Modul 2 MANOVA, MANCOVA, ANCOVA, dan ANOVA
Nagatan Alief Putra silahen (24031554086), Muslim Fazlur Rohman (24031554154), Muhammad Ramadhan Albaary Putra (24031554161), Kafka Praya Firmansyah (24031554182) - 2024C
2026-04-22
Dataset –> Enhancing students’ conceptual understanding
Link Dataset –> https://dataverse.harvard.edu/dataset.xhtml?persistentId=doi:10.7910/DVN/19CRUH&version=3.0.
Variabel
Dependent Variable (DV) = IntrVaPostTS
Dependent Variable (DV) = UtilVaPostTS
Independent Variable (IV) = Groups
Covariat = IntrVaPreTS
Covariat = UtilVaPreTS
Library
library(MVN)
library(biotools)data <- read.delim("CU and TV data.tab", header = TRUE)str(data)'data.frame': 104 obs. of 32 variables:
$ Groups : int 1 1 1 1 1 1 1 1 1 1 ...
$ ID : int 4 5 6 8 10 11 12 13 14 15 ...
$ Age : int 17 17 17 17 18 16 16 17 18 17 ...
$ Gender : int 2 2 2 2 2 2 1 1 2 2 ...
$ Resi : int 1 1 1 2 2 1 1 1 2 1 ...
$ FEL : int 2 2 2 4 4 1 3 2 4 4 ...
$ MEL : int 4 1 1 4 4 2 3 1 4 2 ...
$ FathOcc : int 4 6 1 4 4 1 1 6 4 5 ...
$ MothOcc : int 5 3 5 5 5 5 1 1 5 3 ...
$ FSMS : int 41 53 78 51 40 51 94 51 65 51 ...
$ CUPreTS : int 2 2 1 2 1 0 4 0 1 1 ...
$ CUPostTS : int 3 4 5 4 3 2 6 2 3 2 ...
$ TV1 : int 5 4 3 4 3 4 5 3 4 3 ...
$ TV10 : int 1 2 3 3 2 1 1 2 4 2 ...
$ TV4 : int 2 2 3 2 3 4 1 1 2 1 ...
$ TV9 : int 4 3 2 4 3 4 5 4 4 3 ...
$ TV6 : int 1 2 4 3 2 4 2 4 2 3 ...
$ TV2 : int 3 4 5 3 3 4 5 4 3 4 ...
$ TV5 : int 5 4 3 3 4 5 4 3 4 5 ...
$ TV11 : int 5 3 5 4 5 4 5 3 4 4 ...
$ TV3 : int 4 3 4 4 3 5 4 3 4 3 ...
$ TV12 : int 4 3 5 4 4 3 4 3 4 4 ...
$ TV7 : int 4 3 2 5 3 4 5 3 4 4 ...
$ TV8 : int 3 4 3 3 2 3 1 3 4 3 ...
$ IntrVaPostTS: int 14 13 15 13 12 17 15 11 13 11 ...
$ UtilVaPostTS: int 13 13 12 14 11 16 12 13 14 15 ...
$ AttaVaPostTS: int 14 11 15 15 14 12 15 12 16 13 ...
$ IntrVaPreTS : int 12 9 12 11 13 11 14 7 12 8 ...
$ UtilVaPreTS : int 14 8 9 10 15 11 13 10 11 8 ...
$ AttaVaPreTS : int 11 8 10 9 11 5 11 7 13 12 ...
$ TVPreTS : int 37 25 31 30 39 27 38 24 36 28 ...
$ TVPosTS : int 41 37 42 42 37 45 42 36 43 39 ...summary(data) Groups ID Age Gender Resi
Min. :1.000 Min. : 1.00 Min. :15.0 Min. :1.000 Min. :1.000
1st Qu.:1.000 1st Qu.:13.00 1st Qu.:16.0 1st Qu.:1.000 1st Qu.:1.000
Median :2.000 Median :24.50 Median :17.0 Median :2.000 Median :1.000
Mean :2.029 Mean :24.40 Mean :16.8 Mean :1.673 Mean :1.394
3rd Qu.:3.000 3rd Qu.:35.25 3rd Qu.:17.0 3rd Qu.:2.000 3rd Qu.:2.000
Max. :3.000 Max. :51.00 Max. :24.0 Max. :2.000 Max. :2.000
FEL MEL FathOcc MothOcc
Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
1st Qu.:1.000 1st Qu.:1.000 1st Qu.:3.000 1st Qu.:3.000
Median :2.000 Median :3.000 Median :4.000 Median :5.000
Mean :2.308 Mean :2.615 Mean :3.385 Mean :4.029
3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:5.000
Max. :4.000 Max. :4.000 Max. :6.000 Max. :6.000
FSMS CUPreTS CUPostTS TV1
Min. :35.00 Min. :0.000 Min. : 0.000 Min. :1.000
1st Qu.:47.00 1st Qu.:1.000 1st Qu.: 2.000 1st Qu.:3.000
Median :52.00 Median :1.000 Median : 3.000 Median :3.000
Mean :55.89 Mean :1.856 Mean : 3.303 Mean :3.304
3rd Qu.:62.00 3rd Qu.:3.000 3rd Qu.: 5.000 3rd Qu.:4.000
Max. :99.00 Max. :7.000 Max. :10.000 Max. :5.000
NA's :5 NA's :2
TV10 TV4 TV9 TV6 TV2
Min. :1.000 Min. :1.00 Min. :1.000 Min. :1.000 Min. :1.000
1st Qu.:1.000 1st Qu.:2.00 1st Qu.:3.000 1st Qu.:2.000 1st Qu.:3.000
Median :2.000 Median :2.00 Median :4.000 Median :3.000 Median :3.000
Mean :2.353 Mean :2.48 Mean :3.471 Mean :2.618 Mean :3.275
3rd Qu.:3.000 3rd Qu.:3.00 3rd Qu.:4.000 3rd Qu.:3.000 3rd Qu.:4.000
Max. :5.000 Max. :5.00 Max. :5.000 Max. :5.000 Max. :5.000
NA's :2 NA's :2 NA's :2 NA's :2 NA's :2
TV5 TV11 TV3 TV12 TV7
Min. :1.0 Min. :2.000 Min. :1.000 Min. :1.000 Min. :1.000
1st Qu.:3.0 1st Qu.:3.000 1st Qu.:3.000 1st Qu.:3.000 1st Qu.:3.000
Median :4.0 Median :4.000 Median :3.000 Median :3.500 Median :4.000
Mean :3.5 Mean :3.804 Mean :3.255 Mean :3.461 Mean :3.745
3rd Qu.:4.0 3rd Qu.:5.000 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:5.000
Max. :5.0 Max. :5.000 Max. :5.000 Max. :5.000 Max. :5.000
NA's :2 NA's :2 NA's :2 NA's :2 NA's :2
TV8 IntrVaPostTS UtilVaPostTS AttaVaPostTS
Min. :1.000 Min. : 6.00 Min. : 7.00 Min. : 6.00
1st Qu.:3.000 1st Qu.:11.00 1st Qu.:12.00 1st Qu.:11.25
Median :3.000 Median :12.50 Median :13.50 Median :13.00
Mean :3.402 Mean :12.31 Mean :13.26 Mean :13.09
3rd Qu.:4.000 3rd Qu.:14.00 3rd Qu.:15.00 3rd Qu.:15.00
Max. :5.000 Max. :17.00 Max. :19.00 Max. :20.00
NA's :2 NA's :2 NA's :2 NA's :2
IntrVaPreTS UtilVaPreTS AttaVaPreTS TVPreTS
Min. : 6.00 Min. : 7.00 Min. : 5.00 Min. :23.00
1st Qu.:10.00 1st Qu.:10.00 1st Qu.:10.00 1st Qu.:30.00
Median :11.00 Median :12.00 Median :11.00 Median :35.00
Mean :11.28 Mean :12.09 Mean :11.39 Mean :34.76
3rd Qu.:13.00 3rd Qu.:14.00 3rd Qu.:13.00 3rd Qu.:38.00
Max. :16.00 Max. :16.00 Max. :16.00 Max. :48.00
TVPosTS
Min. :24.00
1st Qu.:36.00
Median :39.00
Mean :38.67
3rd Qu.:42.00
Max. :48.00
NA's :2 Preprocessing
data_clean <- na.omit(data)data_clean$TV_total <- rowSums(data_clean[, paste0("TV", 1:12)], na.rm = TRUE)data$CU_diff <- data$CUPostTS - data$CUPreTSdata_clean$Groups <- as.factor(data_clean$Groups)Uji Multivariate Normality
dv2 <- data_clean[, c("IntrVaPostTS", "UtilVaPostTS")]
mvn(dv2)$multivariate_normality
Test Statistic p.value Method MVN
1 Henze-Zirkler 0.402 0.807 asymptotic ✓ Normal
$univariate_normality
Test Variable Statistic p.value Normality
1 Anderson-Darling IntrVaPostTS 0.912 0.019 ✗ Not normal
2 Anderson-Darling UtilVaPostTS 1.084 0.007 ✗ Not normal
$descriptives
Variable n Mean Std.Dev Median Min Max 25th 75th Skew Kurtosis
1 IntrVaPostTS 99 12.313 2.522 13 6 17 11 14 -0.241 2.512
2 UtilVaPostTS 99 13.313 2.207 14 7 19 12 15 -0.252 3.060
$data
IntrVaPostTS UtilVaPostTS
1 14 13
2 13 13
3 15 12
4 13 14
5 12 11
6 17 16
7 15 12
8 11 13
9 13 14
10 11 15
11 14 13
12 16 16
13 15 13
14 10 12
15 14 12
16 13 17
17 12 14
18 11 14
19 16 13
20 15 15
22 11 12
23 11 11
24 15 11
25 14 13
26 14 11
27 13 11
28 13 16
29 17 13
30 15 17
31 15 14
33 16 16
34 12 11
35 12 9
36 8 8
37 8 14
38 9 11
40 6 7
41 13 13
42 8 10
43 11 12
44 11 15
45 13 14
46 8 14
47 9 11
48 9 13
49 16 15
50 8 16
51 13 15
52 12 15
53 13 10
54 15 15
55 14 14
56 15 13
57 9 13
58 9 13
59 13 16
60 6 11
61 13 14
62 15 12
63 10 15
64 13 14
65 10 14
66 13 15
67 15 16
68 12 13
69 11 11
70 9 13
71 11 16
72 16 14
73 10 12
74 17 15
75 11 11
76 11 15
77 12 14
78 14 12
79 14 11
80 17 16
81 14 17
82 12 15
83 10 12
84 11 15
85 14 9
86 14 19
88 11 14
89 9 15
90 12 15
91 15 10
92 10 16
93 9 18
94 11 14
95 13 14
96 15 14
97 12 12
99 13 14
100 12 11
101 12 13
102 10 14
103 13 9
104 9 10
$subset
NULL
$outlierMethod
[1] "none"
attr(,"class")
[1] "mvn"Uji Dependensi DV
cor(dv2) IntrVaPostTS UtilVaPostTS
IntrVaPostTS 1.0000000 0.2590489
UtilVaPostTS 0.2590489 1.0000000Homogen
boxM(dv2, data_clean$Groups)
Box's M-test for Homogeneity of Covariance Matrices
data: dv2
Chi-Sq (approx.) = 11.802, df = 6, p-value = 0.06653Uji Linear
plot(data_clean$TV_total, data_clean$IntrVaPostTS)
plot(data_clean$TV_total, data_clean$UtilVaPostTS)
MANOVA
model_manova <- manova(
cbind(IntrVaPostTS, UtilVaPostTS) ~ Groups,
data = data_clean
)
summary(model_manova) Df Pillai approx F num Df den Df Pr(>F)
Groups 2 0.15557 4.0487 4 192 0.003561 **
Residuals 96
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1MANCOVA
model_mancova <- manova(
cbind(IntrVaPostTS, UtilVaPostTS) ~ Groups + IntrVaPreTS + UtilVaPreTS,
data = data_clean
)
summary(model_mancova) Df Pillai approx F num Df den Df Pr(>F)
Groups 2 0.186593 4.8361 4 188 0.0009809 ***
IntrVaPreTS 1 0.200411 11.6549 2 93 3.043e-05 ***
UtilVaPreTS 1 0.074593 3.7482 2 93 0.0271938 *
Residuals 94
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1ANCOVA
model_ancova <- aov(
IntrVaPostTS ~ Groups + IntrVaPreTS,
data = data_clean
)
summary(model_ancova) Df Sum Sq Mean Sq F value Pr(>F)
Groups 2 89.9 44.96 9.99 0.000115 ***
IntrVaPreTS 1 105.8 105.81 23.51 4.84e-06 ***
Residuals 95 427.6 4.50
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1ANOVA
model_anova <- aov(
IntrVaPostTS ~ Groups,
data = data_clean
)
summary(model_anova) Df Sum Sq Mean Sq F value Pr(>F)
Groups 2 89.9 44.96 8.092 0.000565 ***
Residuals 96 533.4 5.56
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1