Data

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M1 <- 2000001
M2 <- 3000000
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. 
##    2.79   16.34   20.36   21.02   24.97   64.21
Xsum %>%
  sd %>%
  round(2)
## [1] 6.51
Xsum %>%
  `<=`(5) %>%
  which %>%
  `[`(Xsum, .) %>%
  round(2)
## 2000760 2014441 2018477 2029864 2042204 2042736 2052251 2071601 2076542 2080866 
##    4.66    3.75    4.90    4.10    4.85    4.89    4.52    3.46    4.75    4.60 
## 2082556 2085788 2097100 2098547 2122846 2127932 2138166 2138541 2158792 2161640 
##    4.99    4.80    4.97    4.87    4.98    4.97    4.29    4.95    5.00    4.14 
## 2166995 2171637 2171850 2176868 2190015 2192180 2204839 2214558 2223092 2223907 
##    3.99    4.14    4.73    4.92    4.54    4.31    4.43    4.96    4.41    3.90 
## 2227929 2233162 2236335 2244555 2251094 2258880 2283820 2286599 2295920 2328641 
##    4.73    4.03    4.51    4.26    3.98    3.21    5.00    4.66    4.21    4.40 
## 2347653 2365976 2366585 2377204 2389545 2403306 2408775 2412611 2426702 2439270 
##    3.55    4.78    4.46    4.83    4.78    4.79    4.59    4.93    4.14    3.56 
## 2442371 2442967 2443789 2467279 2473795 2477515 2497882 2500302 2503320 2512864 
##    4.92    4.77    4.54    4.17    4.56    2.79    4.47    4.16    4.44    4.72 
## 2514818 2526394 2527829 2540068 2541043 2548534 2548872 2553029 2563987 2571823 
##    4.91    4.89    4.78    4.95    3.46    4.12    4.34    4.90    4.83    4.84 
## 2577651 2580740 2600744 2627257 2655362 2660227 2665371 2669069 2677086 2677379 
##    4.70    3.58    4.19    4.84    4.95    4.57    4.08    4.80    3.58    4.32 
## 2682230 2701444 2703444 2706325 2716266 2719347 2722204 2722888 2739826 2755452 
##    4.62    4.94    4.71    3.42    3.92    4.72    4.89    4.45    4.52    4.80 
## 2755948 2757971 2772469 2779852 2787555 2802699 2816544 2819951 2827825 2830032 
##    3.70    4.88    4.10    4.54    3.19    4.81    4.46    4.90    3.79    4.82 
## 2849275 2852313 2857002 2873258 2876493 2880033 2881274 2882982 2894363 2898534 
##    3.46    4.73    4.60    4.02    2.93    3.79    4.73    4.71    4.15    4.64 
## 2923509 2932750 2933819 2947620 2951547 2952124 2959045 2961850 2963440 2977515 
##    4.93    4.92    4.76    4.48    4.51    4.67    3.46    4.79    4.86    4.77 
## 2977786 2982046 2988878 
##    4.92    4.94    4.06
Xmin <- names(Xsum[which(Xsum == min(Xsum))])
Xmin
## [1] "2477515"

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] 2.791057

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 20 38 62 75 48 135 25
Black 21 33 59 79 53 134 25 
X1min <- tbl1 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X1min
## X-squared 
## 0.8047835

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 210 193
Black 210 194 
X2min <- tbl2 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X2min
##   X-squared 
## 0.001344824

학적 상태

tbl3 <- class_roll$status %>%
  table(class_roll$group, .) 
tbl3 %>%
  pander
  학생 휴학
Red 327 76
Black 332 72 
X3min <- tbl3 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X3min
## X-squared 
## 0.1448054

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 332 71
Black 332 72 
X4min <- tbl4 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X4min
##   X-squared 
## 0.005753858

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 42 31 32 43 32 48 40 41 42 51
Black 39 34 36 42 32 50 44 36 40 51 
X5min <- tbl5 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X5min
## X-squared 
##  1.096424

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 70 63 29 241
Black 78 58 31 237 
X6min <- tbl6 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X6min
## X-squared 
## 0.7379454

Sum of Chi_Squares

Xsum_min <- X1min + X2min + X3min + X4min + X5min + X6min
Xsum_min
## X-squared 
##  2.791057