library(foreign)
spss<-read.spss("D:/110上程老師作業/110下/MyDATA(delete SE).sav", to.data.frame=TRUE)
## re-encoding from CP950
## Warning in read.spss("D:/110上程老師作業/110下/MyDATA(delete SE).sav", :
## Undeclared level(s) 3 added in variable: Gender
dim(spss)
## [1] 870 133
names(spss)
## [1] "ID" "School" "grade" "Class" "Number" "Gender"
## [7] "EN1T1" "EN2T1" "EN3T1" "EN4T1" "EN5T1" "FR1T1"
## [13] "FR2T1" "FR3T1" "SE1T1" "SE2T1" "SE3T1" "SE4T1"
## [19] "SE5T1" "ENR1T1" "ENR2T1" "ENR3T1" "ENR4T1" "FRR1T1"
## [25] "FRR2T1" "FRR3T1" "FRR4T1" "BO1T1" "BO2T1" "BO3T1"
## [31] "BO4T1" "CB1T1" "CB2T1" "CB3T1" "AC1T1" "AC2T1"
## [37] "AC3T1" "AC4T1" "AC5T1" "AC6T1" "AC7T1" "AC8T1"
## [43] "AC9T1" "PC1T1" "PC2T1" "PC3T1" "PC4T1" "ACHT1"
## [49] "EN1T2" "EN2T2" "EN3T2" "EN4T2" "EN5T2" "FR1T2"
## [55] "FR2T2" "FR3T2" "SE1T2" "SE2T2" "SE3T2" "SE4T2"
## [61] "SE5T2" "ENR1T2" "ENR2T2" "ENR3T2" "ENR4T2" "FRR1T2"
## [67] "FRR2T2" "FRR3T2" "FRR4T2" "BO1T2" "BO2T2" "BO3T2"
## [73] "BO4T2" "CB1T2" "CB2T2" "CB3T2" "AC1T2" "AC2T2"
## [79] "AC3T2" "AC4T2" "AC5T2" "AC6T2" "AC7T2" "AC8T2"
## [85] "AC9T2" "PC1T2" "PC2T2" "PC3T2" "PC4T2" "ACHT2"
## [91] "EN1T3" "EN2T3" "EN3T3" "EN4T3" "EN5T3" "FR1T3"
## [97] "FR2T3" "FR3T3" "SE1T3" "SE2T3" "SE3T3" "SE4T3"
## [103] "SE5T3" "ENR1T3" "ENR2T3" "ENR3T3" "ENR4T3" "FRR1T3"
## [109] "FRR2T3" "FRR3T3" "FRR4T3" "BO1T3" "BO2T3" "BO3T3"
## [115] "BO4T3" "CB1T3" "CB2T3" "CB3T3" "AC1T3" "AC2T3"
## [121] "AC3T3" "AC4T3" "AC5T3" "AC6T3" "AC7T3" "AC8T3"
## [127] "AC9T3" "PC1T3" "PC2T3" "PC3T3" "PC4T3" "ACHT3"
## [133] "filter_."
library(MVN)
numeric_spss <- spss[sapply(spss, is.numeric)]
# 使用 Mardia 的多變量常態性檢驗
result <- mvn(numeric_spss, mvnTest = "mardia")
print(result)
## $multivariateNormality
## Test Statistic p value Result
## 1 Mardia Skewness 710573.610486244 0 NO
## 2 Mardia Kurtosis 336.366970587863 0 NO
## 3 MVN <NA> <NA> NO
##
## $univariateNormality
## Test Variable Statistic p value Normality
## 1 Anderson-Darling ID 13.6351 <0.001 NO
## 2 Anderson-Darling grade 128.4155 <0.001 NO
## 3 Anderson-Darling Class 55.2128 <0.001 NO
## 4 Anderson-Darling Number 6.2315 <0.001 NO
## 5 Anderson-Darling EN1T1 31.6052 <0.001 NO
## 6 Anderson-Darling EN2T1 29.1059 <0.001 NO
## 7 Anderson-Darling EN3T1 34.9702 <0.001 NO
## 8 Anderson-Darling EN4T1 24.1270 <0.001 NO
## 9 Anderson-Darling EN5T1 22.8955 <0.001 NO
## 10 Anderson-Darling FR1T1 21.2588 <0.001 NO
## 11 Anderson-Darling FR2T1 24.4674 <0.001 NO
## 12 Anderson-Darling FR3T1 25.6414 <0.001 NO
## 13 Anderson-Darling SE1T1 26.1544 <0.001 NO
## 14 Anderson-Darling SE2T1 61.4121 <0.001 NO
## 15 Anderson-Darling SE3T1 31.4329 <0.001 NO
## 16 Anderson-Darling SE4T1 21.2496 <0.001 NO
## 17 Anderson-Darling SE5T1 23.1632 <0.001 NO
## 18 Anderson-Darling ENR1T1 30.7181 <0.001 NO
## 19 Anderson-Darling ENR2T1 33.0802 <0.001 NO
## 20 Anderson-Darling ENR3T1 29.3717 <0.001 NO
## 21 Anderson-Darling ENR4T1 25.5817 <0.001 NO
## 22 Anderson-Darling FRR1T1 30.4632 <0.001 NO
## 23 Anderson-Darling FRR2T1 31.6248 <0.001 NO
## 24 Anderson-Darling FRR3T1 23.4120 <0.001 NO
## 25 Anderson-Darling FRR4T1 20.9063 <0.001 NO
## 26 Anderson-Darling BO1T1 20.2674 <0.001 NO
## 27 Anderson-Darling BO2T1 21.2036 <0.001 NO
## 28 Anderson-Darling BO3T1 25.2169 <0.001 NO
## 29 Anderson-Darling BO4T1 23.1165 <0.001 NO
## 30 Anderson-Darling CB1T1 99.3295 <0.001 NO
## 31 Anderson-Darling CB2T1 55.7470 <0.001 NO
## 32 Anderson-Darling CB3T1 27.3544 <0.001 NO
## 33 Anderson-Darling AC1T1 19.9136 <0.001 NO
## 34 Anderson-Darling AC2T1 21.8267 <0.001 NO
## 35 Anderson-Darling AC3T1 77.9024 <0.001 NO
## 36 Anderson-Darling AC4T1 21.0891 <0.001 NO
## 37 Anderson-Darling AC5T1 22.9925 <0.001 NO
## 38 Anderson-Darling AC6T1 60.2446 <0.001 NO
## 39 Anderson-Darling AC7T1 24.0083 <0.001 NO
## 40 Anderson-Darling AC8T1 73.0818 <0.001 NO
## 41 Anderson-Darling AC9T1 21.3724 <0.001 NO
## 42 Anderson-Darling PC1T1 40.2055 <0.001 NO
## 43 Anderson-Darling PC2T1 36.1863 <0.001 NO
## 44 Anderson-Darling PC3T1 39.5708 <0.001 NO
## 45 Anderson-Darling PC4T1 34.8264 <0.001 NO
## 46 Anderson-Darling ACHT1 11.1573 <0.001 NO
## 47 Anderson-Darling EN1T2 28.7163 <0.001 NO
## 48 Anderson-Darling EN2T2 27.1658 <0.001 NO
## 49 Anderson-Darling EN3T2 34.0307 <0.001 NO
## 50 Anderson-Darling EN4T2 22.4044 <0.001 NO
## 51 Anderson-Darling EN5T2 22.5599 <0.001 NO
## 52 Anderson-Darling FR1T2 20.3409 <0.001 NO
## 53 Anderson-Darling FR2T2 23.2234 <0.001 NO
## 54 Anderson-Darling FR3T2 23.8375 <0.001 NO
## 55 Anderson-Darling SE1T2 24.7666 <0.001 NO
## 56 Anderson-Darling SE2T2 52.1536 <0.001 NO
## 57 Anderson-Darling SE3T2 28.9905 <0.001 NO
## 58 Anderson-Darling SE4T2 20.9371 <0.001 NO
## 59 Anderson-Darling SE5T2 22.1372 <0.001 NO
## 60 Anderson-Darling ENR1T2 26.5179 <0.001 NO
## 61 Anderson-Darling ENR2T2 29.2635 <0.001 NO
## 62 Anderson-Darling ENR3T2 23.2681 <0.001 NO
## 63 Anderson-Darling ENR4T2 26.6754 <0.001 NO
## 64 Anderson-Darling FRR1T2 27.4996 <0.001 NO
## 65 Anderson-Darling FRR2T2 30.0486 <0.001 NO
## 66 Anderson-Darling FRR3T2 23.9563 <0.001 NO
## 67 Anderson-Darling FRR4T2 22.7804 <0.001 NO
## 68 Anderson-Darling BO1T2 20.9230 <0.001 NO
## 69 Anderson-Darling BO2T2 20.2531 <0.001 NO
## 70 Anderson-Darling BO3T2 24.3533 <0.001 NO
## 71 Anderson-Darling BO4T2 22.6974 <0.001 NO
## 72 Anderson-Darling CB1T2 77.3523 <0.001 NO
## 73 Anderson-Darling CB2T2 36.7452 <0.001 NO
## 74 Anderson-Darling CB3T2 27.2199 <0.001 NO
## 75 Anderson-Darling AC1T2 20.2131 <0.001 NO
## 76 Anderson-Darling AC2T2 20.5662 <0.001 NO
## 77 Anderson-Darling AC3T2 59.7159 <0.001 NO
## 78 Anderson-Darling AC4T2 21.3325 <0.001 NO
## 79 Anderson-Darling AC5T2 22.6272 <0.001 NO
## 80 Anderson-Darling AC6T2 47.4593 <0.001 NO
## 81 Anderson-Darling AC7T2 22.1243 <0.001 NO
## 82 Anderson-Darling AC8T2 53.9645 <0.001 NO
## 83 Anderson-Darling AC9T2 23.8762 <0.001 NO
## 84 Anderson-Darling PC1T2 35.2939 <0.001 NO
## 85 Anderson-Darling PC2T2 30.9953 <0.001 NO
## 86 Anderson-Darling PC3T2 34.0853 <0.001 NO
## 87 Anderson-Darling PC4T2 31.2026 <0.001 NO
## 88 Anderson-Darling ACHT2 9.0113 <0.001 NO
## 89 Anderson-Darling EN1T3 27.2367 <0.001 NO
## 90 Anderson-Darling EN2T3 24.5468 <0.001 NO
## 91 Anderson-Darling EN3T3 30.3259 <0.001 NO
## 92 Anderson-Darling EN4T3 23.5539 <0.001 NO
## 93 Anderson-Darling EN5T3 22.7556 <0.001 NO
## 94 Anderson-Darling FR1T3 19.7413 <0.001 NO
## 95 Anderson-Darling FR2T3 21.5989 <0.001 NO
## 96 Anderson-Darling FR3T3 21.8624 <0.001 NO
## 97 Anderson-Darling SE1T3 21.4217 <0.001 NO
## 98 Anderson-Darling SE2T3 32.1237 <0.001 NO
## 99 Anderson-Darling SE3T3 27.2485 <0.001 NO
## 100 Anderson-Darling SE4T3 21.3591 <0.001 NO
## 101 Anderson-Darling SE5T3 23.3756 <0.001 NO
## 102 Anderson-Darling ENR1T3 28.4934 <0.001 NO
## 103 Anderson-Darling ENR2T3 28.6474 <0.001 NO
## 104 Anderson-Darling ENR3T3 26.0712 <0.001 NO
## 105 Anderson-Darling ENR4T3 26.4876 <0.001 NO
## 106 Anderson-Darling FRR1T3 30.2115 <0.001 NO
## 107 Anderson-Darling FRR2T3 30.5894 <0.001 NO
## 108 Anderson-Darling FRR3T3 25.6687 <0.001 NO
## 109 Anderson-Darling FRR4T3 22.8832 <0.001 NO
## 110 Anderson-Darling BO1T3 19.6119 <0.001 NO
## 111 Anderson-Darling BO2T3 19.7494 <0.001 NO
## 112 Anderson-Darling BO3T3 22.2439 <0.001 NO
## 113 Anderson-Darling BO4T3 21.2738 <0.001 NO
## 114 Anderson-Darling CB1T3 49.2378 <0.001 NO
## 115 Anderson-Darling CB2T3 27.0767 <0.001 NO
## 116 Anderson-Darling CB3T3 24.4417 <0.001 NO
## 117 Anderson-Darling AC1T3 21.7756 <0.001 NO
## 118 Anderson-Darling AC2T3 20.9967 <0.001 NO
## 119 Anderson-Darling AC3T3 41.9506 <0.001 NO
## 120 Anderson-Darling AC4T3 19.7933 <0.001 NO
## 121 Anderson-Darling AC5T3 20.6109 <0.001 NO
## 122 Anderson-Darling AC6T3 36.3056 <0.001 NO
## 123 Anderson-Darling AC7T3 20.4387 <0.001 NO
## 124 Anderson-Darling AC8T3 38.3588 <0.001 NO
## 125 Anderson-Darling AC9T3 21.1228 <0.001 NO
## 126 Anderson-Darling PC1T3 28.3618 <0.001 NO
## 127 Anderson-Darling PC2T3 25.6749 <0.001 NO
## 128 Anderson-Darling PC3T3 28.3917 <0.001 NO
## 129 Anderson-Darling PC4T3 26.5904 <0.001 NO
## 130 Anderson-Darling ACHT3 7.4112 <0.001 NO
##
## $Descriptives
## n Mean Std.Dev Median Min Max 25th 75th
## ID 870 5.483646e+05 2.813454e+05 530523.5 120201 1120542 220817.2 720510.75
## grade 870 1.774713e+00 5.404721e-01 2.0 1 3 1.0 2.00
## Class 870 4.894253e+00 3.905128e+00 4.0 1 19 2.0 6.00
## Number 870 1.305977e+01 7.661937e+00 13.0 1 42 6.0 19.00
## EN1T1 870 2.910345e+00 1.312508e+00 3.0 1 6 2.0 4.00
## EN2T1 870 3.071264e+00 1.371073e+00 3.0 1 6 2.0 4.00
## EN3T1 870 2.652874e+00 1.244166e+00 3.0 1 6 1.0 3.00
## EN4T1 870 3.165517e+00 1.478720e+00 3.0 1 6 2.0 4.00
## EN5T1 870 3.546710e+00 1.626652e+00 4.0 1 6 2.0 5.00
## FR1T1 870 3.165638e+00 1.546421e+00 3.0 1 6 2.0 4.00
## FR2T1 870 2.834483e+00 1.392139e+00 3.0 1 6 2.0 4.00
## FR3T1 870 3.032184e+00 1.603757e+00 3.0 1 6 2.0 4.00
## SE1T1 870 3.094253e+00 1.428894e+00 3.0 1 6 2.0 4.00
## SE2T1 870 4.709195e+00 1.506956e+00 5.0 1 6 4.0 6.00
## SE3T1 870 4.225287e+00 1.168164e+00 4.0 1 6 4.0 5.00
## SE4T1 870 3.503448e+00 1.371873e+00 4.0 1 6 3.0 4.00
## SE5T1 870 3.859770e+00 1.328146e+00 4.0 1 6 3.0 5.00
## ENR1T1 870 3.741379e+00 1.433935e+00 4.0 1 6 3.0 5.00
## ENR2T1 870 3.752874e+00 1.394493e+00 4.0 1 6 3.0 5.00
## ENR3T1 870 3.544828e+00 1.382012e+00 4.0 1 6 3.0 4.00
## ENR4T1 870 3.719540e+00 1.453367e+00 4.0 1 6 3.0 5.00
## FRR1T1 870 3.713651e+00 1.342275e+00 4.0 1 6 3.0 4.00
## FRR2T1 870 3.737817e+00 1.323509e+00 4.0 1 6 3.0 5.00
## FRR3T1 870 3.629105e+00 1.373962e+00 4.0 1 6 3.0 4.00
## FRR4T1 870 3.787042e+00 1.473034e+00 4.0 1 6 3.0 5.00
## BO1T1 870 3.457471e+00 1.502559e+00 3.0 1 6 2.0 4.00
## BO2T1 870 3.431034e+00 1.502343e+00 3.0 1 6 2.0 4.00
## BO3T1 870 3.102299e+00 1.571428e+00 3.0 1 6 2.0 4.00
## BO4T1 870 3.231133e+00 1.588411e+00 3.0 1 6 2.0 4.00
## CB1T1 870 1.897701e+00 1.312898e+00 1.0 1 6 1.0 3.00
## CB2T1 870 2.326437e+00 1.463516e+00 2.0 1 6 1.0 3.00
## CB3T1 870 3.085057e+00 1.589561e+00 3.0 1 6 2.0 4.00
## AC1T1 870 3.457471e+00 1.483289e+00 4.0 1 6 2.0 4.00
## AC2T1 870 3.331034e+00 1.607900e+00 3.0 1 6 2.0 5.00
## AC3T1 870 1.926226e+00 1.221828e+00 1.0 1 6 1.0 3.00
## AC4T1 870 3.089552e+00 1.486816e+00 3.0 1 6 2.0 4.00
## AC5T1 870 3.158621e+00 1.600529e+00 3.0 1 6 2.0 4.00
## AC6T1 870 2.187356e+00 1.385633e+00 2.0 1 6 1.0 3.00
## AC7T1 870 3.050575e+00 1.566249e+00 3.0 1 6 2.0 4.00
## AC8T1 870 2.106897e+00 1.404849e+00 2.0 1 6 1.0 3.00
## AC9T1 870 3.258712e+00 1.552597e+00 3.0 1 6 2.0 4.00
## PC1T1 870 2.595402e+00 1.555857e+00 2.0 1 6 1.0 3.00
## PC2T1 870 2.683908e+00 1.569295e+00 2.0 1 6 1.0 4.00
## PC3T1 870 2.598851e+00 1.550455e+00 2.0 1 6 1.0 4.00
## PC4T1 870 2.682759e+00 1.550990e+00 2.0 1 6 1.0 4.00
## ACHT1 870 5.824828e+01 2.564690e+01 63.0 0 100 38.0 79.00
## EN1T2 870 2.906897e+00 1.327525e+00 3.0 1 6 2.0 4.00
## EN2T2 870 3.049425e+00 1.383311e+00 3.0 1 6 2.0 4.00
## EN3T2 870 2.693103e+00 1.242264e+00 3.0 1 6 2.0 3.00
## EN4T2 870 3.179310e+00 1.508712e+00 3.0 1 6 2.0 4.00
## EN5T2 870 3.498851e+00 1.566148e+00 4.0 1 6 2.0 5.00
## FR1T2 870 3.271264e+00 1.504876e+00 3.0 1 6 2.0 4.00
## FR2T2 870 2.959770e+00 1.427009e+00 3.0 1 6 2.0 4.00
## FR3T2 870 3.140230e+00 1.579825e+00 3.0 1 6 2.0 4.00
## SE1T2 870 3.201149e+00 1.470774e+00 3.0 1 6 2.0 4.00
## SE2T2 870 4.585890e+00 1.539238e+00 5.0 1 6 4.0 6.00
## SE3T2 870 4.240230e+00 1.202602e+00 4.0 1 6 4.0 5.00
## SE4T2 870 3.643678e+00 1.420522e+00 4.0 1 6 3.0 5.00
## SE5T2 870 3.933495e+00 1.368801e+00 4.0 1 6 3.0 5.00
## ENR1T2 870 3.827586e+00 1.406109e+00 4.0 1 6 3.0 5.00
## ENR2T2 870 3.856322e+00 1.404022e+00 4.0 1 6 3.0 5.00
## ENR3T2 870 3.628736e+00 1.439650e+00 4.0 1 6 3.0 5.00
## ENR4T2 870 3.818391e+00 1.446119e+00 4.0 1 6 3.0 5.00
## FRR1T2 870 3.785057e+00 1.356401e+00 4.0 1 6 3.0 5.00
## FRR2T2 870 3.795402e+00 1.336218e+00 4.0 1 6 3.0 5.00
## FRR3T2 870 3.686207e+00 1.404143e+00 4.0 1 6 3.0 5.00
## FRR4T2 870 3.754962e+00 1.465678e+00 4.0 1 6 3.0 5.00
## BO1T2 870 3.487356e+00 1.533425e+00 3.0 1 6 2.0 4.75
## BO2T2 870 3.500000e+00 1.535727e+00 3.0 1 6 2.0 5.00
## BO3T2 870 3.149425e+00 1.592768e+00 3.0 1 6 2.0 4.00
## BO4T2 870 3.263218e+00 1.601468e+00 3.0 1 6 2.0 4.00
## CB1T2 870 2.050523e+00 1.355966e+00 1.0 1 6 1.0 3.00
## CB2T2 870 2.609195e+00 1.461090e+00 2.0 1 6 1.0 4.00
## CB3T2 870 3.113793e+00 1.551470e+00 3.0 1 6 2.0 4.00
## AC1T2 870 3.418391e+00 1.509352e+00 4.0 1 6 2.0 4.00
## AC2T2 870 3.420690e+00 1.575133e+00 4.0 1 6 2.0 5.00
## AC3T2 870 2.120690e+00 1.309577e+00 2.0 1 6 1.0 3.00
## AC4T2 870 3.180460e+00 1.487450e+00 3.0 1 6 2.0 4.00
## AC5T2 870 3.244828e+00 1.562967e+00 3.0 1 6 2.0 4.00
## AC6T2 870 2.342529e+00 1.418246e+00 2.0 1 6 1.0 3.00
## AC7T2 870 3.126437e+00 1.525424e+00 3.0 1 6 2.0 4.00
## AC8T2 870 2.298162e+00 1.441509e+00 2.0 1 6 1.0 3.00
## AC9T2 870 3.291954e+00 1.552993e+00 3.0 1 6 2.0 4.00
## PC1T2 870 2.701149e+00 1.547967e+00 2.0 1 6 1.0 4.00
## PC2T2 870 2.789655e+00 1.552498e+00 3.0 1 6 1.0 4.00
## PC3T2 870 2.681609e+00 1.530964e+00 2.0 1 6 1.0 4.00
## PC4T2 870 2.778161e+00 1.550895e+00 3.0 1 6 1.0 4.00
## ACHT2 870 5.658506e+01 2.710787e+01 58.0 0 100 35.0 80.00
## EN1T3 870 2.958621e+00 1.340916e+00 3.0 1 6 2.0 4.00
## EN2T3 870 3.013793e+00 1.366976e+00 3.0 1 6 2.0 4.00
## EN3T3 870 2.782759e+00 1.284564e+00 3.0 1 6 2.0 4.00
## EN4T3 870 3.187356e+00 1.440201e+00 3.0 1 6 2.0 4.00
## EN5T3 870 3.570115e+00 1.568983e+00 4.0 1 6 3.0 5.00
## FR1T3 870 3.347126e+00 1.455582e+00 3.0 1 6 2.0 4.00
## FR2T3 870 3.064368e+00 1.366370e+00 3.0 1 6 2.0 4.00
## FR3T3 870 3.155333e+00 1.498764e+00 3.0 1 6 2.0 4.00
## SE1T3 870 3.270691e+00 1.467525e+00 3.0 1 6 2.0 4.00
## SE2T3 870 4.295402e+00 1.525797e+00 4.0 1 6 3.0 6.00
## SE3T3 870 4.140230e+00 1.227275e+00 4.0 1 6 3.0 5.00
## SE4T3 870 3.579310e+00 1.395384e+00 4.0 1 6 3.0 4.00
## SE5T3 870 3.809209e+00 1.340839e+00 4.0 1 6 3.0 5.00
## ENR1T3 870 3.828736e+00 1.372709e+00 4.0 1 6 3.0 5.00
## ENR2T3 870 3.854023e+00 1.377303e+00 4.0 1 6 3.0 5.00
## ENR3T3 870 3.656322e+00 1.370510e+00 4.0 1 6 3.0 4.00
## ENR4T3 870 3.774713e+00 1.427917e+00 4.0 1 6 3.0 5.00
## FRR1T3 870 3.750575e+00 1.339355e+00 4.0 1 6 3.0 5.00
## FRR2T3 870 3.732184e+00 1.317580e+00 4.0 1 6 3.0 4.75
## FRR3T3 870 3.644828e+00 1.352342e+00 4.0 1 6 3.0 4.00
## FRR4T3 870 3.791954e+00 1.409871e+00 4.0 1 6 3.0 5.00
## BO1T3 870 3.518391e+00 1.489204e+00 3.0 1 6 3.0 4.00
## BO2T3 870 3.482759e+00 1.506122e+00 3.0 1 6 2.0 4.00
## BO3T3 870 3.221839e+00 1.541966e+00 3.0 1 6 2.0 4.00
## BO4T3 870 3.344828e+00 1.544340e+00 3.0 1 6 2.0 4.00
## CB1T3 870 2.295402e+00 1.379232e+00 2.0 1 6 1.0 3.00
## CB2T3 870 2.855172e+00 1.439917e+00 3.0 1 6 2.0 4.00
## CB3T3 870 3.175862e+00 1.484904e+00 3.0 1 6 2.0 4.00
## AC1T3 870 3.468966e+00 1.464840e+00 4.0 1 6 2.0 4.00
## AC2T3 870 3.480460e+00 1.537849e+00 4.0 1 6 2.0 5.00
## AC3T3 870 2.341379e+00 1.334507e+00 2.0 1 6 1.0 3.00
## AC4T3 870 3.289655e+00 1.475152e+00 3.0 1 6 2.0 4.00
## AC5T3 870 3.317241e+00 1.488135e+00 3.0 1 6 2.0 4.00
## AC6T3 870 2.517000e+00 1.431509e+00 2.0 1 6 1.0 3.00
## AC7T3 870 3.293433e+00 1.503403e+00 3.0 1 6 2.0 4.00
## AC8T3 870 2.525755e+00 1.458549e+00 2.0 1 6 1.0 3.00
## AC9T3 870 3.333333e+00 1.510734e+00 3.0 1 6 2.0 4.00
## PC1T3 870 2.806897e+00 1.490113e+00 3.0 1 6 2.0 4.00
## PC2T3 870 2.908046e+00 1.508947e+00 3.0 1 6 2.0 4.00
## PC3T3 870 2.781609e+00 1.473395e+00 3.0 1 6 2.0 4.00
## PC4T3 870 2.886207e+00 1.529809e+00 3.0 1 6 2.0 4.00
## ACHT3 870 5.810575e+01 2.562589e+01 60.0 0 100 38.0 80.00
## Skew Kurtosis
## ID 0.123756836 -1.042088903
## grade -0.105485816 -0.233132085
## Class 1.876908494 3.587625040
## Number 0.324178269 -0.320561039
## EN1T1 0.046398477 -0.652641021
## EN2T1 -0.026563073 -0.721453787
## EN3T1 0.219165395 -0.552236147
## EN4T1 0.008718138 -0.926110544
## EN5T1 -0.160277225 -1.078131981
## FR1T1 0.255918791 -0.865164312
## FR2T1 0.424412969 -0.502235558
## FR3T1 0.260309764 -1.014749767
## SE1T1 0.028201905 -0.808414100
## SE2T1 -1.135919276 0.350721987
## SE3T1 -0.508643743 0.334616519
## SE4T1 -0.134075314 -0.600133448
## SE5T1 -0.313371744 -0.357115660
## ENR1T1 -0.474688800 -0.462780858
## ENR2T1 -0.500604403 -0.315107733
## ENR3T1 -0.309843805 -0.442750108
## ENR4T1 -0.366328448 -0.590037249
## FRR1T1 -0.379081865 -0.260989954
## FRR2T1 -0.424909187 -0.198227697
## FRR3T1 -0.210195643 -0.488763139
## FRR4T1 -0.191300336 -0.709773264
## BO1T1 0.129479010 -0.829952259
## BO2T1 0.177315027 -0.817512955
## BO3T1 0.413951657 -0.786238675
## BO4T1 0.291386773 -0.888412843
## CB1T1 1.471740219 1.398845770
## CB2T1 0.863517475 -0.250208428
## CB3T1 0.197234352 -1.025278413
## AC1T1 -0.018754435 -0.830493723
## AC2T1 0.037956466 -1.097255605
## AC3T1 1.430123626 1.615623910
## AC4T1 0.274620875 -0.805461262
## AC5T1 0.181440054 -1.068240251
## AC6T1 1.080773815 0.386194944
## AC7T1 0.226893989 -1.012081703
## AC8T1 1.222938211 0.629067248
## AC9T1 0.079267867 -0.997234763
## PC1T1 0.784625578 -0.368894071
## PC2T1 0.692346362 -0.534181405
## PC3T1 0.770105242 -0.399042956
## PC4T1 0.663989634 -0.562838322
## ACHT1 -0.378609452 -0.922741875
## EN1T2 0.164810910 -0.530667306
## EN2T2 0.088726817 -0.614234727
## EN3T2 0.282304600 -0.289756277
## EN4T2 0.090016113 -0.885651268
## EN5T2 -0.142396221 -0.934129339
## FR1T2 0.177102371 -0.797216176
## FR2T2 0.407664303 -0.518708965
## FR3T2 0.139683027 -1.015116020
## SE1T2 -0.006662741 -0.834430276
## SE2T2 -0.883907709 -0.232668557
## SE3T2 -0.492227350 0.152467405
## SE4T2 -0.119562778 -0.613791213
## SE5T2 -0.305169021 -0.472349157
## ENR1T2 -0.409666870 -0.375576251
## ENR2T2 -0.474286154 -0.334890286
## ENR3T2 -0.231304721 -0.603758439
## ENR4T2 -0.425177838 -0.482996288
## FRR1T2 -0.389387890 -0.270166774
## FRR2T2 -0.438515280 -0.137239686
## FRR3T2 -0.249621165 -0.487911287
## FRR4T2 -0.216078782 -0.617073264
## BO1T2 0.107033535 -0.869062192
## BO2T2 0.079972205 -0.886772911
## BO3T2 0.348988419 -0.862043022
## BO4T2 0.265637384 -0.945168806
## CB1T2 1.211468472 0.680380153
## CB2T2 0.500770495 -0.713913802
## CB3T2 0.133469829 -0.961610147
## AC1T2 -0.052344977 -0.926996895
## AC2T2 -0.034068295 -1.019884246
## AC3T2 1.173968522 0.813126481
## AC4T2 0.098141345 -0.899984489
## AC5T2 0.085808165 -1.002765523
## AC6T2 0.922254842 0.055661741
## AC7T2 0.165552153 -0.929107472
## AC8T2 0.958084370 0.066434485
## AC9T2 -0.020659394 -0.994992630
## PC1T2 0.726396507 -0.393700923
## PC2T2 0.613984901 -0.570084581
## PC3T2 0.695283578 -0.412768420
## PC4T2 0.619818615 -0.556517743
## ACHT2 -0.182693122 -1.105716037
## EN1T3 0.138266398 -0.563936157
## EN2T3 0.158756666 -0.592134695
## EN3T3 0.288732240 -0.312774129
## EN4T3 0.042391500 -0.739272540
## EN5T3 -0.198205841 -0.928559475
## FR1T3 0.039602576 -0.778797555
## FR2T3 0.294896959 -0.530329121
## FR3T3 0.101092913 -0.926607886
## SE1T3 0.013119583 -0.811104663
## SE2T3 -0.607143723 -0.572527246
## SE3T3 -0.398600080 -0.041739349
## SE4T3 -0.109897565 -0.560922310
## SE5T3 -0.264975938 -0.354432396
## ENR1T3 -0.434285102 -0.281877309
## ENR2T3 -0.447145836 -0.252226526
## ENR3T3 -0.290585316 -0.397676794
## ENR4T3 -0.372896372 -0.454408467
## FRR1T3 -0.388956423 -0.196575961
## FRR2T3 -0.395081380 -0.165845785
## FRR3T3 -0.225239941 -0.357306247
## FRR4T3 -0.204691322 -0.511105314
## BO1T3 0.034338854 -0.801742258
## BO2T3 0.058275600 -0.827020954
## BO3T3 0.277277888 -0.810640652
## BO4T3 0.162372999 -0.838742641
## CB1T3 0.893540479 0.009567662
## CB2T3 0.323202477 -0.705020981
## CB3T3 0.072095707 -0.814957493
## AC1T3 -0.121085566 -0.814498568
## AC2T3 -0.098846661 -0.921050202
## AC3T3 0.846081822 0.075450673
## AC4T3 0.061458595 -0.835019013
## AC5T3 0.023258655 -0.845512515
## AC6T3 0.739354483 -0.236303981
## AC7T3 0.056152111 -0.851940625
## AC8T3 0.680412052 -0.378507982
## AC9T3 -0.003185465 -0.894044468
## PC1T3 0.588514003 -0.427697377
## PC2T3 0.489280183 -0.600325128
## PC3T3 0.573188017 -0.407989228
## PC4T3 0.488170673 -0.640540385
## ACHT3 -0.184536131 -1.029391824
# 視覺化檢查多變量常態性
mvn(numeric_spss, mvnTest = "mardia", multivariatePlot = "qq")
## $multivariateNormality
## Test Statistic p value Result
## 1 Mardia Skewness 710573.610486244 0 NO
## 2 Mardia Kurtosis 336.366970587863 0 NO
## 3 MVN <NA> <NA> NO
##
## $univariateNormality
## Test Variable Statistic p value Normality
## 1 Anderson-Darling ID 13.6351 <0.001 NO
## 2 Anderson-Darling grade 128.4155 <0.001 NO
## 3 Anderson-Darling Class 55.2128 <0.001 NO
## 4 Anderson-Darling Number 6.2315 <0.001 NO
## 5 Anderson-Darling EN1T1 31.6052 <0.001 NO
## 6 Anderson-Darling EN2T1 29.1059 <0.001 NO
## 7 Anderson-Darling EN3T1 34.9702 <0.001 NO
## 8 Anderson-Darling EN4T1 24.1270 <0.001 NO
## 9 Anderson-Darling EN5T1 22.8955 <0.001 NO
## 10 Anderson-Darling FR1T1 21.2588 <0.001 NO
## 11 Anderson-Darling FR2T1 24.4674 <0.001 NO
## 12 Anderson-Darling FR3T1 25.6414 <0.001 NO
## 13 Anderson-Darling SE1T1 26.1544 <0.001 NO
## 14 Anderson-Darling SE2T1 61.4121 <0.001 NO
## 15 Anderson-Darling SE3T1 31.4329 <0.001 NO
## 16 Anderson-Darling SE4T1 21.2496 <0.001 NO
## 17 Anderson-Darling SE5T1 23.1632 <0.001 NO
## 18 Anderson-Darling ENR1T1 30.7181 <0.001 NO
## 19 Anderson-Darling ENR2T1 33.0802 <0.001 NO
## 20 Anderson-Darling ENR3T1 29.3717 <0.001 NO
## 21 Anderson-Darling ENR4T1 25.5817 <0.001 NO
## 22 Anderson-Darling FRR1T1 30.4632 <0.001 NO
## 23 Anderson-Darling FRR2T1 31.6248 <0.001 NO
## 24 Anderson-Darling FRR3T1 23.4120 <0.001 NO
## 25 Anderson-Darling FRR4T1 20.9063 <0.001 NO
## 26 Anderson-Darling BO1T1 20.2674 <0.001 NO
## 27 Anderson-Darling BO2T1 21.2036 <0.001 NO
## 28 Anderson-Darling BO3T1 25.2169 <0.001 NO
## 29 Anderson-Darling BO4T1 23.1165 <0.001 NO
## 30 Anderson-Darling CB1T1 99.3295 <0.001 NO
## 31 Anderson-Darling CB2T1 55.7470 <0.001 NO
## 32 Anderson-Darling CB3T1 27.3544 <0.001 NO
## 33 Anderson-Darling AC1T1 19.9136 <0.001 NO
## 34 Anderson-Darling AC2T1 21.8267 <0.001 NO
## 35 Anderson-Darling AC3T1 77.9024 <0.001 NO
## 36 Anderson-Darling AC4T1 21.0891 <0.001 NO
## 37 Anderson-Darling AC5T1 22.9925 <0.001 NO
## 38 Anderson-Darling AC6T1 60.2446 <0.001 NO
## 39 Anderson-Darling AC7T1 24.0083 <0.001 NO
## 40 Anderson-Darling AC8T1 73.0818 <0.001 NO
## 41 Anderson-Darling AC9T1 21.3724 <0.001 NO
## 42 Anderson-Darling PC1T1 40.2055 <0.001 NO
## 43 Anderson-Darling PC2T1 36.1863 <0.001 NO
## 44 Anderson-Darling PC3T1 39.5708 <0.001 NO
## 45 Anderson-Darling PC4T1 34.8264 <0.001 NO
## 46 Anderson-Darling ACHT1 11.1573 <0.001 NO
## 47 Anderson-Darling EN1T2 28.7163 <0.001 NO
## 48 Anderson-Darling EN2T2 27.1658 <0.001 NO
## 49 Anderson-Darling EN3T2 34.0307 <0.001 NO
## 50 Anderson-Darling EN4T2 22.4044 <0.001 NO
## 51 Anderson-Darling EN5T2 22.5599 <0.001 NO
## 52 Anderson-Darling FR1T2 20.3409 <0.001 NO
## 53 Anderson-Darling FR2T2 23.2234 <0.001 NO
## 54 Anderson-Darling FR3T2 23.8375 <0.001 NO
## 55 Anderson-Darling SE1T2 24.7666 <0.001 NO
## 56 Anderson-Darling SE2T2 52.1536 <0.001 NO
## 57 Anderson-Darling SE3T2 28.9905 <0.001 NO
## 58 Anderson-Darling SE4T2 20.9371 <0.001 NO
## 59 Anderson-Darling SE5T2 22.1372 <0.001 NO
## 60 Anderson-Darling ENR1T2 26.5179 <0.001 NO
## 61 Anderson-Darling ENR2T2 29.2635 <0.001 NO
## 62 Anderson-Darling ENR3T2 23.2681 <0.001 NO
## 63 Anderson-Darling ENR4T2 26.6754 <0.001 NO
## 64 Anderson-Darling FRR1T2 27.4996 <0.001 NO
## 65 Anderson-Darling FRR2T2 30.0486 <0.001 NO
## 66 Anderson-Darling FRR3T2 23.9563 <0.001 NO
## 67 Anderson-Darling FRR4T2 22.7804 <0.001 NO
## 68 Anderson-Darling BO1T2 20.9230 <0.001 NO
## 69 Anderson-Darling BO2T2 20.2531 <0.001 NO
## 70 Anderson-Darling BO3T2 24.3533 <0.001 NO
## 71 Anderson-Darling BO4T2 22.6974 <0.001 NO
## 72 Anderson-Darling CB1T2 77.3523 <0.001 NO
## 73 Anderson-Darling CB2T2 36.7452 <0.001 NO
## 74 Anderson-Darling CB3T2 27.2199 <0.001 NO
## 75 Anderson-Darling AC1T2 20.2131 <0.001 NO
## 76 Anderson-Darling AC2T2 20.5662 <0.001 NO
## 77 Anderson-Darling AC3T2 59.7159 <0.001 NO
## 78 Anderson-Darling AC4T2 21.3325 <0.001 NO
## 79 Anderson-Darling AC5T2 22.6272 <0.001 NO
## 80 Anderson-Darling AC6T2 47.4593 <0.001 NO
## 81 Anderson-Darling AC7T2 22.1243 <0.001 NO
## 82 Anderson-Darling AC8T2 53.9645 <0.001 NO
## 83 Anderson-Darling AC9T2 23.8762 <0.001 NO
## 84 Anderson-Darling PC1T2 35.2939 <0.001 NO
## 85 Anderson-Darling PC2T2 30.9953 <0.001 NO
## 86 Anderson-Darling PC3T2 34.0853 <0.001 NO
## 87 Anderson-Darling PC4T2 31.2026 <0.001 NO
## 88 Anderson-Darling ACHT2 9.0113 <0.001 NO
## 89 Anderson-Darling EN1T3 27.2367 <0.001 NO
## 90 Anderson-Darling EN2T3 24.5468 <0.001 NO
## 91 Anderson-Darling EN3T3 30.3259 <0.001 NO
## 92 Anderson-Darling EN4T3 23.5539 <0.001 NO
## 93 Anderson-Darling EN5T3 22.7556 <0.001 NO
## 94 Anderson-Darling FR1T3 19.7413 <0.001 NO
## 95 Anderson-Darling FR2T3 21.5989 <0.001 NO
## 96 Anderson-Darling FR3T3 21.8624 <0.001 NO
## 97 Anderson-Darling SE1T3 21.4217 <0.001 NO
## 98 Anderson-Darling SE2T3 32.1237 <0.001 NO
## 99 Anderson-Darling SE3T3 27.2485 <0.001 NO
## 100 Anderson-Darling SE4T3 21.3591 <0.001 NO
## 101 Anderson-Darling SE5T3 23.3756 <0.001 NO
## 102 Anderson-Darling ENR1T3 28.4934 <0.001 NO
## 103 Anderson-Darling ENR2T3 28.6474 <0.001 NO
## 104 Anderson-Darling ENR3T3 26.0712 <0.001 NO
## 105 Anderson-Darling ENR4T3 26.4876 <0.001 NO
## 106 Anderson-Darling FRR1T3 30.2115 <0.001 NO
## 107 Anderson-Darling FRR2T3 30.5894 <0.001 NO
## 108 Anderson-Darling FRR3T3 25.6687 <0.001 NO
## 109 Anderson-Darling FRR4T3 22.8832 <0.001 NO
## 110 Anderson-Darling BO1T3 19.6119 <0.001 NO
## 111 Anderson-Darling BO2T3 19.7494 <0.001 NO
## 112 Anderson-Darling BO3T3 22.2439 <0.001 NO
## 113 Anderson-Darling BO4T3 21.2738 <0.001 NO
## 114 Anderson-Darling CB1T3 49.2378 <0.001 NO
## 115 Anderson-Darling CB2T3 27.0767 <0.001 NO
## 116 Anderson-Darling CB3T3 24.4417 <0.001 NO
## 117 Anderson-Darling AC1T3 21.7756 <0.001 NO
## 118 Anderson-Darling AC2T3 20.9967 <0.001 NO
## 119 Anderson-Darling AC3T3 41.9506 <0.001 NO
## 120 Anderson-Darling AC4T3 19.7933 <0.001 NO
## 121 Anderson-Darling AC5T3 20.6109 <0.001 NO
## 122 Anderson-Darling AC6T3 36.3056 <0.001 NO
## 123 Anderson-Darling AC7T3 20.4387 <0.001 NO
## 124 Anderson-Darling AC8T3 38.3588 <0.001 NO
## 125 Anderson-Darling AC9T3 21.1228 <0.001 NO
## 126 Anderson-Darling PC1T3 28.3618 <0.001 NO
## 127 Anderson-Darling PC2T3 25.6749 <0.001 NO
## 128 Anderson-Darling PC3T3 28.3917 <0.001 NO
## 129 Anderson-Darling PC4T3 26.5904 <0.001 NO
## 130 Anderson-Darling ACHT3 7.4112 <0.001 NO
##
## $Descriptives
## n Mean Std.Dev Median Min Max 25th 75th
## ID 870 5.483646e+05 2.813454e+05 530523.5 120201 1120542 220817.2 720510.75
## grade 870 1.774713e+00 5.404721e-01 2.0 1 3 1.0 2.00
## Class 870 4.894253e+00 3.905128e+00 4.0 1 19 2.0 6.00
## Number 870 1.305977e+01 7.661937e+00 13.0 1 42 6.0 19.00
## EN1T1 870 2.910345e+00 1.312508e+00 3.0 1 6 2.0 4.00
## EN2T1 870 3.071264e+00 1.371073e+00 3.0 1 6 2.0 4.00
## EN3T1 870 2.652874e+00 1.244166e+00 3.0 1 6 1.0 3.00
## EN4T1 870 3.165517e+00 1.478720e+00 3.0 1 6 2.0 4.00
## EN5T1 870 3.546710e+00 1.626652e+00 4.0 1 6 2.0 5.00
## FR1T1 870 3.165638e+00 1.546421e+00 3.0 1 6 2.0 4.00
## FR2T1 870 2.834483e+00 1.392139e+00 3.0 1 6 2.0 4.00
## FR3T1 870 3.032184e+00 1.603757e+00 3.0 1 6 2.0 4.00
## SE1T1 870 3.094253e+00 1.428894e+00 3.0 1 6 2.0 4.00
## SE2T1 870 4.709195e+00 1.506956e+00 5.0 1 6 4.0 6.00
## SE3T1 870 4.225287e+00 1.168164e+00 4.0 1 6 4.0 5.00
## SE4T1 870 3.503448e+00 1.371873e+00 4.0 1 6 3.0 4.00
## SE5T1 870 3.859770e+00 1.328146e+00 4.0 1 6 3.0 5.00
## ENR1T1 870 3.741379e+00 1.433935e+00 4.0 1 6 3.0 5.00
## ENR2T1 870 3.752874e+00 1.394493e+00 4.0 1 6 3.0 5.00
## ENR3T1 870 3.544828e+00 1.382012e+00 4.0 1 6 3.0 4.00
## ENR4T1 870 3.719540e+00 1.453367e+00 4.0 1 6 3.0 5.00
## FRR1T1 870 3.713651e+00 1.342275e+00 4.0 1 6 3.0 4.00
## FRR2T1 870 3.737817e+00 1.323509e+00 4.0 1 6 3.0 5.00
## FRR3T1 870 3.629105e+00 1.373962e+00 4.0 1 6 3.0 4.00
## FRR4T1 870 3.787042e+00 1.473034e+00 4.0 1 6 3.0 5.00
## BO1T1 870 3.457471e+00 1.502559e+00 3.0 1 6 2.0 4.00
## BO2T1 870 3.431034e+00 1.502343e+00 3.0 1 6 2.0 4.00
## BO3T1 870 3.102299e+00 1.571428e+00 3.0 1 6 2.0 4.00
## BO4T1 870 3.231133e+00 1.588411e+00 3.0 1 6 2.0 4.00
## CB1T1 870 1.897701e+00 1.312898e+00 1.0 1 6 1.0 3.00
## CB2T1 870 2.326437e+00 1.463516e+00 2.0 1 6 1.0 3.00
## CB3T1 870 3.085057e+00 1.589561e+00 3.0 1 6 2.0 4.00
## AC1T1 870 3.457471e+00 1.483289e+00 4.0 1 6 2.0 4.00
## AC2T1 870 3.331034e+00 1.607900e+00 3.0 1 6 2.0 5.00
## AC3T1 870 1.926226e+00 1.221828e+00 1.0 1 6 1.0 3.00
## AC4T1 870 3.089552e+00 1.486816e+00 3.0 1 6 2.0 4.00
## AC5T1 870 3.158621e+00 1.600529e+00 3.0 1 6 2.0 4.00
## AC6T1 870 2.187356e+00 1.385633e+00 2.0 1 6 1.0 3.00
## AC7T1 870 3.050575e+00 1.566249e+00 3.0 1 6 2.0 4.00
## AC8T1 870 2.106897e+00 1.404849e+00 2.0 1 6 1.0 3.00
## AC9T1 870 3.258712e+00 1.552597e+00 3.0 1 6 2.0 4.00
## PC1T1 870 2.595402e+00 1.555857e+00 2.0 1 6 1.0 3.00
## PC2T1 870 2.683908e+00 1.569295e+00 2.0 1 6 1.0 4.00
## PC3T1 870 2.598851e+00 1.550455e+00 2.0 1 6 1.0 4.00
## PC4T1 870 2.682759e+00 1.550990e+00 2.0 1 6 1.0 4.00
## ACHT1 870 5.824828e+01 2.564690e+01 63.0 0 100 38.0 79.00
## EN1T2 870 2.906897e+00 1.327525e+00 3.0 1 6 2.0 4.00
## EN2T2 870 3.049425e+00 1.383311e+00 3.0 1 6 2.0 4.00
## EN3T2 870 2.693103e+00 1.242264e+00 3.0 1 6 2.0 3.00
## EN4T2 870 3.179310e+00 1.508712e+00 3.0 1 6 2.0 4.00
## EN5T2 870 3.498851e+00 1.566148e+00 4.0 1 6 2.0 5.00
## FR1T2 870 3.271264e+00 1.504876e+00 3.0 1 6 2.0 4.00
## FR2T2 870 2.959770e+00 1.427009e+00 3.0 1 6 2.0 4.00
## FR3T2 870 3.140230e+00 1.579825e+00 3.0 1 6 2.0 4.00
## SE1T2 870 3.201149e+00 1.470774e+00 3.0 1 6 2.0 4.00
## SE2T2 870 4.585890e+00 1.539238e+00 5.0 1 6 4.0 6.00
## SE3T2 870 4.240230e+00 1.202602e+00 4.0 1 6 4.0 5.00
## SE4T2 870 3.643678e+00 1.420522e+00 4.0 1 6 3.0 5.00
## SE5T2 870 3.933495e+00 1.368801e+00 4.0 1 6 3.0 5.00
## ENR1T2 870 3.827586e+00 1.406109e+00 4.0 1 6 3.0 5.00
## ENR2T2 870 3.856322e+00 1.404022e+00 4.0 1 6 3.0 5.00
## ENR3T2 870 3.628736e+00 1.439650e+00 4.0 1 6 3.0 5.00
## ENR4T2 870 3.818391e+00 1.446119e+00 4.0 1 6 3.0 5.00
## FRR1T2 870 3.785057e+00 1.356401e+00 4.0 1 6 3.0 5.00
## FRR2T2 870 3.795402e+00 1.336218e+00 4.0 1 6 3.0 5.00
## FRR3T2 870 3.686207e+00 1.404143e+00 4.0 1 6 3.0 5.00
## FRR4T2 870 3.754962e+00 1.465678e+00 4.0 1 6 3.0 5.00
## BO1T2 870 3.487356e+00 1.533425e+00 3.0 1 6 2.0 4.75
## BO2T2 870 3.500000e+00 1.535727e+00 3.0 1 6 2.0 5.00
## BO3T2 870 3.149425e+00 1.592768e+00 3.0 1 6 2.0 4.00
## BO4T2 870 3.263218e+00 1.601468e+00 3.0 1 6 2.0 4.00
## CB1T2 870 2.050523e+00 1.355966e+00 1.0 1 6 1.0 3.00
## CB2T2 870 2.609195e+00 1.461090e+00 2.0 1 6 1.0 4.00
## CB3T2 870 3.113793e+00 1.551470e+00 3.0 1 6 2.0 4.00
## AC1T2 870 3.418391e+00 1.509352e+00 4.0 1 6 2.0 4.00
## AC2T2 870 3.420690e+00 1.575133e+00 4.0 1 6 2.0 5.00
## AC3T2 870 2.120690e+00 1.309577e+00 2.0 1 6 1.0 3.00
## AC4T2 870 3.180460e+00 1.487450e+00 3.0 1 6 2.0 4.00
## AC5T2 870 3.244828e+00 1.562967e+00 3.0 1 6 2.0 4.00
## AC6T2 870 2.342529e+00 1.418246e+00 2.0 1 6 1.0 3.00
## AC7T2 870 3.126437e+00 1.525424e+00 3.0 1 6 2.0 4.00
## AC8T2 870 2.298162e+00 1.441509e+00 2.0 1 6 1.0 3.00
## AC9T2 870 3.291954e+00 1.552993e+00 3.0 1 6 2.0 4.00
## PC1T2 870 2.701149e+00 1.547967e+00 2.0 1 6 1.0 4.00
## PC2T2 870 2.789655e+00 1.552498e+00 3.0 1 6 1.0 4.00
## PC3T2 870 2.681609e+00 1.530964e+00 2.0 1 6 1.0 4.00
## PC4T2 870 2.778161e+00 1.550895e+00 3.0 1 6 1.0 4.00
## ACHT2 870 5.658506e+01 2.710787e+01 58.0 0 100 35.0 80.00
## EN1T3 870 2.958621e+00 1.340916e+00 3.0 1 6 2.0 4.00
## EN2T3 870 3.013793e+00 1.366976e+00 3.0 1 6 2.0 4.00
## EN3T3 870 2.782759e+00 1.284564e+00 3.0 1 6 2.0 4.00
## EN4T3 870 3.187356e+00 1.440201e+00 3.0 1 6 2.0 4.00
## EN5T3 870 3.570115e+00 1.568983e+00 4.0 1 6 3.0 5.00
## FR1T3 870 3.347126e+00 1.455582e+00 3.0 1 6 2.0 4.00
## FR2T3 870 3.064368e+00 1.366370e+00 3.0 1 6 2.0 4.00
## FR3T3 870 3.155333e+00 1.498764e+00 3.0 1 6 2.0 4.00
## SE1T3 870 3.270691e+00 1.467525e+00 3.0 1 6 2.0 4.00
## SE2T3 870 4.295402e+00 1.525797e+00 4.0 1 6 3.0 6.00
## SE3T3 870 4.140230e+00 1.227275e+00 4.0 1 6 3.0 5.00
## SE4T3 870 3.579310e+00 1.395384e+00 4.0 1 6 3.0 4.00
## SE5T3 870 3.809209e+00 1.340839e+00 4.0 1 6 3.0 5.00
## ENR1T3 870 3.828736e+00 1.372709e+00 4.0 1 6 3.0 5.00
## ENR2T3 870 3.854023e+00 1.377303e+00 4.0 1 6 3.0 5.00
## ENR3T3 870 3.656322e+00 1.370510e+00 4.0 1 6 3.0 4.00
## ENR4T3 870 3.774713e+00 1.427917e+00 4.0 1 6 3.0 5.00
## FRR1T3 870 3.750575e+00 1.339355e+00 4.0 1 6 3.0 5.00
## FRR2T3 870 3.732184e+00 1.317580e+00 4.0 1 6 3.0 4.75
## FRR3T3 870 3.644828e+00 1.352342e+00 4.0 1 6 3.0 4.00
## FRR4T3 870 3.791954e+00 1.409871e+00 4.0 1 6 3.0 5.00
## BO1T3 870 3.518391e+00 1.489204e+00 3.0 1 6 3.0 4.00
## BO2T3 870 3.482759e+00 1.506122e+00 3.0 1 6 2.0 4.00
## BO3T3 870 3.221839e+00 1.541966e+00 3.0 1 6 2.0 4.00
## BO4T3 870 3.344828e+00 1.544340e+00 3.0 1 6 2.0 4.00
## CB1T3 870 2.295402e+00 1.379232e+00 2.0 1 6 1.0 3.00
## CB2T3 870 2.855172e+00 1.439917e+00 3.0 1 6 2.0 4.00
## CB3T3 870 3.175862e+00 1.484904e+00 3.0 1 6 2.0 4.00
## AC1T3 870 3.468966e+00 1.464840e+00 4.0 1 6 2.0 4.00
## AC2T3 870 3.480460e+00 1.537849e+00 4.0 1 6 2.0 5.00
## AC3T3 870 2.341379e+00 1.334507e+00 2.0 1 6 1.0 3.00
## AC4T3 870 3.289655e+00 1.475152e+00 3.0 1 6 2.0 4.00
## AC5T3 870 3.317241e+00 1.488135e+00 3.0 1 6 2.0 4.00
## AC6T3 870 2.517000e+00 1.431509e+00 2.0 1 6 1.0 3.00
## AC7T3 870 3.293433e+00 1.503403e+00 3.0 1 6 2.0 4.00
## AC8T3 870 2.525755e+00 1.458549e+00 2.0 1 6 1.0 3.00
## AC9T3 870 3.333333e+00 1.510734e+00 3.0 1 6 2.0 4.00
## PC1T3 870 2.806897e+00 1.490113e+00 3.0 1 6 2.0 4.00
## PC2T3 870 2.908046e+00 1.508947e+00 3.0 1 6 2.0 4.00
## PC3T3 870 2.781609e+00 1.473395e+00 3.0 1 6 2.0 4.00
## PC4T3 870 2.886207e+00 1.529809e+00 3.0 1 6 2.0 4.00
## ACHT3 870 5.810575e+01 2.562589e+01 60.0 0 100 38.0 80.00
## Skew Kurtosis
## ID 0.123756836 -1.042088903
## grade -0.105485816 -0.233132085
## Class 1.876908494 3.587625040
## Number 0.324178269 -0.320561039
## EN1T1 0.046398477 -0.652641021
## EN2T1 -0.026563073 -0.721453787
## EN3T1 0.219165395 -0.552236147
## EN4T1 0.008718138 -0.926110544
## EN5T1 -0.160277225 -1.078131981
## FR1T1 0.255918791 -0.865164312
## FR2T1 0.424412969 -0.502235558
## FR3T1 0.260309764 -1.014749767
## SE1T1 0.028201905 -0.808414100
## SE2T1 -1.135919276 0.350721987
## SE3T1 -0.508643743 0.334616519
## SE4T1 -0.134075314 -0.600133448
## SE5T1 -0.313371744 -0.357115660
## ENR1T1 -0.474688800 -0.462780858
## ENR2T1 -0.500604403 -0.315107733
## ENR3T1 -0.309843805 -0.442750108
## ENR4T1 -0.366328448 -0.590037249
## FRR1T1 -0.379081865 -0.260989954
## FRR2T1 -0.424909187 -0.198227697
## FRR3T1 -0.210195643 -0.488763139
## FRR4T1 -0.191300336 -0.709773264
## BO1T1 0.129479010 -0.829952259
## BO2T1 0.177315027 -0.817512955
## BO3T1 0.413951657 -0.786238675
## BO4T1 0.291386773 -0.888412843
## CB1T1 1.471740219 1.398845770
## CB2T1 0.863517475 -0.250208428
## CB3T1 0.197234352 -1.025278413
## AC1T1 -0.018754435 -0.830493723
## AC2T1 0.037956466 -1.097255605
## AC3T1 1.430123626 1.615623910
## AC4T1 0.274620875 -0.805461262
## AC5T1 0.181440054 -1.068240251
## AC6T1 1.080773815 0.386194944
## AC7T1 0.226893989 -1.012081703
## AC8T1 1.222938211 0.629067248
## AC9T1 0.079267867 -0.997234763
## PC1T1 0.784625578 -0.368894071
## PC2T1 0.692346362 -0.534181405
## PC3T1 0.770105242 -0.399042956
## PC4T1 0.663989634 -0.562838322
## ACHT1 -0.378609452 -0.922741875
## EN1T2 0.164810910 -0.530667306
## EN2T2 0.088726817 -0.614234727
## EN3T2 0.282304600 -0.289756277
## EN4T2 0.090016113 -0.885651268
## EN5T2 -0.142396221 -0.934129339
## FR1T2 0.177102371 -0.797216176
## FR2T2 0.407664303 -0.518708965
## FR3T2 0.139683027 -1.015116020
## SE1T2 -0.006662741 -0.834430276
## SE2T2 -0.883907709 -0.232668557
## SE3T2 -0.492227350 0.152467405
## SE4T2 -0.119562778 -0.613791213
## SE5T2 -0.305169021 -0.472349157
## ENR1T2 -0.409666870 -0.375576251
## ENR2T2 -0.474286154 -0.334890286
## ENR3T2 -0.231304721 -0.603758439
## ENR4T2 -0.425177838 -0.482996288
## FRR1T2 -0.389387890 -0.270166774
## FRR2T2 -0.438515280 -0.137239686
## FRR3T2 -0.249621165 -0.487911287
## FRR4T2 -0.216078782 -0.617073264
## BO1T2 0.107033535 -0.869062192
## BO2T2 0.079972205 -0.886772911
## BO3T2 0.348988419 -0.862043022
## BO4T2 0.265637384 -0.945168806
## CB1T2 1.211468472 0.680380153
## CB2T2 0.500770495 -0.713913802
## CB3T2 0.133469829 -0.961610147
## AC1T2 -0.052344977 -0.926996895
## AC2T2 -0.034068295 -1.019884246
## AC3T2 1.173968522 0.813126481
## AC4T2 0.098141345 -0.899984489
## AC5T2 0.085808165 -1.002765523
## AC6T2 0.922254842 0.055661741
## AC7T2 0.165552153 -0.929107472
## AC8T2 0.958084370 0.066434485
## AC9T2 -0.020659394 -0.994992630
## PC1T2 0.726396507 -0.393700923
## PC2T2 0.613984901 -0.570084581
## PC3T2 0.695283578 -0.412768420
## PC4T2 0.619818615 -0.556517743
## ACHT2 -0.182693122 -1.105716037
## EN1T3 0.138266398 -0.563936157
## EN2T3 0.158756666 -0.592134695
## EN3T3 0.288732240 -0.312774129
## EN4T3 0.042391500 -0.739272540
## EN5T3 -0.198205841 -0.928559475
## FR1T3 0.039602576 -0.778797555
## FR2T3 0.294896959 -0.530329121
## FR3T3 0.101092913 -0.926607886
## SE1T3 0.013119583 -0.811104663
## SE2T3 -0.607143723 -0.572527246
## SE3T3 -0.398600080 -0.041739349
## SE4T3 -0.109897565 -0.560922310
## SE5T3 -0.264975938 -0.354432396
## ENR1T3 -0.434285102 -0.281877309
## ENR2T3 -0.447145836 -0.252226526
## ENR3T3 -0.290585316 -0.397676794
## ENR4T3 -0.372896372 -0.454408467
## FRR1T3 -0.388956423 -0.196575961
## FRR2T3 -0.395081380 -0.165845785
## FRR3T3 -0.225239941 -0.357306247
## FRR4T3 -0.204691322 -0.511105314
## BO1T3 0.034338854 -0.801742258
## BO2T3 0.058275600 -0.827020954
## BO3T3 0.277277888 -0.810640652
## BO4T3 0.162372999 -0.838742641
## CB1T3 0.893540479 0.009567662
## CB2T3 0.323202477 -0.705020981
## CB3T3 0.072095707 -0.814957493
## AC1T3 -0.121085566 -0.814498568
## AC2T3 -0.098846661 -0.921050202
## AC3T3 0.846081822 0.075450673
## AC4T3 0.061458595 -0.835019013
## AC5T3 0.023258655 -0.845512515
## AC6T3 0.739354483 -0.236303981
## AC7T3 0.056152111 -0.851940625
## AC8T3 0.680412052 -0.378507982
## AC9T3 -0.003185465 -0.894044468
## PC1T3 0.588514003 -0.427697377
## PC2T3 0.489280183 -0.600325128
## PC3T3 0.573188017 -0.407989228
## PC4T3 0.488170673 -0.640540385
## ACHT3 -0.184536131 -1.029391824