Data

Search for Best Configuration

M1 <- 8000001
M2 <- 9000000
Xsum <- sapply(M1:M2, red_and_black)
names(Xsum) <- M1:M2
Xsum %>%
  summary %>%
  round(2) 
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    2.48   16.36   20.35   21.02   24.97   67.80
Xsum %>%
  sd %>%
  round(2)
## [1] 6.49
Xsum %>%
  `<=`(5) %>%
  which %>%
  `[`(Xsum, .) %>%
  round(2)
## 8004270 8006298 8015783 8030538 8035483 8036233 8043725 8054933 8055383 8056171 
##    4.96    4.66    4.89    4.93    4.34    4.78    4.72    4.48    4.96    4.70 
## 8064920 8070521 8074361 8075393 8079322 8091918 8099683 8103402 8104143 8114250 
##    3.37    4.95    4.48    4.96    4.69    4.45    4.60    3.64    4.85    4.66 
## 8150811 8158787 8169541 8169914 8172715 8187551 8207794 8211438 8220933 8243946 
##    4.48    4.72    4.37    4.99    3.95    4.81    4.46    4.92    3.54    4.39 
## 8250609 8254590 8257799 8261598 8271777 8274045 8277171 8279547 8281502 8285687 
##    3.89    4.74    4.39    4.98    4.65    4.96    4.62    4.69    3.92    4.48 
## 8294502 8295003 8295803 8296097 8300261 8306056 8316593 8328167 8337350 8342004 
##    4.54    4.48    3.81    4.65    2.48    4.81    3.94    3.84    4.93    4.87 
## 8344497 8345629 8345636 8359382 8364267 8366442 8380458 8380590 8382479 8404685 
##    4.35    4.21    4.82    4.74    3.60    3.82    3.91    4.41    4.96    4.38 
## 8405160 8405414 8408741 8423973 8444246 8446121 8452247 8458507 8461695 8463382 
##    4.86    3.87    4.68    4.33    3.85    4.88    4.48    4.97    4.54    2.88 
## 8472484 8475397 8481819 8486243 8488683 8499716 8510688 8513265 8515187 8516943 
##    3.82    4.88    3.78    4.29    4.57    4.17    3.93    4.91    4.60    3.94 
## 8520747 8534949 8544561 8556019 8560368 8566677 8568919 8573199 8584043 8605782 
##    4.80    4.78    3.78    4.83    4.31    3.87    4.29    4.95    4.06    4.42 
## 8620895 8625865 8638610 8652692 8652984 8656731 8658025 8668709 8669741 8671463 
##    4.11    4.98    4.75    4.77    4.95    4.56    4.89    3.50    4.84    4.94 
## 8674938 8677050 8686810 8690367 8697464 8697826 8715291 8719886 8727970 8729939 
##    4.73    3.45    4.94    3.57    4.23    4.38    3.11    4.36    4.43    4.81 
## 8742692 8758118 8778737 8796542 8803157 8810101 8811099 8831413 8874683 8882953 
##    4.02    4.85    4.96    3.68    3.23    4.25    4.94    3.85    4.59    4.61 
## 8899380 8903761 8912003 8925155 8944100 8954457 8959840 8967224 8971428 8975355 
##    4.66    4.79    4.48    4.83    3.49    4.11    4.08    4.89    4.53    4.16 
## 8993502 8994654 8996645 
##    4.90    4.33    4.60
Xmin <- names(Xsum[which(Xsum == min(Xsum))])
Xmin
## [1] "8300261"

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] 2.48382

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 28 55 66 45 70 228
Black 16 30 57 65 39 66 234 
X1min <- tbl1 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X1min
## X-squared 
##  0.868801

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 271 235
Black 267 240 
X2min <- tbl2 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X2min
##  X-squared 
## 0.08138427

학적 상태

tbl3 <- class_roll$status %>%
  table(class_roll$group, .) 
tbl3 %>%
  pander
  학생 휴학
Red 465 41
Black 464 43 
X3min <- tbl3 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X3min
##  X-squared 
## 0.04770835

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 402 104
Black 410 97 
X4min <- tbl4 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X4min
## X-squared 
##  0.321612

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 48 44 44 53 58 53 59 56 42 49
Black 45 48 48 47 59 52 57 58 43 50 
X5min <- tbl5 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X5min
## X-squared 
##  0.913121

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 116 70 41 279
Black 118 72 37 280 
X6min <- tbl6 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X6min
## X-squared 
## 0.2511932

Sum of Chi_Squares

Xsum_min <- X1min + X2min + X3min + X4min + X5min + X6min
Xsum_min
## X-squared 
##   2.48382