclusion
This paper proposes a measurement method of teaching quality by using T statistics. Statistics T is used to measure the teaching quality. Using the proposed
statistics, the course which is has highest quality among 15 courses can be determined.
Acknowledgement
This research is funded by Satya Wacana Christian University.
References
[1] Ahmed, I, M. M. Nawaz, Z. Ahmad, Zafar Ahmad, M. Z, Shaukat, A. Usman,
Wasim-ul-Rehman, N. Ahmed, (2010), Does service quality affect student’s
performance? Evidence from institutes of higher learing, Af rican Journal of
Bussiness M anagement Vol. 4 (12)
[2] Barone, S and E. L. Franco, 2010, TESF Methodology for Statistics Education
Improvement, Journal of Statistics Education, Vol. 18 (3)
[3] Johnson ,R.A., and Wichern, D.W., 2007. Applied M ultivariate Statistical
Analysis, 6th ed., Prentice Hall, New York.
[4] Tabachnick, B. G. and L. S. Fidell., 2007. U sing M ultivariate Statistics 5th
edition, Pearson Education, Boston.
.
Appendix
Question for students observation to measure the teaching quality :
1. Utilize content scope and sequence planning.
2. Clearness of assignment and evaluations.
4
3. Systematical in Lecturing
4. Encourages Students attendance
5. Demonstrate accurate and current knowledge in subject field.
6. Creates and maintains an environment that supports learning.
7. Clearness of purpose on each assignment.
8. Attractiveness of the lecture.
9. Clearness of purpose on each assignment.
10. Lecture’s competence on stimulating students excitement.
11. Lecture’s competence on delivering idea.
12. Does teacher have available time to help students for the related topic outside
the class ?
13. Effectiveness of time used in the class.
14. Provides relevant examples and demonstrations to illustrate concepts.
15. The quality of lecturer’s feedback due to the given assignment.
16. Score the overall the lecturer’s performance.
5