#Chapitre 2 : solution des exercices
library(BioStatR)
data("Quetelet")
Quetelet$BMI=with(Quetelet,poids/(taille/100)^2)
library(MVN)
## Registered S3 method overwritten by 'GGally':
## method from
## +.gg ggplot2
## sROC 0.1-2 loaded
mvn(Quetelet[,-1], mvnTest = "mardia",
univariateTest = "SW", univariatePlot = "histogram",
multivariatePlot = "qq", multivariateOutlierMethod = "adj",
showOutliers = TRUE, showNewData = TRUE)
## $multivariateNormality
## Test Statistic p value Result
## 1 Mardia Skewness 69.6790258334751 5.11364246753169e-11 NO
## 2 Mardia Kurtosis 5.38926570325248 7.074614538638e-08 NO
## 3 MVN <NA> <NA> NO
##
## $univariateNormality
## Test Variable Statistic p value Normality
## 1 Shapiro-Wilk poids 0.9399 0.0031 NO
## 2 Shapiro-Wilk taille 0.9877 0.7585 YES
## 3 Shapiro-Wilk BMI 0.9802 0.3741 YES
##
## $Descriptives
## n Mean Std.Dev Median Min Max 25th
## poids 66 64.51515 11.116505 65.50000 47.00000 86.00000 53.00000
## taille 66 174.06061 9.313148 174.50000 150.00000 200.00000 168.00000
## BMI 66 21.15609 2.266562 20.89342 16.91723 26.76978 19.52229
## 75th Skew Kurtosis
## poids 73.00000 0.04322566 -1.26787864
## taille 180.00000 -0.05066418 -0.09962364
## BMI 22.38163 0.35034822 -0.50614393
##
## $multivariateOutliers
## Observation Mahalanobis Distance Outlier
## 65 65 34.446 TRUE
## 54 54 30.836 TRUE
## 12 12 27.148 TRUE
## 7 7 24.711 TRUE
## 21 21 24.213 TRUE
## 6 6 18.274 TRUE
## 42 42 17.442 TRUE
## 31 31 17.024 TRUE
## 22 22 16.455 TRUE
## 16 16 15.875 TRUE
## 9 9 12.458 TRUE
##
## $newData
## poids taille BMI
## 1 60 170 20.76125
## 10 64 175 20.89796
## 11 53 165 19.46740
## 13 61 175 19.91837
## 14 78 184 23.03875
## 15 68 178 21.46194
## 17 53 164 19.70553
## 18 79 179 24.65591
## 19 74 182 22.34030
## 2 57 169 19.95728
## 20 62 174 20.47827
## 23 74 172 25.01352
## 24 80 185 23.37473
## 25 53 170 18.33910
## 26 73 178 23.04002
## 27 70 180 21.60494
## 28 72 189 20.15621
## 29 70 172 23.66144
## 3 51 172 17.23905
## 30 62 174 20.47827
## 32 70 178 22.09317
## 33 76 178 23.98687
## 34 51 168 18.06973
## 35 52 170 17.99308
## 36 57 160 22.26562
## 37 53 163 19.94806
## 38 55 168 19.48696
## 39 66 172 22.30936
## 4 55 174 18.16620
## 40 65 175 21.22449
## 41 75 180 23.14815
## 43 53 177 16.91723
## 44 55 169 19.25703
## 45 55 173 18.37683
## 46 72 182 21.73651
## 47 75 183 22.39541
## 48 73 184 21.56191
## 49 71 181 21.67211
## 5 50 168 17.71542
## 50 66 180 20.37037
## 51 71 178 22.40879
## 52 79 178 24.93372
## 53 62 168 21.96712
## 55 73 171 24.96495
## 56 72 180 22.22222
## 57 60 174 19.81768
## 58 67 175 21.87755
## 59 85 182 25.66115
## 60 73 181 22.28259
## 61 82 188 23.20054
## 62 86 182 25.96305
## 63 85 189 23.79553
## 64 65 178 20.51509
## 66 74 186 21.38976
## 8 72 189 20.15621
Quetelet_H=subset(Quetelet,subset=Quetelet$sexe=="h")
Quetelet_F=subset(Quetelet,subset=Quetelet$sexe=="f")
mvn(Quetelet_H[,-1], mvnTest = "mardia",
univariateTest = "SW", univariatePlot = "histogram",
multivariatePlot = "qq", multivariateOutlierMethod = "adj",
showOutliers = TRUE, showNewData = TRUE)
## $multivariateNormality
## Test Statistic p value Result
## 1 Mardia Skewness 94.4778475662391 6.90120959921686e-16 NO
## 2 Mardia Kurtosis 8.12335586778857 4.44089209850063e-16 NO
## 3 MVN <NA> <NA> NO
##
## $univariateNormality
## Test Variable Statistic p value Normality
## 1 Shapiro-Wilk poids 0.9728 0.4238 YES
## 2 Shapiro-Wilk taille 0.9737 0.4511 YES
## 3 Shapiro-Wilk BMI 0.9776 0.5874 YES
##
## $Descriptives
## n Mean Std.Dev Median Min Max 25th
## poids 41 71.29268 7.619855 72.00000 55.00000 86.00000 66.00000
## taille 41 179.19512 6.738767 179.00000 164.00000 200.00000 175.00000
## BMI 41 22.18880 1.964237 21.96712 18.37683 26.76978 20.76125
## 75th Skew Kurtosis
## poids 75.00000 -0.1912013 -0.4367203
## taille 182.00000 0.3912155 0.8351991
## BMI 23.20054 0.3705053 -0.5164511
##
## $multivariateOutliers
## Observation Mahalanobis Distance Outlier
## 12 12 425.575 TRUE
## 63 63 118.562 TRUE
## 31 31 111.068 TRUE
## 44 44 69.381 TRUE
## 55 55 59.623 TRUE
## 61 61 56.435 TRUE
## 23 23 48.616 TRUE
## 62 62 42.313 TRUE
## 59 59 36.419 TRUE
## 45 45 31.723 TRUE
## 24 24 26.002 TRUE
## 8 8 19.838 TRUE
## 28 28 19.838 TRUE
## 14 14 11.973 TRUE
## 1 1 11.434 TRUE
##
## $newData
## poids taille BMI
## 10 64 175 20.89796
## 13 61 175 19.91837
## 15 68 178 21.46194
## 18 79 179 24.65591
## 19 74 182 22.34030
## 20 62 174 20.47827
## 26 73 178 23.04002
## 27 70 180 21.60494
## 32 70 178 22.09317
## 33 76 178 23.98687
## 40 65 175 21.22449
## 41 75 180 23.14815
## 46 72 182 21.73651
## 47 75 183 22.39541
## 48 73 184 21.56191
## 49 71 181 21.67211
## 50 66 180 20.37037
## 51 71 178 22.40879
## 52 79 178 24.93372
## 53 62 168 21.96712
## 56 72 180 22.22222
## 57 60 174 19.81768
## 58 67 175 21.87755
## 60 73 181 22.28259
## 64 65 178 20.51509
## 66 74 186 21.38976
mvn(Quetelet_F[,-1], mvnTest = "mardia",
univariateTest = "SW", univariatePlot = "histogram",
multivariatePlot = "qq", multivariateOutlierMethod = "adj",
showOutliers = TRUE, showNewData = TRUE)
## $multivariateNormality
## Test Statistic p value Result
## 1 Mardia Skewness 37.2056843384273 5.21388957554759e-05 NO
## 2 Mardia Kurtosis 2.48592654811622 0.0129214632354677 NO
## 3 MVN <NA> <NA> NO
##
## $univariateNormality
## Test Variable Statistic p value Normality
## 1 Shapiro-Wilk poids 0.8297 0.0007 NO
## 2 Shapiro-Wilk taille 0.9677 0.5864 YES
## 3 Shapiro-Wilk BMI 0.9471 0.2152 YES
##
## $Descriptives
## n Mean Std.Dev Median Min Max 25th
## poids 25 53.40000 5.545268 52.0000 47.00000 70.00000 50.0000
## taille 25 165.64000 6.350066 165.0000 150.00000 177.00000 161.0000
## BMI 25 19.46244 1.635013 19.4674 16.91723 23.66144 18.1662
## 75th Skew Kurtosis
## poids 55.0000 1.4874294 1.74551814
## taille 170.0000 -0.2756669 -0.48263809
## BMI 20.3125 0.7163074 0.01586493
##
## $multivariateOutliers
## Observation Mahalanobis Distance Outlier
## 29 29 547.900 TRUE
## 43 43 330.073 TRUE
## 39 39 255.928 TRUE
## 3 3 145.619 TRUE
## 30 30 61.975 TRUE
## 4 4 58.988 TRUE
## 35 35 48.558 TRUE
## 5 5 45.119 TRUE
## 34 34 30.206 TRUE
## 25 25 29.705 TRUE
##
## $newData
## poids taille BMI
## 11 53 165 19.46740
## 16 51 158 20.42942
## 17 53 164 19.70553
## 2 57 169 19.95728
## 21 49 158 19.62826
## 22 50 163 18.81892
## 36 57 160 22.26562
## 37 53 163 19.94806
## 38 55 168 19.48696
## 42 50 162 19.05197
## 54 47 161 18.13202
## 6 50 161 19.28938
## 65 47 150 20.88889
## 7 48 162 18.28989
## 9 52 160 20.31250
cor(Quetelet[,-1], method="spearman")
## poids taille BMI
## poids 1.0000000 0.8435359 0.8221544
## taille 0.8435359 1.0000000 0.4586364
## BMI 0.8221544 0.4586364 1.0000000
library(corrplot)
## corrplot 0.84 loaded
cor.mtest(Quetelet[,-1], method="spearman")
## Warning in cor.test.default(x = mat[, i], y = mat[, j], ...): Cannot
## compute exact p-value with ties
## Warning in cor.test.default(x = mat[, i], y = mat[, j], ...): Cannot
## compute exact p-value with ties
## Warning in cor.test.default(x = mat[, i], y = mat[, j], ...): Cannot
## compute exact p-value with ties
## $p
## [,1] [,2] [,3]
## [1,] 0.000000e+00 6.173648e-19 2.625473e-17
## [2,] 6.173648e-19 0.000000e+00 1.075634e-04
## [3,] 2.625473e-17 1.075634e-04 0.000000e+00
##
## $lowCI
## [,1] [,2] [,3]
## [1,] 1 NA NA
## [2,] NA 1 NA
## [3,] NA NA 1
##
## $uppCI
## [,1] [,2] [,3]
## [1,] 1 NA NA
## [2,] NA 1 NA
## [3,] NA NA 1
#d'apres la formule du BMI, mauvais signe pour cor BMI et taille
library(ppcor)
## Loading required package: MASS
pcor(Quetelet[,-1], method = "spearman")
## $estimate
## poids taille BMI
## poids 1.0000000 0.9221206 0.9120436
## taille 0.9221206 1.0000000 -0.7682441
## BMI 0.9120436 -0.7682441 1.0000000
##
## $p.value
## poids taille BMI
## poids 0.000000e+00 1.131073e-27 4.475042e-26
## taille 1.131073e-27 0.000000e+00 8.064386e-14
## BMI 4.475042e-26 8.064386e-14 0.000000e+00
##
## $statistic
## poids taille BMI
## poids 0.00000 18.917181 17.652378
## taille 18.91718 0.000000 -9.525396
## BMI 17.65238 -9.525396 0.000000
##
## $n
## [1] 66
##
## $gp
## [1] 1
##
## $method
## [1] "spearman"
#d'apres la formule du BMI, bon signe pour cor BMI et taille
cor(Quetelet[,-1], method="kendall")
## poids taille BMI
## poids 1.0000000 0.6806185 0.6495408
## taille 0.6806185 1.0000000 0.3060194
## BMI 0.6495408 0.3060194 1.0000000
cor.mtest(Quetelet[,-1], method="kendall")
## $p
## [,1] [,2] [,3]
## [1,] 0.000000e+00 4.023325e-15 2.776287e-14
## [2,] 4.023325e-15 0.000000e+00 3.491883e-04
## [3,] 2.776287e-14 3.491883e-04 0.000000e+00
##
## $lowCI
## [,1] [,2] [,3]
## [1,] 1 NA NA
## [2,] NA 1 NA
## [3,] NA NA 1
##
## $uppCI
## [,1] [,2] [,3]
## [1,] 1 NA NA
## [2,] NA 1 NA
## [3,] NA NA 1
#d'apres la formule du BMI, mauvais signe pour cor BMI et taille
pcor(Quetelet[,-1], method = "kendall")
## $estimate
## poids taille BMI
## poids 1.0000000 0.6656714 0.6326376
## taille 0.6656714 1.0000000 -0.2442715
## BMI 0.6326376 -0.2442715 1.0000000
##
## $p.value
## poids taille BMI
## poids 0.000000e+00 4.551113e-15 9.352566e-14
## taille 4.551113e-15 0.000000e+00 4.021582e-03
## BMI 9.352566e-14 4.021582e-03 0.000000e+00
##
## $statistic
## poids taille BMI
## poids 0.000000 7.838734 7.449738
## taille 7.838734 0.000000 -2.876464
## BMI 7.449738 -2.876464 0.000000
##
## $n
## [1] 66
##
## $gp
## [1] 1
##
## $method
## [1] "kendall"
#d'apres la formule du BMI, bon signe pour cor BMI et taille
cor(Quetelet_H[,-1], method="spearman")
## poids taille BMI
## poids 1.0000000 0.65435663 0.73250254
## taille 0.6543566 1.00000000 0.06367584
## BMI 0.7325025 0.06367584 1.00000000
cor.mtest(Quetelet_H[,-1], method="spearman")
## Warning in cor.test.default(x = mat[, i], y = mat[, j], ...): Cannot
## compute exact p-value with ties
## Warning in cor.test.default(x = mat[, i], y = mat[, j], ...): Cannot
## compute exact p-value with ties
## Warning in cor.test.default(x = mat[, i], y = mat[, j], ...): Cannot
## compute exact p-value with ties
## $p
## [,1] [,2] [,3]
## [1,] 0.000000e+00 3.476465e-06 5.211433e-08
## [2,] 3.476465e-06 0.000000e+00 6.924613e-01
## [3,] 5.211433e-08 6.924613e-01 0.000000e+00
##
## $lowCI
## [,1] [,2] [,3]
## [1,] 1 NA NA
## [2,] NA 1 NA
## [3,] NA NA 1
##
## $uppCI
## [,1] [,2] [,3]
## [1,] 1 NA NA
## [2,] NA 1 NA
## [3,] NA NA 1
#d'apres la formule du BMI, mauvais signe pour cor BMI et taille
pcor(Quetelet_H[,-1], method = "spearman")
## $estimate
## poids taille BMI
## poids 1.0000000 0.8945089 0.9154369
## taille 0.8945089 1.0000000 -0.8074098
## BMI 0.9154369 -0.8074098 1.0000000
##
## $p.value
## poids taille BMI
## poids 0.000000e+00 7.387085e-15 1.333566e-16
## taille 7.387085e-15 0.000000e+00 3.080328e-10
## BMI 1.333566e-16 3.080328e-10 0.000000e+00
##
## $statistic
## poids taille BMI
## poids 0.00000 12.334460 14.021543
## taille 12.33446 0.000000 -8.436075
## BMI 14.02154 -8.436075 0.000000
##
## $n
## [1] 41
##
## $gp
## [1] 1
##
## $method
## [1] "spearman"
#d'apres la formule du BMI, bon signe pour cor BMI et taille
cor(Quetelet_H[,-1], method="kendall")
## poids taille BMI
## poids 1.0000000 0.51311252 0.58853704
## taille 0.5131125 1.00000000 0.07154546
## BMI 0.5885370 0.07154546 1.00000000
cor.mtest(Quetelet_H[,-1], method="kendall")
## Warning in cor.test.default(x = mat[, i], y = mat[, j], ...): Cannot
## compute exact p-value with ties
## Warning in cor.test.default(x = mat[, i], y = mat[, j], ...): Cannot
## compute exact p-value with ties
## Warning in cor.test.default(x = mat[, i], y = mat[, j], ...): Cannot
## compute exact p-value with ties
## $p
## [,1] [,2] [,3]
## [1,] 0.000000e+00 5.418566e-06 9.445912e-08
## [2,] 5.418566e-06 0.000000e+00 5.199700e-01
## [3,] 9.445912e-08 5.199700e-01 0.000000e+00
##
## $lowCI
## [,1] [,2] [,3]
## [1,] 1 NA NA
## [2,] NA 1 NA
## [3,] NA NA 1
##
## $uppCI
## [,1] [,2] [,3]
## [1,] 1 NA NA
## [2,] NA 1 NA
## [3,] NA NA 1
#d'apres la formule du BMI, mauvais signe pour cor BMI et taille
pcor(Quetelet_H[,-1], method = "kendall")
## $estimate
## poids taille BMI
## poids 1.0000000 0.5840852 0.6445651
## taille 0.5840852 1.0000000 -0.3320813
## BMI 0.6445651 -0.3320813 1.0000000
##
## $p.value
## poids taille BMI
## poids 0.000000e+00 1.108022e-07 4.693702e-09
## taille 1.108022e-07 0.000000e+00 2.545407e-03
## BMI 4.693702e-09 2.545407e-03 0.000000e+00
##
## $statistic
## poids taille BMI
## poids 0.000000 5.308053 5.857683
## taille 5.308053 0.000000 -3.017891
## BMI 5.857683 -3.017891 0.000000
##
## $n
## [1] 41
##
## $gp
## [1] 1
##
## $method
## [1] "kendall"
#d'apres la formule du BMI, bon signe pour cor BMI et taille
cor(Quetelet_F[,-1], method="spearman")
## poids taille BMI
## poids 1.0000000 0.6248362 0.4366643
## taille 0.6248362 1.0000000 -0.2877543
## BMI 0.4366643 -0.2877543 1.0000000
cor.mtest(Quetelet_F[,-1], method="spearman")
## Warning in cor.test.default(x = mat[, i], y = mat[, j], ...): Cannot
## compute exact p-value with ties
## Warning in cor.test.default(x = mat[, i], y = mat[, j], ...): Cannot
## compute exact p-value with ties
## Warning in cor.test.default(x = mat[, i], y = mat[, j], ...): Cannot
## compute exact p-value with ties
## $p
## [,1] [,2] [,3]
## [1,] 0.0000000000 0.0008402762 0.02907721
## [2,] 0.0008402762 0.0000000000 0.16307019
## [3,] 0.0290772141 0.1630701918 0.00000000
##
## $lowCI
## [,1] [,2] [,3]
## [1,] 1 NA NA
## [2,] NA 1 NA
## [3,] NA NA 1
##
## $uppCI
## [,1] [,2] [,3]
## [1,] 1 NA NA
## [2,] NA 1 NA
## [3,] NA NA 1
#d'apres la formule du BMI, mauvais signe pour cor BMI et taille
pcor(Quetelet_F[,-1], method = "spearman")
## $estimate
## poids taille BMI
## poids 1.0000000 0.8710663 0.8244433
## taille 0.8710663 1.0000000 -0.7981326
## BMI 0.8244433 -0.7981326 1.0000000
##
## $p.value
## poids taille BMI
## poids 0.000000e+00 3.070201e-08 7.285921e-07
## taille 3.070201e-08 0.000000e+00 2.969505e-06
## BMI 7.285921e-07 2.969505e-06 0.000000e+00
##
## $statistic
## poids taille BMI
## poids 0.000000 8.318303 6.832793
## taille 8.318303 0.000000 -6.213587
## BMI 6.832793 -6.213587 0.000000
##
## $n
## [1] 25
##
## $gp
## [1] 1
##
## $method
## [1] "spearman"
#d'apres la formule du BMI, bon signe pour cor BMI et taille
cor(Quetelet_F[,-1], method="kendall")
## poids taille BMI
## poids 1.0000000 0.4823453 0.3226134
## taille 0.4823453 1.0000000 -0.2419674
## BMI 0.3226134 -0.2419674 1.0000000
cor.mtest(Quetelet_F[,-1], method="kendall")
## Warning in cor.test.default(x = mat[, i], y = mat[, j], ...): Cannot
## compute exact p-value with ties
## Warning in cor.test.default(x = mat[, i], y = mat[, j], ...): Cannot
## compute exact p-value with ties
## Warning in cor.test.default(x = mat[, i], y = mat[, j], ...): Cannot
## compute exact p-value with ties
## $p
## [,1] [,2] [,3]
## [1,] 0.000000000 0.001294553 0.02839192
## [2,] 0.001294553 0.000000000 0.09596802
## [3,] 0.028391922 0.095968017 0.00000000
##
## $lowCI
## [,1] [,2] [,3]
## [1,] 1 NA NA
## [2,] NA 1 NA
## [3,] NA NA 1
##
## $uppCI
## [,1] [,2] [,3]
## [1,] 1 NA NA
## [2,] NA 1 NA
## [3,] NA NA 1
#d'apres la formule du BMI, mauvais signe pour cor BMI et taille
pcor(Quetelet_F[,-1], method = "kendall")
## $estimate
## poids taille BMI
## poids 1.0000000 0.6101968 0.5168831
## taille 0.6101968 1.0000000 -0.4795052
## BMI 0.5168831 -0.4795052 1.0000000
##
## $p.value
## poids taille BMI
## poids 0.000000e+00 2.948386e-05 0.0004022705
## taille 2.948386e-05 0.000000e+00 0.0010281813
## BMI 4.022705e-04 1.028181e-03 0.0000000000
##
## $statistic
## poids taille BMI
## poids 0.000000 4.177417 3.53859
## taille 4.177417 0.000000 -3.28270
## BMI 3.538590 -3.282700 0.00000
##
## $n
## [1] 25
##
## $gp
## [1] 1
##
## $method
## [1] "kendall"
#d'apres la formule du BMI, bon signe pour cor BMI et taille
library(GGally)
## Loading required package: ggplot2
ggpairs(Quetelet)
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
#Pour sauvegarder le graphique enlever les commentaires des trois commandes ci-dessous
# pdf("ggpairsBMI.pdf")
# print(ggpairs(Quetelet))
# dev.off()
#generation de donnees de type Ecole
library(mvtnorm)
sigma <- matrix(c(4,-.5,2.5,-.5,4,3,2.5,3,4),byrow=TRUE, ncol=3)
sigma
## [,1] [,2] [,3]
## [1,] 4.0 -0.5 2.5
## [2,] -0.5 4.0 3.0
## [3,] 2.5 3.0 4.0
library(corpcor)
pcor2cor(cov2cor(sigma))
## [,1] [,2] [,3]
## [1,] 1.0000000 0.6657503 0.8095238
## [2,] 0.6657503 1.0000000 0.8674928
## [3,] 0.8095238 0.8674928 1.0000000
aaa=rmvnorm(n=119, mean=c(11,11,14), sigma=pcor2cor(cov2cor(sigma)))
cor(aaa[,2],(aaa[,3]-5)/10)
## [1] 0.8875335
bbb=aaa
bbb[,3]<-(aaa[,3]-1)
bbb[,1]<-((aaa[,1])-7)/6*17
bbb[,2]<-((aaa[,2])-7)/6*17
round(aaa,digits = 2)
## [,1] [,2] [,3]
## [1,] 10.42 11.84 14.41
## [2,] 9.97 9.91 12.94
## [3,] 11.23 11.03 14.12
## [4,] 10.68 10.15 13.05
## [5,] 10.60 10.44 13.36
## [6,] 12.73 11.80 14.47
## [7,] 11.88 11.09 14.35
## [8,] 11.50 11.04 14.20
## [9,] 10.73 10.74 13.92
## [10,] 11.68 10.70 14.37
## [11,] 11.90 12.61 15.23
## [12,] 10.35 9.84 13.04
## [13,] 11.29 12.24 15.15
## [14,] 11.80 11.42 14.83
## [15,] 9.81 9.85 12.71
## [16,] 11.34 11.14 13.84
## [17,] 11.10 11.20 14.43
## [18,] 11.13 10.49 13.92
## [19,] 11.51 12.02 14.92
## [20,] 10.83 11.41 14.68
## [21,] 11.28 10.72 14.10
## [22,] 11.08 10.31 13.92
## [23,] 12.53 11.21 15.21
## [24,] 10.08 9.87 12.79
## [25,] 10.57 11.81 14.56
## [26,] 10.97 11.21 14.51
## [27,] 11.40 11.51 14.30
## [28,] 11.66 11.24 14.09
## [29,] 9.72 8.94 12.61
## [30,] 10.61 10.96 14.32
## [31,] 9.51 10.57 12.80
## [32,] 9.37 8.75 11.26
## [33,] 11.53 13.04 15.38
## [34,] 10.17 10.60 13.82
## [35,] 11.42 10.99 13.94
## [36,] 10.45 10.99 13.58
## [37,] 12.59 12.23 15.34
## [38,] 10.03 9.88 12.91
## [39,] 10.68 10.81 13.58
## [40,] 10.30 10.33 13.15
## [41,] 11.81 11.43 14.82
## [42,] 9.90 11.26 14.19
## [43,] 11.08 12.37 14.66
## [44,] 12.07 12.46 15.63
## [45,] 11.47 10.60 14.49
## [46,] 11.47 10.86 14.43
## [47,] 9.88 10.55 13.90
## [48,] 9.70 10.97 14.58
## [49,] 12.06 11.92 14.80
## [50,] 11.19 12.09 13.99
## [51,] 10.20 11.31 13.28
## [52,] 10.14 10.66 13.57
## [53,] 9.05 9.91 12.57
## [54,] 11.11 11.65 14.89
## [55,] 10.78 10.82 14.14
## [56,] 12.22 11.94 15.22
## [57,] 11.83 9.86 13.32
## [58,] 11.92 10.86 14.28
## [59,] 12.46 11.26 14.89
## [60,] 10.26 10.71 14.25
## [61,] 10.27 10.70 13.38
## [62,] 12.10 12.44 15.30
## [63,] 12.97 13.32 16.59
## [64,] 13.43 12.53 15.79
## [65,] 13.14 12.40 16.30
## [66,] 13.16 12.86 16.23
## [67,] 11.31 13.25 16.25
## [68,] 11.45 12.06 14.94
## [69,] 10.23 11.43 13.50
## [70,] 12.10 11.25 14.89
## [71,] 10.57 10.42 13.19
## [72,] 11.43 11.23 14.21
## [73,] 10.32 11.58 14.34
## [74,] 9.99 11.46 14.09
## [75,] 11.42 12.77 15.57
## [76,] 9.18 10.44 12.85
## [77,] 12.28 11.17 14.97
## [78,] 10.30 9.67 12.61
## [79,] 12.97 11.83 14.82
## [80,] 11.93 12.05 15.01
## [81,] 10.77 10.55 13.75
## [82,] 9.88 10.71 13.61
## [83,] 10.29 11.43 14.55
## [84,] 8.84 9.65 11.74
## [85,] 11.72 11.44 14.91
## [86,] 12.40 12.77 15.25
## [87,] 12.17 11.70 15.26
## [88,] 11.09 11.90 14.47
## [89,] 12.56 12.64 15.79
## [90,] 10.99 11.15 14.36
## [91,] 10.24 9.79 12.08
## [92,] 11.26 11.61 14.73
## [93,] 10.19 11.33 14.53
## [94,] 11.27 11.47 14.75
## [95,] 11.15 10.94 14.44
## [96,] 10.50 11.10 13.90
## [97,] 11.93 12.33 14.42
## [98,] 10.53 12.36 14.30
## [99,] 10.74 10.35 13.33
## [100,] 11.68 11.22 14.45
## [101,] 11.23 11.71 14.73
## [102,] 12.81 12.57 15.95
## [103,] 10.09 9.28 12.29
## [104,] 10.99 10.58 13.47
## [105,] 9.46 10.76 12.62
## [106,] 11.08 11.04 14.82
## [107,] 11.87 11.25 14.44
## [108,] 10.58 11.14 13.89
## [109,] 9.85 10.49 13.01
## [110,] 10.88 10.82 13.92
## [111,] 11.36 11.11 13.59
## [112,] 12.64 12.15 15.31
## [113,] 12.64 12.66 15.28
## [114,] 11.38 10.16 13.02
## [115,] 12.38 11.94 15.63
## [116,] 10.86 10.08 13.17
## [117,] 11.60 11.94 15.10
## [118,] 10.88 11.41 13.44
## [119,] 11.48 11.22 14.69
round(bbb,digits = 2)
## [,1] [,2] [,3]
## [1,] 9.68 13.70 13.41
## [2,] 8.43 8.24 11.94
## [3,] 11.99 11.41 13.12
## [4,] 10.42 8.93 12.05
## [5,] 10.20 9.75 12.36
## [6,] 16.24 13.61 13.47
## [7,] 13.82 11.60 13.35
## [8,] 12.76 11.45 13.20
## [9,] 10.56 10.61 12.92
## [10,] 13.26 10.49 13.37
## [11,] 13.88 15.89 14.23
## [12,] 9.48 8.05 12.04
## [13,] 12.14 14.86 14.15
## [14,] 13.59 12.53 13.83
## [15,] 7.97 8.08 11.71
## [16,] 12.29 11.73 12.84
## [17,] 11.63 11.90 13.43
## [18,] 11.69 9.88 12.92
## [19,] 12.77 14.22 13.92
## [20,] 10.84 12.50 13.68
## [21,] 12.13 10.54 13.10
## [22,] 11.56 9.37 12.92
## [23,] 15.66 11.92 14.21
## [24,] 8.73 8.15 11.79
## [25,] 10.11 13.64 13.56
## [26,] 11.25 11.92 13.51
## [27,] 12.46 12.78 13.30
## [28,] 13.21 12.02 13.09
## [29,] 7.70 5.51 11.61
## [30,] 10.22 11.23 13.32
## [31,] 7.12 10.13 11.80
## [32,] 6.70 4.96 10.26
## [33,] 12.84 17.10 14.38
## [34,] 8.99 10.19 12.82
## [35,] 12.52 11.30 12.94
## [36,] 9.76 11.31 12.58
## [37,] 15.83 14.82 14.34
## [38,] 8.58 8.16 11.91
## [39,] 10.44 10.80 12.58
## [40,] 9.36 9.42 12.15
## [41,] 13.62 12.54 13.82
## [42,] 8.22 12.08 13.19
## [43,] 11.57 15.21 13.66
## [44,] 14.37 15.48 14.63
## [45,] 12.68 10.19 13.49
## [46,] 12.66 10.93 13.43
## [47,] 8.15 10.07 12.90
## [48,] 7.66 11.24 13.58
## [49,] 14.35 13.94 13.80
## [50,] 11.88 14.42 12.99
## [51,] 9.07 12.21 12.28
## [52,] 8.89 10.36 12.57
## [53,] 5.81 8.25 11.57
## [54,] 11.64 13.19 13.89
## [55,] 10.71 10.83 13.14
## [56,] 14.79 13.99 14.22
## [57,] 13.69 8.10 12.32
## [58,] 13.94 10.93 13.28
## [59,] 15.46 12.08 13.89
## [60,] 9.22 10.52 13.25
## [61,] 9.27 10.47 12.38
## [62,] 14.44 15.41 14.30
## [63,] 16.92 17.91 15.59
## [64,] 18.20 15.67 14.79
## [65,] 17.40 15.31 15.30
## [66,] 17.45 16.60 15.23
## [67,] 12.21 17.71 15.25
## [68,] 12.62 14.35 13.94
## [69,] 9.15 12.55 12.50
## [70,] 14.45 12.03 13.89
## [71,] 10.13 9.69 12.19
## [72,] 12.55 11.99 13.21
## [73,] 9.41 12.97 13.34
## [74,] 8.47 12.63 13.09
## [75,] 12.51 16.34 14.57
## [76,] 6.18 9.76 11.85
## [77,] 14.97 11.83 13.97
## [78,] 9.35 7.57 11.61
## [79,] 16.90 13.69 13.82
## [80,] 13.96 14.31 14.01
## [81,] 10.68 10.07 12.75
## [82,] 8.17 10.50 12.61
## [83,] 9.32 12.54 13.55
## [84,] 5.22 7.52 10.74
## [85,] 13.38 12.57 13.91
## [86,] 15.29 16.35 14.25
## [87,] 14.66 13.30 14.26
## [88,] 11.58 13.88 13.47
## [89,] 15.75 15.99 14.79
## [90,] 11.31 11.77 13.36
## [91,] 9.19 7.89 11.08
## [92,] 12.08 13.05 13.73
## [93,] 9.05 12.28 13.53
## [94,] 12.11 12.67 13.75
## [95,] 11.76 11.15 13.44
## [96,] 9.92 11.61 12.90
## [97,] 13.97 15.09 13.42
## [98,] 10.01 15.20 13.30
## [99,] 10.59 9.49 12.33
## [100,] 13.25 11.96 13.45
## [101,] 11.98 13.34 13.73
## [102,] 16.47 15.78 14.95
## [103,] 8.76 6.45 11.29
## [104,] 11.32 10.15 12.47
## [105,] 6.96 10.64 11.62
## [106,] 11.57 11.45 13.82
## [107,] 13.81 12.03 13.44
## [108,] 10.16 11.73 12.89
## [109,] 8.06 9.88 12.01
## [110,] 11.00 10.82 12.92
## [111,] 12.35 11.66 12.59
## [112,] 15.97 14.60 14.31
## [113,] 15.97 16.04 14.28
## [114,] 12.40 8.95 12.02
## [115,] 15.25 14.00 14.63
## [116,] 10.94 8.71 12.17
## [117,] 13.02 13.98 14.10
## [118,] 11.00 12.49 12.44
## [119,] 12.69 11.96 13.69
boxplot(bbb)
colnames(bbb) <- c("Maths","Sport","Age")
bbb <- data.frame(bbb)
ccc <- round(bbb, 2)
ccc <- data.frame(ccc)
#Pour sauvegarder les jeux de donnees enlever les commentaires des deux commandes ci-dessous
# write.csv(ccc,file="Ecole3.csv",row.names = FALSE)
# write.csv(ccc[,1:2],file="Ecole2.csv",row.names = FALSE)
mvn(ccc, mvnTest = "mardia",
univariateTest = "SW", univariatePlot = "histogram",
multivariatePlot = "qq", multivariateOutlierMethod = "adj",
showOutliers = TRUE, showNewData = TRUE)
## $multivariateNormality
## Test Statistic p value Result
## 1 Mardia Skewness 8.16781185199805 0.612449259212444 YES
## 2 Mardia Kurtosis -0.220229240847874 0.825692624711392 YES
## 3 MVN <NA> <NA> YES
##
## $univariateNormality
## Test Variable Statistic p value Normality
## 1 Shapiro-Wilk Maths 0.9930 0.8131 YES
## 2 Shapiro-Wilk Sport 0.9925 0.7723 YES
## 3 Shapiro-Wilk Age 0.9911 0.6394 YES
##
## $Descriptives
## n Mean Std.Dev Median Min Max 25th 75th Skew
## Maths 119 11.68655 2.7476666 11.69 5.22 18.20 9.445 13.605 0.08565721
## Sport 119 11.92933 2.5767259 11.92 4.96 17.91 10.275 13.695 -0.03735769
## Age 119 13.21706 0.9928647 13.34 10.26 15.59 12.575 13.860 -0.24752051
## Kurtosis
## Maths -0.49930432
## Sport -0.18100674
## Age 0.01724051
##
## $multivariateOutliers
## [1] Observation Mahalanobis Distance Outlier
## <0 rows> (or 0-length row.names)
##
## $newData
## Maths Sport Age
## 1 9.68 13.70 13.41
## 10 13.26 10.49 13.37
## 100 13.25 11.96 13.45
## 101 11.98 13.34 13.73
## 102 16.47 15.78 14.95
## 103 8.76 6.45 11.29
## 104 11.32 10.15 12.47
## 105 6.96 10.64 11.62
## 106 11.57 11.45 13.82
## 107 13.81 12.03 13.44
## 108 10.16 11.73 12.89
## 109 8.06 9.88 12.01
## 11 13.88 15.89 14.23
## 110 11.00 10.82 12.92
## 111 12.35 11.66 12.59
## 112 15.97 14.60 14.31
## 113 15.97 16.04 14.28
## 114 12.40 8.95 12.02
## 115 15.25 14.00 14.63
## 116 10.94 8.71 12.17
## 117 13.02 13.98 14.10
## 118 11.00 12.49 12.44
## 119 12.69 11.96 13.69
## 12 9.48 8.05 12.04
## 13 12.14 14.86 14.15
## 14 13.59 12.53 13.83
## 15 7.97 8.08 11.71
## 16 12.29 11.73 12.84
## 17 11.63 11.90 13.43
## 18 11.69 9.88 12.92
## 19 12.77 14.22 13.92
## 2 8.43 8.24 11.94
## 20 10.84 12.50 13.68
## 21 12.13 10.54 13.10
## 22 11.56 9.37 12.92
## 23 15.66 11.92 14.21
## 24 8.73 8.15 11.79
## 25 10.11 13.64 13.56
## 26 11.25 11.92 13.51
## 27 12.46 12.78 13.30
## 28 13.21 12.02 13.09
## 29 7.70 5.51 11.61
## 3 11.99 11.41 13.12
## 30 10.22 11.23 13.32
## 31 7.12 10.13 11.80
## 32 6.70 4.96 10.26
## 33 12.84 17.10 14.38
## 34 8.99 10.19 12.82
## 35 12.52 11.30 12.94
## 36 9.76 11.31 12.58
## 37 15.83 14.82 14.34
## 38 8.58 8.16 11.91
## 39 10.44 10.80 12.58
## 4 10.42 8.93 12.05
## 40 9.36 9.42 12.15
## 41 13.62 12.54 13.82
## 42 8.22 12.08 13.19
## 43 11.57 15.21 13.66
## 44 14.37 15.48 14.63
## 45 12.68 10.19 13.49
## 46 12.66 10.93 13.43
## 47 8.15 10.07 12.90
## 48 7.66 11.24 13.58
## 49 14.35 13.94 13.80
## 5 10.20 9.75 12.36
## 50 11.88 14.42 12.99
## 51 9.07 12.21 12.28
## 52 8.89 10.36 12.57
## 53 5.81 8.25 11.57
## 54 11.64 13.19 13.89
## 55 10.71 10.83 13.14
## 56 14.79 13.99 14.22
## 57 13.69 8.10 12.32
## 58 13.94 10.93 13.28
## 59 15.46 12.08 13.89
## 6 16.24 13.61 13.47
## 60 9.22 10.52 13.25
## 61 9.27 10.47 12.38
## 62 14.44 15.41 14.30
## 63 16.92 17.91 15.59
## 64 18.20 15.67 14.79
## 65 17.40 15.31 15.30
## 66 17.45 16.60 15.23
## 67 12.21 17.71 15.25
## 68 12.62 14.35 13.94
## 69 9.15 12.55 12.50
## 7 13.82 11.60 13.35
## 70 14.45 12.03 13.89
## 71 10.13 9.69 12.19
## 72 12.55 11.99 13.21
## 73 9.41 12.97 13.34
## 74 8.47 12.63 13.09
## 75 12.51 16.34 14.57
## 76 6.18 9.76 11.85
## 77 14.97 11.83 13.97
## 78 9.35 7.57 11.61
## 79 16.90 13.69 13.82
## 8 12.76 11.45 13.20
## 80 13.96 14.31 14.01
## 81 10.68 10.07 12.75
## 82 8.17 10.50 12.61
## 83 9.32 12.54 13.55
## 84 5.22 7.52 10.74
## 85 13.38 12.57 13.91
## 86 15.29 16.35 14.25
## 87 14.66 13.30 14.26
## 88 11.58 13.88 13.47
## 89 15.75 15.99 14.79
## 9 10.56 10.61 12.92
## 90 11.31 11.77 13.36
## 91 9.19 7.89 11.08
## 92 12.08 13.05 13.73
## 93 9.05 12.28 13.53
## 94 12.11 12.67 13.75
## 95 11.76 11.15 13.44
## 96 9.92 11.61 12.90
## 97 13.97 15.09 13.42
## 98 10.01 15.20 13.30
## 99 10.59 9.49 12.33
mvn(ccc[,1:2], mvnTest = "mardia",
univariateTest = "SW", univariatePlot = "histogram",
multivariatePlot = "qq", multivariateOutlierMethod = "adj",
showOutliers = TRUE, showNewData = TRUE)
## $multivariateNormality
## Test Statistic p value Result
## 1 Mardia Skewness 1.09415871038731 0.895197881286257 YES
## 2 Mardia Kurtosis -1.13437875788271 0.25663570552363 YES
## 3 MVN <NA> <NA> YES
##
## $univariateNormality
## Test Variable Statistic p value Normality
## 1 Shapiro-Wilk Maths 0.9930 0.8131 YES
## 2 Shapiro-Wilk Sport 0.9925 0.7723 YES
##
## $Descriptives
## n Mean Std.Dev Median Min Max 25th 75th Skew
## Maths 119 11.68655 2.747667 11.69 5.22 18.20 9.445 13.605 0.08565721
## Sport 119 11.92933 2.576726 11.92 4.96 17.91 10.275 13.695 -0.03735769
## Kurtosis
## Maths -0.4993043
## Sport -0.1810067
##
## $multivariateOutliers
## [1] Observation Mahalanobis Distance Outlier
## <0 rows> (or 0-length row.names)
##
## $newData
## Maths Sport
## 1 9.68 13.70
## 10 13.26 10.49
## 100 13.25 11.96
## 101 11.98 13.34
## 102 16.47 15.78
## 103 8.76 6.45
## 104 11.32 10.15
## 105 6.96 10.64
## 106 11.57 11.45
## 107 13.81 12.03
## 108 10.16 11.73
## 109 8.06 9.88
## 11 13.88 15.89
## 110 11.00 10.82
## 111 12.35 11.66
## 112 15.97 14.60
## 113 15.97 16.04
## 114 12.40 8.95
## 115 15.25 14.00
## 116 10.94 8.71
## 117 13.02 13.98
## 118 11.00 12.49
## 119 12.69 11.96
## 12 9.48 8.05
## 13 12.14 14.86
## 14 13.59 12.53
## 15 7.97 8.08
## 16 12.29 11.73
## 17 11.63 11.90
## 18 11.69 9.88
## 19 12.77 14.22
## 2 8.43 8.24
## 20 10.84 12.50
## 21 12.13 10.54
## 22 11.56 9.37
## 23 15.66 11.92
## 24 8.73 8.15
## 25 10.11 13.64
## 26 11.25 11.92
## 27 12.46 12.78
## 28 13.21 12.02
## 29 7.70 5.51
## 3 11.99 11.41
## 30 10.22 11.23
## 31 7.12 10.13
## 32 6.70 4.96
## 33 12.84 17.10
## 34 8.99 10.19
## 35 12.52 11.30
## 36 9.76 11.31
## 37 15.83 14.82
## 38 8.58 8.16
## 39 10.44 10.80
## 4 10.42 8.93
## 40 9.36 9.42
## 41 13.62 12.54
## 42 8.22 12.08
## 43 11.57 15.21
## 44 14.37 15.48
## 45 12.68 10.19
## 46 12.66 10.93
## 47 8.15 10.07
## 48 7.66 11.24
## 49 14.35 13.94
## 5 10.20 9.75
## 50 11.88 14.42
## 51 9.07 12.21
## 52 8.89 10.36
## 53 5.81 8.25
## 54 11.64 13.19
## 55 10.71 10.83
## 56 14.79 13.99
## 57 13.69 8.10
## 58 13.94 10.93
## 59 15.46 12.08
## 6 16.24 13.61
## 60 9.22 10.52
## 61 9.27 10.47
## 62 14.44 15.41
## 63 16.92 17.91
## 64 18.20 15.67
## 65 17.40 15.31
## 66 17.45 16.60
## 67 12.21 17.71
## 68 12.62 14.35
## 69 9.15 12.55
## 7 13.82 11.60
## 70 14.45 12.03
## 71 10.13 9.69
## 72 12.55 11.99
## 73 9.41 12.97
## 74 8.47 12.63
## 75 12.51 16.34
## 76 6.18 9.76
## 77 14.97 11.83
## 78 9.35 7.57
## 79 16.90 13.69
## 8 12.76 11.45
## 80 13.96 14.31
## 81 10.68 10.07
## 82 8.17 10.50
## 83 9.32 12.54
## 84 5.22 7.52
## 85 13.38 12.57
## 86 15.29 16.35
## 87 14.66 13.30
## 88 11.58 13.88
## 89 15.75 15.99
## 9 10.56 10.61
## 90 11.31 11.77
## 91 9.19 7.89
## 92 12.08 13.05
## 93 9.05 12.28
## 94 12.11 12.67
## 95 11.76 11.15
## 96 9.92 11.61
## 97 13.97 15.09
## 98 10.01 15.20
## 99 10.59 9.49
mvn(read.csv("https://tinyurl.com/y2c68uvw"), mvnTest = "mardia",
univariateTest = "SW", univariatePlot = "histogram",
multivariatePlot = "qq", multivariateOutlierMethod = "adj",
showOutliers = TRUE, showNewData = TRUE)
## $multivariateNormality
## Test Statistic p value Result
## 1 Mardia Skewness 2.60917512706068 0.625198653395491 YES
## 2 Mardia Kurtosis -0.584809559089414 0.558675776111823 YES
## 3 MVN <NA> <NA> YES
##
## $univariateNormality
## Test Variable Statistic p value Normality
## 1 Shapiro-Wilk Maths 0.9904 0.5745 YES
## 2 Shapiro-Wilk Sport 0.9949 0.9447 YES
##
## $Descriptives
## n Mean Std.Dev Median Min Max 25th 75th Skew
## Maths 119 11.56353 3.039590 11.66 3.54 19.95 9.715 13.19 0.1241263
## Sport 119 11.55899 2.962568 11.50 3.62 19.10 9.510 13.88 -0.1423103
## Kurtosis
## Maths 0.1995491
## Sport -0.3439857
##
## $multivariateOutliers
## [1] Observation Mahalanobis Distance Outlier
## <0 rows> (or 0-length row.names)
##
## $newData
## Maths Sport
## 1 13.12 14.44
## 10 13.86 10.76
## 100 8.60 10.57
## 101 10.81 11.37
## 102 15.34 11.84
## 103 12.18 12.26
## 104 11.40 13.31
## 105 12.21 10.92
## 106 10.31 10.95
## 107 11.06 5.82
## 108 8.03 5.72
## 109 15.61 17.34
## 11 15.57 14.58
## 110 11.01 11.00
## 111 7.92 8.70
## 112 14.04 11.20
## 113 6.64 10.32
## 114 10.28 8.43
## 115 10.52 14.37
## 116 8.91 10.55
## 117 14.98 15.75
## 118 10.21 10.94
## 119 11.78 10.18
## 12 19.43 17.05
## 13 14.76 13.35
## 14 10.03 7.27
## 15 13.74 15.60
## 16 12.01 11.16
## 17 9.06 9.59
## 18 10.26 14.21
## 19 6.86 9.01
## 2 12.43 14.32
## 20 11.41 9.10
## 21 11.96 13.93
## 22 10.19 6.61
## 23 10.19 9.75
## 24 7.83 11.11
## 25 9.63 9.24
## 26 10.67 12.61
## 27 13.10 12.67
## 28 11.99 11.50
## 29 15.23 14.41
## 3 16.26 15.85
## 30 19.42 19.10
## 31 13.29 12.00
## 32 8.85 8.42
## 33 13.34 12.15
## 34 11.61 11.76
## 35 8.72 8.17
## 36 9.03 12.82
## 37 7.27 8.69
## 38 10.82 12.64
## 39 15.25 16.28
## 4 12.61 7.68
## 40 10.78 12.83
## 41 11.60 9.68
## 42 12.43 9.93
## 43 10.60 11.30
## 44 11.98 7.43
## 45 9.78 12.03
## 46 9.88 8.70
## 47 15.15 11.93
## 48 7.54 10.71
## 49 11.30 7.42
## 5 3.54 6.12
## 50 12.20 12.90
## 51 12.88 12.47
## 52 14.99 15.75
## 53 12.25 13.83
## 54 11.79 11.33
## 55 11.66 12.33
## 56 12.17 13.50
## 57 8.61 9.77
## 58 4.70 8.02
## 59 5.99 3.62
## 6 11.50 13.08
## 60 12.26 10.35
## 61 12.01 12.87
## 62 12.89 10.76
## 63 10.34 9.34
## 64 5.48 6.90
## 65 11.99 14.00
## 66 8.93 10.80
## 67 15.30 13.46
## 68 8.04 10.32
## 69 16.82 16.21
## 7 6.43 5.71
## 70 12.63 9.43
## 71 12.87 11.87
## 72 12.64 11.50
## 73 6.32 6.74
## 74 9.03 5.18
## 75 17.12 15.43
## 76 7.84 8.64
## 77 11.18 11.90
## 78 13.56 16.16
## 79 13.00 14.25
## 8 15.79 12.91
## 80 10.90 9.90
## 81 16.33 14.32
## 82 6.83 9.09
## 83 11.81 10.88
## 84 15.98 14.01
## 85 13.38 8.91
## 86 9.65 15.28
## 87 10.54 13.41
## 88 11.38 12.39
## 89 12.37 9.19
## 9 8.02 14.32
## 90 11.38 14.09
## 91 12.29 14.93
## 92 13.26 8.13
## 93 14.65 16.29
## 94 15.52 13.06
## 95 19.95 15.08
## 96 14.76 16.23
## 97 8.95 12.39
## 98 8.64 10.85
## 99 12.04 13.99
mvn(read.csv("https://tinyurl.com/y2asrzgk"), mvnTest = "mardia",
univariateTest = "SW", univariatePlot = "histogram",
multivariatePlot = "qq", multivariateOutlierMethod = "adj",
showOutliers = TRUE, showNewData = TRUE)
## $multivariateNormality
## Test Statistic p value Result
## 1 Mardia Skewness 12.9057396369826 0.22898988609509 YES
## 2 Mardia Kurtosis -0.574084544554668 0.565910591483027 YES
## 3 MVN <NA> <NA> YES
##
## $univariateNormality
## Test Variable Statistic p value Normality
## 1 Shapiro-Wilk Maths 0.9904 0.5745 YES
## 2 Shapiro-Wilk Sport 0.9949 0.9447 YES
## 3 Shapiro-Wilk Age 0.9855 0.2327 YES
##
## $Descriptives
## n Mean Std.Dev Median Min Max 25th 75th Skew
## Maths 119 11.56353 3.039590 11.66 3.54 19.95 9.715 13.190 0.1241263
## Sport 119 11.55899 2.962568 11.50 3.62 19.10 9.510 13.880 -0.1423103
## Age 119 13.07538 1.014806 12.99 10.77 15.44 12.355 13.705 0.2857010
## Kurtosis
## Maths 0.1995491
## Sport -0.3439857
## Age -0.2784684
##
## $multivariateOutliers
## [1] Observation Mahalanobis Distance Outlier
## <0 rows> (or 0-length row.names)
##
## $newData
## Maths Sport Age
## 1 13.12 14.44 13.40
## 10 13.86 10.76 12.92
## 100 8.60 10.57 12.07
## 101 10.81 11.37 12.98
## 102 15.34 11.84 13.89
## 103 12.18 12.26 13.51
## 104 11.40 13.31 13.00
## 105 12.21 10.92 12.91
## 106 10.31 10.95 12.96
## 107 11.06 5.82 12.18
## 108 8.03 5.72 12.02
## 109 15.61 17.34 15.44
## 11 15.57 14.58 14.83
## 110 11.01 11.00 12.50
## 111 7.92 8.70 12.31
## 112 14.04 11.20 13.79
## 113 6.64 10.32 13.09
## 114 10.28 8.43 12.63
## 115 10.52 14.37 13.84
## 116 8.91 10.55 12.40
## 117 14.98 15.75 14.14
## 118 10.21 10.94 12.29
## 119 11.78 10.18 12.68
## 12 19.43 17.05 15.24
## 13 14.76 13.35 13.66
## 14 10.03 7.27 11.63
## 15 13.74 15.60 14.37
## 16 12.01 11.16 12.48
## 17 9.06 9.59 11.89
## 18 10.26 14.21 12.58
## 19 6.86 9.01 12.67
## 2 12.43 14.32 14.44
## 20 11.41 9.10 11.72
## 21 11.96 13.93 13.47
## 22 10.19 6.61 11.91
## 23 10.19 9.75 12.65
## 24 7.83 11.11 12.78
## 25 9.63 9.24 12.45
## 26 10.67 12.61 12.88
## 27 13.10 12.67 13.44
## 28 11.99 11.50 12.70
## 29 15.23 14.41 14.35
## 3 16.26 15.85 14.17
## 30 19.42 19.10 15.38
## 31 13.29 12.00 12.96
## 32 8.85 8.42 11.93
## 33 13.34 12.15 13.84
## 34 11.61 11.76 12.99
## 35 8.72 8.17 10.77
## 36 9.03 12.82 12.86
## 37 7.27 8.69 11.60
## 38 10.82 12.64 13.25
## 39 15.25 16.28 14.15
## 4 12.61 7.68 12.76
## 40 10.78 12.83 12.15
## 41 11.60 9.68 13.25
## 42 12.43 9.93 12.73
## 43 10.60 11.30 12.68
## 44 11.98 7.43 12.23
## 45 9.78 12.03 12.92
## 46 9.88 8.70 11.43
## 47 15.15 11.93 13.26
## 48 7.54 10.71 12.55
## 49 11.30 7.42 12.25
## 5 3.54 6.12 11.29
## 50 12.20 12.90 13.35
## 51 12.88 12.47 13.20
## 52 14.99 15.75 15.08
## 53 12.25 13.83 13.60
## 54 11.79 11.33 13.58
## 55 11.66 12.33 12.40
## 56 12.17 13.50 13.18
## 57 8.61 9.77 11.71
## 58 4.70 8.02 11.84
## 59 5.99 3.62 10.89
## 6 11.50 13.08 13.38
## 60 12.26 10.35 13.29
## 61 12.01 12.87 13.19
## 62 12.89 10.76 13.18
## 63 10.34 9.34 12.45
## 64 5.48 6.90 11.59
## 65 11.99 14.00 13.83
## 66 8.93 10.80 12.24
## 67 15.30 13.46 13.47
## 68 8.04 10.32 12.27
## 69 16.82 16.21 15.31
## 7 6.43 5.71 11.53
## 70 12.63 9.43 12.65
## 71 12.87 11.87 12.83
## 72 12.64 11.50 13.13
## 73 6.32 6.74 11.33
## 74 9.03 5.18 11.64
## 75 17.12 15.43 14.51
## 76 7.84 8.64 12.31
## 77 11.18 11.90 12.24
## 78 13.56 16.16 14.57
## 79 13.00 14.25 14.17
## 8 15.79 12.91 13.77
## 80 10.90 9.90 12.18
## 81 16.33 14.32 13.88
## 82 6.83 9.09 12.21
## 83 11.81 10.88 13.11
## 84 15.98 14.01 14.16
## 85 13.38 8.91 13.37
## 86 9.65 15.28 13.63
## 87 10.54 13.41 13.91
## 88 11.38 12.39 13.32
## 89 12.37 9.19 13.12
## 9 8.02 14.32 13.54
## 90 11.38 14.09 14.10
## 91 12.29 14.93 13.75
## 92 13.26 8.13 12.40
## 93 14.65 16.29 14.28
## 94 15.52 13.06 15.08
## 95 19.95 15.08 15.15
## 96 14.76 16.23 15.15
## 97 8.95 12.39 13.26
## 98 8.64 10.85 12.54
## 99 12.04 13.99 13.63
cor(ccc)
## Maths Sport Age
## Maths 1.0000000 0.6706710 0.7958409
## Sport 0.6706710 1.0000000 0.8874844
## Age 0.7958409 0.8874844 1.0000000
cor.mtest(ccc)
## $p
## [,1] [,2] [,3]
## [1,] 0.000000e+00 7.186614e-17 2.963818e-27
## [2,] 7.186614e-17 0.000000e+00 3.571910e-41
## [3,] 2.963818e-27 3.571910e-41 0.000000e+00
##
## $lowCI
## [,1] [,2] [,3]
## [1,] 1.0000000 0.5580410 0.7188138
## [2,] 0.5580410 1.0000000 0.8419913
## [3,] 0.7188138 0.8419913 1.0000000
##
## $uppCI
## [,1] [,2] [,3]
## [1,] 1.0000000 0.7590373 0.8535651
## [2,] 0.7590373 1.0000000 0.9204451
## [3,] 0.8535651 0.9204451 1.0000000
pcor(ccc)
## $estimate
## Maths Sport Age
## Maths 1.0000000 -0.1276710 0.5869337
## Sport -0.1276710 1.0000000 0.7875928
## Age 0.5869337 0.7875928 1.0000000
##
## $p.value
## Maths Sport Age
## Maths 0.000000e+00 1.682823e-01 2.850986e-12
## Sport 1.682823e-01 0.000000e+00 3.781357e-26
## Age 2.850986e-12 3.781357e-26 0.000000e+00
##
## $statistic
## Maths Sport Age
## Maths 0.000000 -1.386405 7.807802
## Sport -1.386405 0.000000 13.766126
## Age 7.807802 13.766126 0.000000
##
## $n
## [1] 119
##
## $gp
## [1] 1
##
## $method
## [1] "pearson"
ggpairs(ccc)
res1=residuals(lm(Maths~Age,data=ccc))
res2=residuals(lm(Sport~Age,data=ccc))
plot(res1,res2)
cor(ccc, method="spearman")
## Maths Sport Age
## Maths 1.0000000 0.6527990 0.7832539
## Sport 0.6527990 1.0000000 0.8678691
## Age 0.7832539 0.8678691 1.0000000
cor.mtest(ccc, method="spearman")
## Warning in cor.test.default(x = mat[, i], y = mat[, j], ...): Cannot
## compute exact p-value with ties
## Warning in cor.test.default(x = mat[, i], y = mat[, j], ...): Cannot
## compute exact p-value with ties
## Warning in cor.test.default(x = mat[, i], y = mat[, j], ...): Cannot
## compute exact p-value with ties
## $p
## [,1] [,2] [,3]
## [1,] 0.000000e+00 8.653942e-16 6.604889e-26
## [2,] 8.653942e-16 0.000000e+00 2.397734e-37
## [3,] 6.604889e-26 2.397734e-37 0.000000e+00
##
## $lowCI
## [,1] [,2] [,3]
## [1,] 1 NA NA
## [2,] NA 1 NA
## [3,] NA NA 1
##
## $uppCI
## [,1] [,2] [,3]
## [1,] 1 NA NA
## [2,] NA 1 NA
## [3,] NA NA 1
pcor(ccc, method = "spearman")
## $estimate
## Maths Sport Age
## Maths 1.00000000 -0.08729888 0.5758412
## Sport -0.08729888 1.00000000 0.7570978
## Age 0.57584119 0.75709782 1.0000000
##
## $p.value
## Maths Sport Age
## Maths 0.000000e+00 3.472125e-01 8.989092e-12
## Sport 3.472125e-01 0.000000e+00 3.468246e-23
## Age 8.989092e-12 3.468246e-23 0.000000e+00
##
## $statistic
## Maths Sport Age
## Maths 0.0000000 -0.9438412 7.585972
## Sport -0.9438412 0.0000000 12.481515
## Age 7.5859723 12.4815155 0.000000
##
## $n
## [1] 119
##
## $gp
## [1] 1
##
## $method
## [1] "spearman"
cor(ccc, method="kendall")
## Maths Sport Age
## Maths 1.0000000 0.4712005 0.5994584
## Sport 0.4712005 1.0000000 0.6994577
## Age 0.5994584 0.6994577 1.0000000
cor.mtest(ccc, method="kendall")
## $p
## [,1] [,2] [,3]
## [1,] 0.000000e+00 3.171405e-14 4.938679e-22
## [2,] 3.171405e-14 0.000000e+00 2.237647e-29
## [3,] 4.938679e-22 2.237647e-29 0.000000e+00
##
## $lowCI
## [,1] [,2] [,3]
## [1,] 1 NA NA
## [2,] NA 1 NA
## [3,] NA NA 1
##
## $uppCI
## [,1] [,2] [,3]
## [1,] 1 NA NA
## [2,] NA 1 NA
## [3,] NA NA 1
pcor(ccc, method = "kendall")
## $estimate
## Maths Sport Age
## Maths 1.00000000 0.09073793 0.4281253
## Sport 0.09073793 1.00000000 0.5906587
## Age 0.42812527 0.59065871 1.0000000
##
## $p.value
## Maths Sport Age
## Maths 0.000000e+00 1.451525e-01 6.247467e-12
## Sport 1.451525e-01 0.000000e+00 2.459129e-21
## Age 6.247467e-12 2.459129e-21 0.000000e+00
##
## $statistic
## Maths Sport Age
## Maths 0.000000 1.456869 6.873889
## Sport 1.456869 0.000000 9.483492
## Age 6.873889 9.483492 0.000000
##
## $n
## [1] 119
##
## $gp
## [1] 1
##
## $method
## [1] "kendall"
ggpairs(ccc)
