Data

Search for Best Configuration

M1 <- 3000001
M2 <- 4000000
Xsum <- sapply(M1:M2, red_and_black)
names(Xsum) <- M1:M2
Xsum %>%
  summary %>%
  round(2) 
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    2.75   16.36   20.35   21.02   24.97   68.35
Xsum %>%
  sd %>%
  round(2)
## [1] 6.5
Xsum %>%
  `<=`(5) %>%
  which %>%
  `[`(Xsum, .) %>%
  round(2)
## 3003155 3014324 3021965 3033272 3040635 3045211 3047669 3049713 3055251 3057520 
##    4.78    4.95    4.69    4.87    4.22    4.77    4.75    3.66    2.75    4.09 
## 3068669 3075337 3092233 3095165 3097913 3100068 3101475 3107528 3109487 3120024 
##    4.80    4.56    4.85    4.57    4.71    4.28    4.92    3.52    4.95    4.82 
## 3125052 3127948 3130544 3132523 3146165 3147683 3162792 3164721 3166288 3167717 
##    3.97    4.93    4.23    4.43    4.51    4.71    4.41    4.60    4.54    4.91 
## 3169517 3170471 3171466 3176729 3187040 3188650 3198647 3203500 3204617 3220994 
##    4.76    4.29    4.50    3.83    3.93    4.91    3.64    4.32    4.91    4.92 
## 3223953 3227899 3252175 3257569 3257785 3272917 3274903 3278990 3280901 3285562 
##    4.63    4.63    4.78    4.49    3.19    3.15    3.53    4.01    4.47    4.14 
## 3285999 3288653 3291512 3299486 3320138 3335711 3337561 3340264 3341394 3341455 
##    4.20    4.86    4.90    3.34    4.83    4.51    4.68    4.78    4.50    4.70 
## 3345460 3350125 3351526 3351720 3361770 3377092 3388394 3400685 3403447 3416434 
##    4.84    4.39    4.79    4.80    4.94    4.45    4.59    3.66    4.67    4.92 
## 3423818 3430141 3431271 3436340 3466467 3466824 3471138 3475991 3483959 3511774 
##    4.14    3.65    4.76    4.92    4.73    4.85    4.81    4.22    4.77    4.45 
## 3531818 3532860 3549366 3554124 3559951 3561208 3564421 3565934 3566993 3568558 
##    4.79    4.11    4.75    4.64    3.68    4.82    4.49    4.80    4.36    3.90 
## 3580421 3583145 3591595 3591813 3592416 3613077 3621577 3642611 3643053 3643838 
##    4.57    3.46    4.72    4.16    4.52    4.60    4.22    4.93    3.67    3.92 
## 3644273 3649014 3651041 3654101 3657302 3694245 3706817 3717726 3732856 3743214 
##    4.56    4.97    4.90    4.88    4.91    4.92    4.99    3.93    4.62    4.01 
## 3743810 3754127 3762242 3767506 3808318 3823264 3823302 3832603 3836716 3849107 
##    4.47    3.65    4.62    4.89    3.99    4.68    4.18    4.75    4.93    3.78 
## 3855340 3874088 3887493 3891912 3895982 3904456 3913467 3916078 3924496 3927228 
##    4.43    4.02    4.53    4.95    4.82    4.44    4.84    4.75    4.03    4.98 
## 3930785 3935504 3950515 3963477 
##    4.72    4.92    4.56    4.05
Xmin <- names(Xsum[which(Xsum == min(Xsum))])
Xmin
## [1] "3055251"

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), ylim = c(0, 0.065), 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] 2.750325

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 16 30 55 66 40 70 229
Black 14 28 57 65 44 66 233 
X1min <- tbl1 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X1min
## X-squared 
## 0.5874154

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 262 244
Black 276 231 
X2min <- tbl2 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X2min
## X-squared 
## 0.7191153

학적 상태

tbl3 <- class_roll$status %>%
  table(class_roll$group, .) 
tbl3 %>%
  pander
  학생 휴학
Red 466 40
Black 463 44 
X3min <- tbl3 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X3min
## X-squared 
## 0.1991771

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 405 101
Black 407 100 
X4min <- tbl4 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X4min
##   X-squared 
## 0.008914075

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 45 44 48 50 59 52 58 58 41 51
Black 48 48 44 50 58 53 58 56 44 48 
X5min <- tbl5 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X5min
## X-squared 
## 0.6935638

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 119 68 41 278
Black 115 74 37 281 
X6min <- tbl6 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X6min
## X-squared 
## 0.5421389

Sum of Chi_Squares

Xsum_min <- X1min + X2min + X3min + X4min + X5min + X6min
Xsum_min
## X-squared 
##  2.750325