Data

Search for Best Configuration

M1 <- 1000001
M2 <- 2000000
Xsum <- numeric(0)
Values_mat <- numeric(0)
for(k in M1:M2){
  set.seed(k)
  N <- nrow(class_roll) 
  class_roll$group <- 
    sample(1:N) %%
    2 %>%
    factor(levels = c(0, 1), labels = c("Red", "Black"))
  Xsum <- c(Xsum, red_and_black(class_roll)$Xsum)
  Values_mat <- rbind(Values_mat, red_and_black(class_roll)$Values)
}
colnames(Values_mat) <- paste0("X", 1:6)
# Values_mat
# pairs(Values_mat)
cor(Values_mat) %>%
  round(4)
##         X1      X2      X3      X4      X5      X6
## X1  1.0000 -0.0032  0.0205  0.0055 -0.0014 -0.0048
## X2 -0.0032  1.0000 -0.0040 -0.0002 -0.0026  0.0017
## X3  0.0205 -0.0040  1.0000  0.0023 -0.0018 -0.0044
## X4  0.0055 -0.0002  0.0023  1.0000 -0.0026  0.0015
## X5 -0.0014 -0.0026 -0.0018 -0.0026  1.0000 -0.0025
## X6 -0.0048  0.0017 -0.0044  0.0015 -0.0025  1.0000
names(Xsum) <- M1:M2
Xsum %>%
  summary %>%
  round(2) 
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    2.70   16.43   20.41   21.05   24.96   64.05
Xsum %>%
  sd %>%
  round(2)
## [1] 6.42
Xsum %>%
  `<=`(5) %>%
  which %>%
  `[`(Xsum, .) %>%
  round(2)
## 1018104 1037045 1041956 1049824 1061039 1069521 1085722 1095609 1110740 1112269 
##    3.70    4.51    4.74    4.20    4.09    4.94    4.00    4.74    4.61    4.39 
## 1118034 1123352 1137351 1171643 1177936 1181085 1198449 1203583 1224986 1225143 
##    4.18    4.85    4.95    4.92    4.65    4.85    4.69    4.81    3.04    4.92 
## 1238856 1247492 1268598 1270360 1270872 1277724 1308287 1338454 1341067 1355056 
##    3.79    4.92    4.09    4.94    4.85    4.89    3.58    4.85    4.96    4.94 
## 1370886 1373575 1380383 1383911 1384735 1387329 1391248 1394924 1429714 1441114 
##    4.12    3.66    3.88    4.57    4.74    4.45    4.85    4.42    4.82    2.70 
## 1463676 1468769 1472420 1474897 1475765 1480132 1496299 1512072 1523295 1531738 
##    4.76    4.79    4.77    4.70    4.70    4.37    3.21    4.81    4.41    4.67 
## 1541593 1545993 1550187 1553129 1558254 1560098 1584945 1610184 1619881 1622213 
##    4.91    4.73    4.84    4.74    4.56    4.28    4.11    4.03    4.28    3.80 
## 1626416 1627520 1632961 1640255 1643641 1648515 1654738 1668062 1669372 1673015 
##    4.66    4.29    2.97    4.45    4.19    4.78    4.80    3.85    4.87    3.76 
## 1677633 1678909 1690878 1703196 1704560 1732088 1743416 1744583 1745877 1750073 
##    3.38    4.31    3.85    3.90    4.33    4.80    4.59    4.73    4.73    4.97 
## 1758681 1759019 1801476 1810071 1838888 1845775 1867753 1869142 1881400 1887657 
##    4.76    4.56    4.96    5.00    4.61    4.99    4.94    4.49    4.85    4.88 
## 1920200 1927516 1934565 1971266 1974611 1987441 
##    5.00    4.33    4.87    3.27    4.81    4.89
Xmin <- names(Xsum[which(Xsum == min(Xsum))])
Xmin
## [1] "1441114"

Plot

hist(Xsum, prob = TRUE, nclass = 30, xlim = c(0, 50), ylim = c(0, 0.065))
x <- seq(0, 50, by = 0.1)
lines(x, dchisq(x, df = 21), col = "red")
legend("topright", inset = 0.05, legend = c("Xsum", "Chi-square(21)"), col = c("black", "red"), lty = 1)

plot(density(Xsum), xlim = c(0, 50), main = "Density Estimation of Xsum")
lines(x, dchisq(x, df = 21), col = "red")
legend("topright", inset = 0.05, legend = c("Xsum", "Chi-square(21)"), col = c("black", "red"), lty = 1)

Randomization

set.seed(Xmin)
N <- nrow(class_roll) 
class_roll$group <- 
  sample(1:N) %%
  2 %>%
  factor(levels = c(0, 1), labels = c("Red", "Black"))
red_and_black(class_roll)
## $Values
## [1] 1.2869471 0.2058171 0.0000000 0.3941606 0.4497599 0.3595136
## 
## $Xsum
## [1] 2.696198

학번

class_roll$id_2 <-
  class_roll$id %>%
  ifelse(. <= 2015, "2015", .)
tbl1 <- class_roll %$%
  table(.$group, .$id_2 %>% substr(1, 4)) %>%
  `colnames<-`(c("2015 이전", 2016:2021)) 
tbl1 %>%
  pander
  2015 이전 2016 2017 2018 2019 2020 2021
Red 16 37 31 38 16 63 42
Black 16 31 33 36 19 69 39 
X1min <- tbl1 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X1min
## X-squared 
##  1.286947

학번 홀짝

tbl2 <- class_roll$id %>%
  as.numeric %>%
  `%%`(2) %>%
  factor(levels = c(1, 0), labels = c("홀", "짝")) %>%
  table(class_roll$group, .) 
tbl2 %>%
  pander
  홀 짝
Red 122 121
Black 117 126 
X2min <- tbl2 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X2min
## X-squared 
## 0.2058171

학적 상태

tbl3 <- class_roll$status %>%
  table(class_roll$group, .) 
tbl3 %>%
  pander
  학생 휴학
Red 239 4
Black 239 4 
X3min <- tbl3 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X3min
## X-squared 
##         0

e-mail 서비스업체

tbl4 <- class_roll$email %>%
  strsplit("@", fixed = TRUE) %>%
  sapply("[", 2) %>%
  `==`("naver.com") %>%
  ifelse("네이버", "기타서비스") %>%
  factor(levels = c("네이버", "기타서비스")) %>%
  table(class_roll$group, .) 
tbl4 %>%
  pander
  네이버 기타서비스
Red 208 35
Black 203 40 
X4min <- tbl4 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X4min
## X-squared 
## 0.3941606

전화번호의 분포

cut_label <- paste(paste0(0:9, "000"), paste0(0:9, "999"), 
                   sep = "~")
tbl5 <- class_roll$cell_no %>%
  substr(start = 8, stop = 11) %>%
  sapply(as.numeric) %>%
  cut(labels = cut_label, 
      breaks = seq(0, 10000, by = 1000)) %>%
  table(class_roll$group, .) 
tbl5 %>%
  pander
  0000~0999 1000~1999 2000~2999 3000~3999 4000~4999 5000~5999 6000~6999 7000~7999 8000~8999 9000~9999
Red 21 22 21 26 30 22 21 28 25 27
Black 20 21 24 27 29 22 21 30 24 25 
X5min <- tbl5 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X5min
## X-squared 
## 0.4497599

성씨 분포

f_name <- class_roll$name %>%
  substring(first = 1, last = 1) 
tbl6 <- f_name %>%
  `%in%`(c("김", "이", "박")) %>%
  ifelse(f_name, "기타") %>%
  factor(levels = c("김", "이", "박", "기타")) %>%
  table(class_roll$group, .) 
tbl6 %>%
  pander
  김 이 박 기타
Red 46 42 17 138
Black 46 41 14 142 
X6min <- tbl6 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X6min
## X-squared 
## 0.3595136

Sum of Chi_Squares

Xsum_min <- X1min + X2min + X3min + X4min + X5min + X6min
Xsum_min
## X-squared 
##  2.696198