Discriminant Analysis Through Fisher Method on Student's Materials Building in SMP 1 Banda Aceh Yuhasriati,Johan Yunus.
Erni Maidiyah.
Bintang Zaura Jurnal Geuthyy: Penelitian Multidisiplin Vol.
No.
02, (Agustus, 2.
, pp.
DISCRIMINANT ANALYSIS THROUGH FISHER METHOD ON
STUDENT'S MATERIALS BUILDING IN SMP 1 BANDA ACEH
Yuhasriati 1.
Johan Yunus 2.
Erni Maidiyah3.
Bintang Zaura4 Department of Mathematic Education.
Syiah Kuala University E-mail: yuhasriati@unsyiah.
Diterima: 09/08/2019.
Disetujui: 29/08/2019 ABSTRAK The study is done for determining how many students and how the percentage of students who have mastered the material geometry about prism and pyramid, and getting the discriminant function about the mastery of the material.
The study population was the entire eighth grade students of SMP Kasih Banda Aceh while the sample were students of class Vi-1 and Vi-8 to 66 students.
Based on the research that has been done using the fisher discriminant analysis method, 18,18% of students have mastered the material geometry and 81,82% of students have not mastered the material geometry.
It means that from 66 students only 12 students were able to master the material geometry about well- prism and pyramid.
The discriminant function that is formed is Y1 = 955,086X1 1583,05X2 Oe 28,202X3 Oe 127,773X4 Oe 120,111X5 Oe 92,511X6 and Y2 = 956,411X1 1589,179X2 Oe 34,065X3 Oe 137,536X4 Oe 120,797X5 Oe 82,946X6 .
Kata Kunci: Discriminant Analysis.
Fisher.
Geometry.
Prism.
And Pyramid Jurnal Geuthyy: Penelitian Multidisiplin.
Geuthyy Institute.
Banda Aceh.
E-ISSN: 2614-6096.
Open access:
http://w.
Jurnal Geuthyy: Penelitian Multidisiplin Vol.
No.
02, (Agustus, 2.
, pp.
Discriminant Analysis Through Fisher Method on Student's Materials Building in SMP 1 Banda Aceh Yuhasriati.
Johan Yunus.
Erni Maidiyah.
Bintang Zaura
BACKGROUND
Mathematics has an important role in everyday life.
Therefore, this math needs to be taught from every level of education from elementary to university.
According to Ockroft in (Abdurrahman, 2003: .
suggests that mathematics should be taught to students because .
Always used in all aspects of life, .
All fields of study require appropriate mathematical skills, .
Is a powerful, clear, .
Can be used to present information in various ways, .
Improve the ability of logical thinking, thoroughness, and spatial awareness, .
Give satisfaction to the business of solving challenging problems.
According to Slameto .
0: .
, learning is a process of business undertaken by a person to gain a new change of behavior as a whole, as a result of his own experience in interaction with his environment.
Learning is a process marked by a change in a person.
Change as a result of various forms such as changes in knowledge, understanding of attitudes, behavior, skills, abilities, habits and other aspects of change that exist in the learning individual.
The process of learning is very difficult to observe.
Therefore, people tend to see human behavior to be organized into patterns of behavior that eventually composed a model that became the principles of learning that are useful as a provision to understand, encourage, and give direction learning activities.
According to Slameto .
0: .
that the principles of learning that can be implemented in different situations and conditions and by each learner individually is .
Based on the necessary prerequisites for learning.
In learning learners cultivated active participation, increased interest, and guided to achieve the instructional .
According to the nature of Learning is the process of contingency .
he relationship of other understanding.
so it gets the expected understanding of the given stimulus can cause the expected response.
Appropriate material or materials to be learning is overall and the material must have a presentation structure that can be caught .
Terms of learning success.
Learning requires adequate facilities so that learners can learn quietly.
According to the development team of MKDK IKIP Semarang in Sacramento .
, student learning is influenced by two factors, namely internal factors and external Internal factors are factors that exist within the individual, while external factors are factors that exist outside the individual self.
Internal factors include .
physical factors, ie factors related to one's condition, .
psychological factors, there are several factors included in the factor psychology, among others:
intelligence, attention, interest, talent, motive, maturity, and also fatigue, .
fatigue factor, physical fatigue seen from weak body, spiritual fatigue can be seen from the lethargy and External factors include .
family factors, including economic circumstances, parenting ways of education, relationships among family members, parental understanding, home atmosphere, and cultural background, .
school factors, affecting learning including relationships between teachers and students, the relationship between students and students, and learning tools, .
environmental factors, which affect learning are classified into two groups, namely social environmental factors and nonsocial environmental factors.
A school institution has a responsibility to carry out the objectives of the learning process, specially for geometry materials.
Geometry is an important component of the mathematics curriculum in junior high school.
One of the topics discussed in geometry is waking up space.
Some sub-spaces in the wake of space are prisms and pyramid.
In the implementation not far from the mistakes that occur so that the achievement of the implementation of learning objectives inhibited such as mistakes in understanding the concept of a material.
To prevent errors that occur in the learning process can be done by grouping students who are able to master the learning materials with the less able to understand the subject matter so that for students who have not been able to master the material can be added to Discriminant Analysis Through Fisher Method on Student's Materials Building in SMP 1 Banda Aceh Yuhasriati.
Johan Yunus.
Erni Maidiyah.
Bintang Zaura the lesson.
Teachers can group the students using discriminant analysis.
Discriminant analysis is one of the statistical techniques that can be used in the dependency relationship .
he relationship between variables where it can be distinguished where the response variable and where the explanatory variabl.
Discriminant analysis can be done manually and SPSS software assistance .
By using the software will be easier for us in determining the discriminant of these variables.
This analysis is based on a discriminant function that has a common form:
ycUycn = yu0 yu1 ycU1 yu2 ycU2 U yuycy ycUycy yuAyco Johnson and Wichern in Wahyuni .
1: .
explains that Fisher discriminant analysis is one method of obtaining the discriminant function.
Fisher's linear method actually comes from linear classification statistics for two normal In this method X, multivariate observations are transformed to univariate observations of Y where Y comes from the first and second populations to be separated as much as possible for other observations.
Fisher's suggests taking a linear combination of X to produce Y which is a fairly simple function for installation of X.
The formulation of the underlying problem of this research is how many students and what percentage of mastery of the waking material about the prism and pyramid that have been achieved by students, and how the grouping of students who master and who have not mastered the material through discriminant analysis with SPSS software .
in SMP Kasih Banda Aceh.
The author will discuss discriminant analysis through fisher method to the students' ability in mastering the class Vi SMP Kasih Banda Aceh class building materials.
This research was conducted to get discriminant function about the mastery of wake up space about prism and pyramid at SMP Kasih Banda Aceh students.
RESEARCH METHODOLOGY
The approach used in this research is qualitatively supported by quantitative, while the type of research used is descriptive.
As for how Jurnal Geuthyy: Penelitian Multidisiplin Vol.
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02, (Agustus, 2.
, pp.
to obtain data in this study based on the purpose of this study, the subject of research focused on Vi-1 and Vi-8, because basically all classes consist of heterogeneous students, the researchers chose the class randomly.
The way to get data in this research is by using the instrument in the form of pretest, final test .
ost-tes.
, and semester evaluation value .
eport car.
math and science lesson.
Grouping by discriminant analysis occurs because there is the influence of one or more other variables that are independent variables.
The linear combination of these variables will form a discriminant function (Tatham et al.
Discriminant analysis is an accurate technique for predicting a person falling into what category, with the records involved ensuring accuracy.
Prior to data processing in discriminant analysis, it is necessary to test the three Fisher's assumptions.
This is done to obtain discriminant function as an indicator that gives minimum placement error opportunity.
Before the data are analyzed by discriminant, the data are tested the normality by using Q-Q Plots in SPSS .
and also testing the similarity .
of the matrix.
Testing the equality of the covariance variance matrix of each group to determine the discriminant analysis method to be used.
To test the similarity of covariance matrix between variables should be obtained statistic Box's M.
If the data are not normal, changing the data to normal is needed by using function in SPSS.
If the data were normal, testing of average vector difference, because the discriminant analysis was done to data that has been valid .
its grouping.
Discriminant analysis is not useful if the data that has been grouped has a mean value vector that is not significantly If the discriminant analysis is still done, then there will be a very big mistake in the To test the average vector difference can be seen using Wilks' Lambda whose value lies between 0 and 1.
Each new data .
entered into one of the functions of Y.
)will be obtained in the form of a value.
The value of each function Y.
) is different, the function Y.
) to be selected .
is the function Y.
)which Discriminant Analysis Through Fisher Method on Student's Materials Building in SMP 1 Banda Aceh Yuhasriati.
Johan Yunus.
Erni Maidiyah.
Bintang Zaura Jurnal Geuthyy: Penelitian Multidisiplin Vol.
No.
02, (Agustus, 2.
, pp.
yields the highest value.
Kathleen and Carmen .
argue that each function Y.
) in the SPSS process consists of the variable Xp .
for a classification function for one Variables in this Fisher linear discriminant function may be used continuously for the classification or grouping of new data.
These variables are obtained for each group and from any new cases inputted and processed, the results are grouped into groups whose discriminant value Y.
) is higher.
A25
A26
A27
A28
A29
A30
A31
A32
A33
A34
A35
A36
A37
RESULTS AND DISCUSSION
The data collected in this study is derived from initial and final tests of prism and pyramid subjects and for initial test scores and final tests documentation of student learning outcomes in schools as well as the mean values of mathematics and value of science.
This is because the value of algebra in this study is only used as a comparison for the value of prism and The following table is the data of geometry and algebra materials as well as grades of math and science lesson.
A38
A39
A40
A41
A42
A43
A44
A45
A46
A47
A48
A49
A50
A51
A52
A53
A54
Sample The rate of the Report
Math
Science Prism and Pyramid
Pre Post
Pre
Post
Algebra
A55
A56
A57
A58
A59
A60
A61
A62
A63
A10
A64
A11
A65
A12
A66
A13
A14
A15
A16
A17
A18
A19
A20
A21
A22
A23
A24
Source: (Nadya, 2014:43.
Mentari, 2014:.
The data above is nor normal and that is not fulfill the discriminant assumption.
That is why the data is normalized to minimize errors One way to normalize data is to use natural Data after the normalization of the studentAos scores on the material of space and algebra and the value of the math and science report cards are showed in the followig table.
GROUP
Discriminant Analysis Through Fisher Method on Student's Materials Building in SMP 1 Banda Aceh Yuhasriati.
Johan Yunus.
Erni Maidiyah.
Bintang Zaura Jurnal Geuthyy: Penelitian Multidisiplin Vol.
No.
02, (Agustus, 2.
, pp.
4,431
4,431
3,689
4,094
4,489
4,407
4,382
4,331
4,248
4,382
2,996
4,007
4,477
4,477
4,382
4,443
3,912
4,407
4,394
4,344
4,500
4,248
3,401
4,174
4,564
4,533
4,466
4,500
4,443
4,533
4,431
4,431
3,912
4,419
4,500
4,605
4,564
4,522
4,522
4,500
4,318
4,511
4,382
4,344
4,500
4,500
3,689
4,318
4,543
4,522
4,443
4,466
4,443
4,443
4,357
4,369
4,007
4,219
3,555
3,850
4,564
4,533
4,443
4,500
4,248
4,522
4,431
4,454
4,007
4,533
4,318
4,605
4,564
4,522
4,466
4,500
4,466
4,511
4,407
4,431
3,912
4,318
3,689
4,466
4,511
4,477
3,555
4,094
3,912
4,407
4,407
4,382
4,248
4,248
3,401
4,330
4,419
4,419
3,912
4,094
3,807
4,407
4,394
4,382
4,605
4,248
4,248
3,912
4,554
4,543
4,500
4,554
4,443
4,522
4,369
4,344
4,094
3,807
3,401
4,330
4,407
4,407
4,466
4,500
4,466
4,443
4,407
4,369
4,500
4,533
3,401
3,761
4,564
4,533
4,500
4,554
4,443
4,522
4,407
4,419
4,554
4,554
3,807
4,248
4,521
4,450
4,500
4,500
4,407
4,466
4,369
4,382
4,382
4,2905
2,708
4,007
4,521
4,477
4,443
4,500
4,466
4,500
4,394
4,407
4,094
4,382
3,401
3,689
4,521
4,489
4,407
4,443
4,407
4,407
4,407
4,431
4,025
4,382
2,996
4,007
4,466
4,454
4,443
4,443
4,500
4,443
4,369
4,394
4,318
3,689
4,318
4,174
4,454
4,443
4,174
4,382
4,248
4,382
4,344
4,331
4,094
3,555
2,303
3,689
4,466
4,466
4,443
4,382
4,477
4,407
4,394
4,357
3,912
4,290
4,094
4,318
4,533
4,511
4,382
4,443
4,382
4,511
4,382
4,407
4,094
4,382
3,689
4,554
4,533
4,543
4,318
4,443
4,522
4,500
4,419
4,394
4,318
4,419
4,094
4,060
4,477
4,454
4,466
4,500
4,522
4,466
4,407
4,431
4,382
4,605
4,094
3,807
4,454
4,431
3,555
4,248
4,443
4,407
4,407
4,407
3,689
4,318
4,248
4,407
4,522
4,466
4,248
4,443
4,007
4,394
4,407
4,431
4,007
4,248
4,500
4,174
4,407
4,44
4,174
4,382
4,174
3,912
4,443
4,4067
4,318
4,443
4,248
4,382
4,407
4,500
3,807
4,248
4,357
4,407
4,431
4,489
4,174
4,382
4,007
4,318
4,407
4,522
4,248
4,500
3,807
4,248
4,489
4,477
4,318
4,605
4,094
4,318
4,431
4,431
4,318
4,500
3,689
4,554
4,443
4,443
4,382
4,500
4,094
4,060
4,477
4,489
4,500
4,605
4,094
3,807
4,477
4,489
3,689
4,511
4,500
4,554
4,454
4,443
4,443
4,554
3,401
4,007
4,419
4,431
4,554
4,382
4,500
4,318
4,407
4,394
4,443
4,290
3,401
4,094
4,394
4,394
4,094
3,912
4,094
4,382
4,489
4,500
4,605
4,554
4,094
4,318
4,419
4,407
4,318
3,971
3,912
3,807
4,443
4,443
4,382
4,605
3,219
4,318
4,382
4,369
3,807
4,443
2,996
4,007
4,357
4,331
4,094
4,248
3,219
3,807
4,419
4,394
4,094
4,174
3,555
4,219
Using SPSS software .
analyzed by discriminant and the discriminant analysis results will be formed on the new sheet.
The main thing that is obtained through SPSS software is the relationship between all variables.
Then, obtained Fisher linear discriminant function in the following table.
Based on the classification above, so the discriminant function we have:
ycUycyycycnycyco&ycyycycycaycoycnycc = 955,086ycU1 1583,05ycU2 Oe 28,202ycU3 Oe 127,773ycU4 Oe 120,111ycU5 Oe 92,511ycU6 ycUycaycoyciyceycaycyca = 956,411ycU1 1589,179ycU2 Oe 34,065ycU3 Oe 137,536ycU4 Oe 120,797ycU5 Oe 82,946ycU6 Jurnal Geuthyy: Penelitian Multidisiplin Vol.
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02, (Agustus, 2.
, pp.
Classification Function Coefficients Student Identity DOMINA
NOT
MASTER
The Value of Mathematics Report Card of Science Pretest P&L Postest P&L Pretest Algebra -120.
Postest Algebra -92.
(Constan.
Fisher's linear discriminant functions By using descriptive analysis, through software SPSS .
obtained students who have mastered the building material about the prism and pyramid of 12 students and if in the percentage of students who have mastered the material is 18.
18% and students who have not mastered the material is 54 students with the percentage of 81,82%.
For example, suppose there are Z1 students with math grades 89.
IPA 91 grades, pre-test prism and 50 peak, post prism and pyramid 90 preliminary, algebra pre-test value 78, and algebraic post-test value 90 After normalized with natural logarithm becomes X_1 = 4,4886.
X_2 = 4,5108.
X_3 = 3,912.
X_4 =
4,4998.
X_5 = 4,3567.
and X_6 = 4,4998.
Substituting into discriminant function will be ycUycyycycnycyco ycaycuycc ycoycnycoycayc = 955,086.
,4.
1583,05.
,5.
Oe 28,202.
Oe 127,773.
,4.
Discriminant Analysis Through Fisher Method on Student's Materials Building in SMP 1 Banda Aceh Yuhasriati.
Johan Yunus.
Erni Maidiyah.
Bintang Zaura 120,111.
,3.
92,511.
,4.
ycUycyycycnycyco&ycyycycycaycoycnycc = 9802,9732 ycUycaycoycycaycaycayc = 956,411.
,4.
1589,179.
,5.
Oe 34,065.
Oe 137,536.
,4.
Oe 120,797.
,3.
Oe 82,946.
,4.
ycUycaycoycycaycaycayc = 9809,7515 The above results show Y_algebraAn > YA _ .
rism and pyrami.
, so that Z1 students enter into a controlling group or group that has not mastered prism and pyramid.
CONCLUSION
Referring to the results of this study obtained some conclusions, including:
Prism and pyramid material is one of the material that is difficult to be mastered by grade Vi students in SMP Kasih Banda Aceh.
This is indicated by the results of research calculations through the linear discriminant function fisher with the help of software SPSS .
where the students who master the material wake up space about prism and pyramid as many as 12 people with percentage of 18.
18% and students who have not mastered the material as much as 54 people with a percentage of 81.
This indicates that students who have not mastered the building material about prism and pyramid more than students who mastered the material.
Fisher linear discriminant functions obtained through SPSS software .
ycUycyycycnycyco&ycyycycycaycoycnycc = 955,086ycU1 1583,05ycU2 Oe 28,202ycU3 Oe 127,773ycU4 Oe 120,111ycU5 Oe 92,511ycU6 ycUycaycoyciyceycaycyca = 956,411ycU1 1589,179ycU2 Oe 34,065ycU3 Oe 137,536ycU4 Oe 120,797ycU5 Oe 82,946ycU6 Discriminant Analysis Through Fisher Method on Student's Materials Building in SMP 1 Banda Aceh Yuhasriati.
Johan Yunus.
Erni Maidiyah.
Bintang Zaura Jurnal Geuthyy: Penelitian Multidisiplin Vol.
No.
02, (Agustus, 2.
, pp.
REFERENCE