One Way Manova & Two Way Manova
Samih
2024-10-28
DATA
This dataset was generated using statistics from the 2024 Joint Admissions and Matriculation Board (JAMB) examination to predict students performance. JAMB is a standardized test for university admissions in Nigeria. It aims to identify factors affecting student performance and support the development of targeted interventions to improve outcomes. Study_Hours_Per_Week : Number of hours spent studying per week. Attendance_Rate : Percentage of classes attended. JAMB_Score : Scores at JAMB Examination Access_To_Learning_Materials : Availability of educational resources (Yes, No). School_Type : Student’s type of School (Public, Private).
library(readr)## Warning: package 'readr' was built under R version 4.3.3jamb_exam_results1 = read.csv(file.choose(), header=TRUE, sep=";", dec=",")head(jamb_exam_results1)## JAMB_Score Study_Hours_Per_Week Attendance_Rate School_Type
## 1 192 22 78 Public
## 2 207 14 88 Public
## 3 182 29 87 Public
## 4 210 29 99 Public
## 5 199 12 98 Public
## 6 202 25 85 Public
## Access_To_Learning_Materials
## 1 Yes
## 2 Yes
## 3 Yes
## 4 Yes
## 5 Yes
## 6 Nostr(jamb_exam_results1)## 'data.frame': 5000 obs. of 5 variables:
## $ JAMB_Score : int 192 207 182 210 199 202 251 129 220 157 ...
## $ Study_Hours_Per_Week : int 22 14 29 29 12 25 35 27 23 15 ...
## $ Attendance_Rate : int 78 88 87 99 98 85 85 75 85 79 ...
## $ School_Type : chr "Public" "Public" "Public" "Public" ...
## $ Access_To_Learning_Materials: chr "Yes" "Yes" "Yes" "Yes" ...data1=jamb_exam_results1[1:3]
head(data1)## JAMB_Score Study_Hours_Per_Week Attendance_Rate
## 1 192 22 78
## 2 207 14 88
## 3 182 29 87
## 4 210 29 99
## 5 199 12 98
## 6 202 25 85Uji Normalitas Multivariat
Hipotesis
H0 : Data berdistribusi normal multivariat H1 : Data tidak berdistribusi normal multivariat
Taraf Signifikansi
alpha = 5% = 0,05
library(MVN)## Warning: package 'MVN' was built under R version 4.3.3test = mvn(data1, mvnTest = "mardia", univariateTest = "SW", multivariatePlot = "qq")
print(test)## $multivariateNormality
## Test Statistic p value Result
## 1 Mardia Skewness 278.361435895676 5.77109125244121e-54 NO
## 2 Mardia Kurtosis -7.09233473926237 1.31872290864976e-12 NO
## 3 MVN <NA> <NA> NO
##
## $univariateNormality
## Test Variable Statistic p value Normality
## 1 Shapiro-Wilk JAMB_Score 0.9676 <0.001 NO
## 2 Shapiro-Wilk Study_Hours_Per_Week 0.9882 <0.001 NO
## 3 Shapiro-Wilk Attendance_Rate 0.9812 <0.001 NO
##
## $Descriptives
## n Mean Std.Dev Median Min Max 25th 75th
## JAMB_Score 5000 174.0746 47.616477 170 100 367 135 209
## Study_Hours_Per_Week 5000 19.5212 9.634569 19 0 40 13 26
## Attendance_Rate 5000 84.2352 9.485688 84 50 100 78 91
## Skew Kurtosis
## JAMB_Score 0.48759701 -0.2030800
## Study_Hours_Per_Week 0.05363223 -0.5712452
## Attendance_Rate -0.28637201 -0.2854344Dikarenakan datanya tidak normal maka dilakukan pemotongan data, di mana data asli sebanyak 5000, dipotong menjadi 50 dengan data yang diambil adalah data ke 1 sampai 50
data2=jamb_exam_results1[1:50,1:3]
head(data2)## JAMB_Score Study_Hours_Per_Week Attendance_Rate
## 1 192 22 78
## 2 207 14 88
## 3 182 29 87
## 4 210 29 99
## 5 199 12 98
## 6 202 25 85library(MVN)
test = mvn(data2, mvnTest = "mardia", univariateTest = "SW", multivariatePlot = "qq")
print(test)## $multivariateNormality
## Test Statistic p value Result
## 1 Mardia Skewness 12.6588680182531 0.243375091551997 YES
## 2 Mardia Kurtosis -0.76602059960464 0.443664045216431 YES
## 3 MVN <NA> <NA> YES
##
## $univariateNormality
## Test Variable Statistic p value Normality
## 1 Shapiro-Wilk JAMB_Score 0.9569 0.0662 YES
## 2 Shapiro-Wilk Study_Hours_Per_Week 0.9820 0.6407 YES
## 3 Shapiro-Wilk Attendance_Rate 0.9573 0.0688 YES
##
## $Descriptives
## n Mean Std.Dev Median Min Max 25th 75th
## JAMB_Score 50 175.46 49.503333 165.5 100 274 140.0 207.00
## Study_Hours_Per_Week 50 20.98 9.575671 21.0 0 40 14.0 27.75
## Attendance_Rate 50 86.00 8.930571 87.0 58 100 79.5 91.00
## Skew Kurtosis
## JAMB_Score 0.29626215 -0.9623107
## Study_Hours_Per_Week 0.01090125 -0.7414480
## Attendance_Rate -0.52396698 0.2926658Didapatkan p-value :
Mardia Skewness : 0.243375091551997
Mardia Kurtosis : 0.443664045216431
Kriteria Uji
(Skewness) tolak H0 jika p-value < α
(Kurtosis) tolak H0 jika p-value < α
Keputusan
(Skewness) p-value (0.243375091551997) > α (Terima H0)
(Kurtosis) p-value (0.443664045216431) > α (Terima H0)
Kesimpulan
Dengan tingkat signifikansi 0,05 diperoleh keputusan terima H0, yang menunjukkan bahwa data tersebut berdistribusi normal secara multivariat.
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Uji Homogenitas Multivariat
Hipotesis :
H0 = s1 = s2 = s3, matriks kovarians grup adalah sama.
H1 = Minimal ada satu matriks kovarians grup (sk) yang berbeda
Taraf Signifikansi :
alpha = 5%
library(biotools)## Warning: package 'biotools' was built under R version 4.3.3## Loading required package: MASS## Warning: package 'MASS' was built under R version 4.3.3## ---
## biotools version 4.2sekolah <-jamb_exam_results1$School_Type[1:50]
print(sekolah)## [1] "Public" "Public" "Public" "Public" "Public" "Public" "Public"
## [8] "Public" "Public" "Public" "Private" "Public" "Public" "Public"
## [15] "Public" "Public" "Private" "Public" "Public" "Private" "Public"
## [22] "Public" "Public" "Public" "Private" "Public" "Private" "Public"
## [29] "Private" "Public" "Private" "Public" "Public" "Public" "Public"
## [36] "Public" "Public" "Public" "Public" "Public" "Private" "Public"
## [43] "Public" "Public" "Public" "Private" "Public" "Public" "Public"
## [50] "Public"akses <-jamb_exam_results1$Access_To_Learning_Materials[1:50]
print(akses)## [1] "Yes" "Yes" "Yes" "Yes" "Yes" "No" "Yes" "Yes" "No" "Yes" "No" "Yes"
## [13] "Yes" "No" "No" "Yes" "Yes" "Yes" "Yes" "No" "Yes" "No" "Yes" "No"
## [25] "Yes" "Yes" "No" "Yes" "Yes" "No" "Yes" "Yes" "Yes" "No" "No" "Yes"
## [37] "No" "No" "No" "No" "No" "Yes" "Yes" "Yes" "Yes" "Yes" "Yes" "Yes"
## [49] "Yes" "No"Statistik Uji :
hom1 <-boxM(data = data2, grouping = sekolah)
print(hom1)##
## Box's M-test for Homogeneity of Covariance Matrices
##
## data: data2
## Chi-Sq (approx.) = 4.4818, df = 6, p-value = 0.6118Kriteria Uji
Tolak H0 jika P-Value < alpha
Keputusan
P-Value = 0.6118 > alpha, maka Terima H0
Kesimpulan
Dengan tingkat signifikansi 0,05, diperoleh keputusan untuk menerima H0, sehingga dapat disimpulkan bahwa data memiliki matriks kovarians yang sama di setiap grup.
hom2 <-boxM(data = data2, grouping = akses)
print(hom2)##
## Box's M-test for Homogeneity of Covariance Matrices
##
## data: data2
## Chi-Sq (approx.) = 1.9679, df = 6, p-value = 0.9226Kriteria Uji
Tolak H0 jika P-Value < alpha
Keputusan
P-Value = 0.9226 > alpha, maka Terima H0
Kesimpulan
Dengan tingkat signifikansi 0,05, diperoleh keputusan untuk menerima H0, sehingga dapat disimpulkan bahwa data memiliki matriks kovarians yang sama di setiap grup.
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One Way Manova
Hipotesis
H0 : μ 1 = μ 2 = 0.
H1 : Terdapat minimal satu μi ≠ 0.
Taraf Signifikansi
alpha = 0,05
Statistik Uji
owm<-manova(cbind(data2$JAMB_Score, data2$Study_Hours_Per_Week, data2$Attendance_Rate)~akses)
sowm <-summary(owm)
print(sowm)## Df Pillai approx F num Df den Df Pr(>F)
## akses 1 0.048108 0.77494 3 46 0.514
## Residuals 48Kriteria Uji
Tolak H0 jika P-Value < α
Keputusan
P-Value = 0.514 > α (Terima H0)
Kesimpulan
Dengan taraf signifikansi 0,05, diperoleh keputusan terima H0. Sehingga belom ada cukup bukti untuk menyatakan akses ke materi pembelajaran mempengaruhi secara signifikan terhadap JAMB Score, waktu belajar per minggu, dan kehadiran.
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Two Way Manova
H0 : α 1 = α 2 = 0
H1 : Setidaknya ada satu αi yang tidak sama dengan 0
H0 : β1=β2=0
H1 : Setidaknya ada satu β j yang tidak sama dengan 0
H0 : αβ ij = 0
H1 : Setidaknya ada satu αβ ij yang tidak sama dengan 0
Statistik Uji
manova<-manova(cbind(data2$JAMB_Score, data2$Study_Hours_Per_Week, data2$Attendance_Rate)~akses*sekolah, data=data2)
sman<-summary(manova)
print(sman)## Df Pillai approx F num Df den Df Pr(>F)
## akses 1 0.050818 0.78523 3 44 0.5086
## sekolah 1 0.082157 1.31283 3 44 0.2822
## akses:sekolah 1 0.089915 1.44905 3 44 0.2415
## Residuals 46Kriteria Uji
Tolak H0 jika p-value < alpha
Keputusan
akses
p-value = 0.5086 > alpha (Terima H0)
sekolah
p-value = 0.2822 > alpha Terima H0)
akses : sekolah
p-value = 0.2415 > alpha (Terima H0)
Kesimpulan
Akses ke materi pembelajaran tidak berpengaruh signifikan terhadap JAMB Score, waktu belajar per minggu, dan kehadiran.
Jenis sekolah tidak berpengaruh signifikan terhadap JAMB Score, waktu belajar per minggu, dan kehadiran.
Interaksi antara akses ke materi pembelajaran dan jenis sekolah tidak berpengaruh signifikan terhadap JAMB Score, waktu belajar per minggu, dan kehadiran.