Data

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M1 <- 7000001
M2 <- 8000000
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. 
##    3.34   16.36   20.36   21.03   24.97   75.83
Xsum %>%
  sd %>%
  round(2)
## [1] 6.51
Xsum %>%
  `<=`(5) %>%
  which %>%
  `[`(Xsum, .) %>%
  round(2)
## 7011506 7040646 7042999 7044285 7048958 7055717 7075141 7096175 7103635 7105486 
##    4.85    4.86    4.66    4.78    4.95    4.93    4.36    4.03    4.92    4.81 
## 7108477 7113523 7132440 7133825 7134961 7139463 7153238 7153385 7159123 7168791 
##    4.08    4.69    3.86    3.69    4.88    4.93    4.46    4.48    3.76    3.53 
## 7175637 7182541 7183708 7185847 7223147 7230628 7234414 7237837 7240315 7261430 
##    4.53    4.67    5.00    4.63    4.85    3.47    4.92    4.78    4.99    4.37 
## 7273106 7284623 7286035 7298459 7306975 7310120 7317732 7318261 7323325 7328867 
##    4.37    4.34    4.21    4.78    3.91    4.76    4.67    4.09    4.81    4.93 
## 7372209 7383358 7383560 7392876 7394623 7406712 7407009 7415792 7438462 7447383 
##    4.20    4.88    4.86    4.18    3.46    4.07    4.27    4.90    4.16    3.91 
## 7454325 7454701 7461881 7471545 7476641 7476645 7484860 7492137 7508176 7519947 
##    4.98    4.73    4.89    4.86    4.97    3.34    4.55    4.39    4.34    4.18 
## 7525137 7525496 7536153 7544480 7549707 7551632 7555080 7561397 7565310 7581457 
##    4.96    4.89    4.94    4.94    4.96    4.57    3.90    4.23    4.70    4.51 
## 7583587 7584841 7591705 7594663 7597834 7602815 7603217 7604105 7616416 7616722 
##    4.79    4.78    4.55    4.90    4.56    4.36    4.14    3.52    4.54    4.94 
## 7630447 7640533 7640863 7651379 7651567 7653887 7655437 7658280 7677872 7708158 
##    4.95    4.54    4.74    4.89    4.61    4.19    4.72    4.76    4.58    4.80 
## 7715572 7741942 7753049 7764101 7776731 7779899 7794946 7796130 7806911 7820216 
##    4.53    4.67    4.78    3.73    4.44    4.96    4.37    4.76    4.64    4.37 
## 7829726 7832011 7834018 7856368 7877432 7886923 7890915 7915390 7916968 7920253 
##    4.86    4.89    4.99    4.81    3.98    4.66    4.86    4.55    4.80    4.48 
## 7923367 7930275 7946607 7966363 7975498 7980371 7993241 
##    3.43    4.13    4.27    4.20    4.61    3.93    3.76
Xmin <- names(Xsum[which(Xsum == min(Xsum))])
Xmin
## [1] "7476645"

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] 3.337422

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 36 64 77 48 134 23
Black 20 35 57 77 53 135 27 
X1min <- tbl1 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X1min
## X-squared 
##  1.013438

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 209 194
Black 211 193 
X2min <- tbl2 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X2min
##  X-squared 
## 0.01086865

학적 상태

tbl3 <- class_roll$status %>%
  table(class_roll$group, .) 
tbl3 %>%
  pander
  학생 휴학
Red 330 73
Black 329 75 
X3min <- tbl3 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X3min
##  X-squared 
## 0.02730536

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 328 75
Black 336 68 
X4min <- tbl4 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X4min
## X-squared 
## 0.4378044

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 40 32 35 45 30 48 39 39 41 53
Black 41 33 33 40 34 50 45 38 41 49 
X5min <- tbl5 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X5min
## X-squared 
##  1.264954

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 77 59 28 239
Black 71 62 32 239 
X6min <- tbl6 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X6min
## X-squared 
## 0.5830518

Sum of Chi_Squares

Xsum_min <- X1min + X2min + X3min + X4min + X5min + X6min
Xsum_min
## X-squared 
##  3.337422