Data

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M1 <- 4000001
M2 <- 5000000
Xsum <- numeric(0)
Xsum <- sapply(M1:M2, red_and_black)
# 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)
names(Xsum) <- M1:M2
Xsum %>%
  summary %>%
  round(2) 
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    2.85   16.37   20.37   21.04   24.98   66.21
Xsum %>%
  sd %>%
  round(2)
## [1] 6.5
Xsum %>%
  `<=`(5) %>%
  which %>%
  `[`(Xsum, .) %>%
  round(2)
## 4001372 4002786 4004592 4012003 4014411 4015923 4016240 4031294 4056464 4066589 
##    4.76    4.73    4.37    4.80    4.62    4.85    4.63    4.72    4.98    3.65 
## 4098303 4128775 4145741 4153060 4156130 4156490 4169366 4175647 4177207 4195935 
##    3.76    3.63    4.36    4.86    4.57    3.49    4.41    4.46    4.47    4.23 
## 4196958 4199171 4208393 4229234 4243718 4275580 4278493 4285089 4289902 4297200 
##    3.30    4.84    4.30    4.99    4.98    3.75    3.90    3.62    4.13    4.78 
## 4313772 4314593 4315839 4332033 4340396 4375663 4376321 4379724 4380904 4384734 
##    4.45    4.50    4.63    4.46    4.63    3.61    4.26    4.47    4.79    4.73 
## 4391514 4403708 4407276 4423845 4426224 4427872 4437582 4438861 4440694 4443097 
##    4.50    4.43    3.88    4.64    4.52    4.41    4.75    4.53    4.29    3.50 
## 4444897 4447595 4463277 4468192 4468411 4469424 4480568 4487022 4490880 4499283 
##    4.37    4.57    4.82    4.86    4.65    4.51    4.05    4.95    4.67    3.96 
## 4500483 4507062 4522258 4535747 4535920 4540134 4551532 4580442 4585363 4590874 
##    2.85    4.99    4.80    3.30    4.89    4.56    4.75    3.17    4.91    4.93 
## 4594518 4596379 4602860 4611248 4615088 4616121 4636223 4655873 4660006 4666837 
##    4.57    4.32    4.87    4.83    4.96    4.92    4.67    4.87    3.77    4.55 
## 4668230 4671919 4674696 4676155 4692218 4702892 4712314 4721354 4723224 4725047 
##    4.45    4.80    4.63    4.42    4.65    4.24    3.83    4.38    4.66    4.40 
## 4725802 4729419 4732632 4735190 4744270 4750711 4751665 4756084 4757461 4768114 
##    4.97    4.50    4.84    4.36    4.86    4.76    4.44    4.73    3.76    4.63 
## 4769392 4772557 4778602 4778893 4780070 4780184 4817572 4818597 4819465 4829185 
##    4.88    3.68    3.26    4.91    4.98    4.51    4.69    4.95    4.52    3.93 
## 4831839 4836300 4836356 4840202 4853769 4854220 4867426 4878221 4878242 4884123 
##    4.90    4.92    3.54    4.69    3.56    4.36    4.96    4.60    4.62    4.31 
## 4903452 4943776 4990383 4994859 
##    3.04    4.21    3.88    4.65
Xmin <- names(Xsum[which(Xsum == min(Xsum))])
Xmin
## [1] "4500483"

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(Xmin)
## [1] 2.853183

학번

class_roll$id_2 <-
  class_roll$id %>%
  ifelse(. <= 2016, "2016", .)
tbl1 <- class_roll %$%
  table(.$group, .$id_2 %>% substr(1, 4)) %>%
  `colnames<-`(c("2016 이전", 2017:2022)) 
tbl1 %>%
  pander
  2016 이전 2017 2018 2019 2020 2021 2022
Red 21 35 62 78 52 130 25
Black 20 36 59 76 49 139 25 
X1min <- tbl1 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X1min
## X-squared 
## 0.5278147

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 213 190
Black 207 197 
X2min <- tbl2 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X2min
## X-squared 
## 0.2110904

학적 상태

tbl3 <- class_roll$status %>%
  table(class_roll$group, .) 
tbl3 %>%
  pander
  학생 휴학
Red 324 79
Black 335 69 
X3min <- tbl3 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X3min
## X-squared 
## 0.8580494

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 330 73
Black 334 70 
X4min <- tbl4 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X4min
##  X-squared 
## 0.08579442

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 41 36 34 42 32 48 41 39 41 49
Black 40 29 34 43 32 50 43 38 41 53 
X5min <- tbl5 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X5min
## X-squared 
##  1.036242

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 73 60 29 241
Black 75 61 31 237 
X6min <- tbl6 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X6min
## X-squared 
##  0.134192

Sum of Chi_Squares

Xsum_min <- X1min + X2min + X3min + X4min + X5min + X6min
Xsum_min
## X-squared 
##  2.853183