Data

Search for Best Configuration

M1 <- 6000001
M2 <- 7000000
Xsum <- sapply(M1:M2, red_and_black)
names(Xsum) <- M1:M2
Xsum %>%
  summary %>%
  round(2) 
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    2.94   16.36   20.36   21.03   24.98   66.80
Xsum %>%
  sd %>%
  round(2)
## [1] 6.5
Xsum %>%
  `<=`(5) %>%
  which %>%
  `[`(Xsum, .) %>%
  round(2)
## 6001314 6003188 6015041 6044584 6047857 6052567 6061663 6062903 6066215 6071182 
##    4.27    4.95    4.59    4.43    4.26    4.51    4.27    4.67    4.07    3.62 
## 6080564 6091575 6092144 6104876 6112351 6117966 6118713 6127742 6128067 6130231 
##    4.95    4.85    4.94    4.96    4.94    3.01    4.08    4.76    4.57    4.91 
## 6134976 6137865 6142178 6145637 6152527 6154813 6159876 6166688 6175296 6204692 
##    4.14    4.74    4.64    3.88    4.97    4.74    4.65    4.73    4.85    4.92 
## 6204847 6208675 6218670 6220020 6223526 6231485 6232695 6244760 6251672 6265867 
##    4.56    4.84    4.94    4.67    4.11    4.93    4.96    4.96    4.12    4.84 
## 6270946 6276347 6281013 6284939 6288274 6291333 6300203 6301798 6304377 6314112 
##    4.97    4.79    4.64    4.73    4.65    4.57    3.33    4.96    4.42    3.47 
## 6321218 6345157 6364749 6381020 6386216 6406986 6412035 6414954 6415879 6419752 
##    4.99    4.33    4.70    4.98    4.38    4.85    3.42    4.99    4.97    4.60 
## 6425830 6426053 6436529 6447190 6495569 6504032 6527706 6528341 6529613 6532852 
##    4.29    4.67    4.69    4.70    4.35    3.39    4.60    3.17    4.91    4.40 
## 6533253 6534526 6535932 6541274 6551107 6556068 6557320 6557365 6562253 6573601 
##    4.82    4.19    4.19    5.00    4.76    4.64    4.33    4.75    4.77    4.70 
## 6575193 6575909 6578220 6579968 6581972 6587225 6592552 6611006 6614563 6618686 
##    4.38    4.35    4.13    4.64    4.16    2.94    4.77    4.83    4.96    4.62 
## 6631168 6633624 6642924 6643452 6662807 6664536 6677421 6688302 6698035 6703998 
##    4.97    4.03    4.82    4.75    4.73    4.76    4.65    4.61    4.95    4.62 
## 6713496 6728370 6729717 6736067 6739154 6744817 6745073 6745157 6766924 6768064 
##    4.79    4.88    5.00    4.06    4.70    4.60    4.77    4.69    4.43    4.90 
## 6768787 6775365 6784802 6794919 6808448 6812467 6831091 6833245 6843605 6863214 
##    4.91    4.79    4.32    4.93    4.26    4.62    4.76    4.02    4.10    4.66 
## 6886558 6903446 6923137 6926136 6926640 6928369 6937487 6941244 6959961 6977797 
##    4.41    4.79    3.37    4.71    4.65    4.84    4.47    4.65    3.90    4.82 
## 6979643 6979766 6991091 6991820 
##    4.92    4.07    4.91    3.47
Xmin <- names(Xsum[which(Xsum == min(Xsum))])
Xmin
## [1] "6587225"

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] 2.935213

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 14 26 59 64 44 71 228
Black 16 32 53 67 40 65 234 
X1min <- tbl1 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X1min
## X-squared 
##  1.676272

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 265 241
Black 273 234 
X2min <- tbl2 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X2min
## X-squared 
## 0.2211301

학적 상태

tbl3 <- class_roll$status %>%
  table(class_roll$group, .) 
tbl3 %>%
  pander
  학생 휴학
Red 464 42
Black 465 42 
X3min <- tbl3 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X3min
##    X-squared 
## 8.925952e-05

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 410 96
Black 402 105 
X4min <- tbl4 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X4min
## X-squared 
## 0.4808161

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 47 45 44 50 58 52 59 58 43 50
Black 46 47 48 50 59 53 57 56 42 49 
X5min <- tbl5 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X5min
## X-squared 
## 0.3366642

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 117 71 37 281
Black 117 71 41 278 
X6min <- tbl6 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X6min
## X-squared 
## 0.2202414

Sum of Chi_Squares

Xsum_min <- X1min + X2min + X3min + X4min + X5min + X6min
Xsum_min
## X-squared 
##  2.935213