Data

Search for Best Configuration

M1 <- 9000001
M2 <- 10000000
Xsum <- sapply(M1:M2, red_and_black)
names(Xsum) <- M1:M2
Xsum %>%
  summary %>%
  round(2) 
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    2.59   16.36   20.36   21.03   24.98   67.39
Xsum %>%
  sd %>%
  round(2)
## [1] 6.5
Xsum %>%
  `<=`(5) %>%
  which %>%
  `[`(Xsum, .) %>%
  round(2)
## 9004066 9018708 9023741 9026180 9028697 9032827 9034215 9047732 9050124 9051521 
##    4.86    4.86    4.44    4.46    4.24    2.59    3.66    5.00    4.06    4.59 
## 9053346 9061087 9068264 9083029 9109328 9112192 9115218 9125567 9128243 9129459 
##    4.87    4.89    3.97    4.66    4.89    4.34    4.69    4.63    3.57    4.20 
## 9130667 9141661 9150714 9156091 9165595 9185245 9186522 9190959 9191711 9194677 
##    4.61    4.66    4.56    3.77    4.18    4.87    4.83    4.84    4.95    4.97 
## 9195318 9200792 9207814 9214653 9219163 9223666 9223972 9224654 9226262 9227529 
##    4.91    4.81    4.72    4.45    4.75    4.25    4.91    4.44    4.68    4.92 
## 9235361 9239307 9251127 9275533 9286134 9290669 9297417 9298831 9302743 9316079 
##    4.55    3.67    4.57    3.37    3.71    4.67    4.98    4.69    4.93    4.73 
## 9317354 9326232 9336148 9351316 9360077 9361481 9367655 9386609 9391141 9392934 
##    4.96    4.49    4.84    3.65    4.26    4.91    4.60    4.64    4.83    3.92 
## 9397651 9402948 9404973 9411311 9413348 9415595 9418756 9424593 9463619 9465704 
##    4.33    3.39    4.28    4.66    4.93    4.94    5.00    4.27    3.97    4.79 
## 9474036 9474078 9474202 9477422 9487376 9491456 9529265 9542671 9545073 9547950 
##    4.80    4.96    4.54    4.87    4.88    4.08    4.78    4.77    4.66    4.23 
## 9554301 9563923 9566022 9586941 9592365 9597328 9613489 9613734 9615388 9615479 
##    3.74    4.70    4.96    4.49    4.74    4.68    4.76    4.87    4.93    3.92 
## 9617012 9631105 9644452 9645532 9651019 9652046 9663938 9672318 9673081 9683108 
##    4.85    2.90    4.17    4.37    4.56    3.87    4.70    5.00    4.73    4.72 
## 9693532 9714275 9728662 9733924 9734934 9748293 9761145 9766838 9771341 9775688 
##    4.80    4.53    4.47    4.56    4.58    4.97    4.43    3.63    4.65    4.88 
## 9786042 9793043 9794109 9815159 9817124 9818944 9825446 9826464 9831394 9837016 
##    4.97    4.95    4.64    4.52    4.91    4.87    4.59    4.32    4.67    3.06 
## 9837471 9840891 9857715 9876386 9883643 9885422 9887339 9889983 9898994 9901736 
##    4.45    4.98    4.50    4.97    4.44    4.95    4.57    3.12    4.33    3.81 
## 9907203 9907557 9913016 9918059 9924312 9969824 9984365 
##    4.64    4.92    3.76    3.94    3.61    3.69    4.88
Xmin <- names(Xsum[which(Xsum == min(Xsum))])
Xmin
## [1] "9032827"

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] 2.590867

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 15 28 54 70 41 68 230
Black 15 30 58 61 43 68 232 
X1min <- tbl1 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X1min
## X-squared 
##  0.885434

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 269 237
Black 269 238 
X2min <- tbl2 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X2min
##   X-squared 
## 0.001118097

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 406 100
Black 406 101 
X4min <- tbl4 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X4min
##   X-squared 
## 0.003987961

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 46 48 44 49 58 54 59 56 42 50
Black 47 44 48 51 59 51 57 58 43 49 
X5min <- tbl5 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X5min
## X-squared 
## 0.5832897

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 72 35 280
Black 115 70 43 279 
X6min <- tbl6 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X6min
## X-squared 
## 0.9178605

Sum of Chi_Squares

Xsum_min <- X1min + X2min + X3min + X4min + X5min + X6min
Xsum_min
## X-squared 
##  2.590867