Data

Search for Best Configuration

M1 <- 7000001
M2 <- 8000000
Xsum <- sapply(M1:M2, red_and_black)
names(Xsum) <- M1:M2
Xsum %>%
  summary %>%
  round(2) 
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    2.89   16.36   20.37   21.03   24.98   82.98
Xsum %>%
  sd %>%
  round(2)
## [1] 6.5
Xsum %>%
  `<=`(5) %>%
  which %>%
  `[`(Xsum, .) %>%
  round(2)
## 7001946 7008403 7016585 7025745 7041842 7048960 7074640 7081298 7085202 7095301 
##    4.66    4.89    4.72    4.65    4.07    3.68    4.43    4.76    4.90    4.40 
## 7096276 7115963 7125585 7127156 7129340 7129702 7130537 7145744 7157678 7160035 
##    4.30    4.30    4.89    3.85    4.58    4.64    4.81    4.74    4.71    4.74 
## 7166896 7167677 7171752 7175371 7176150 7176185 7183879 7184722 7185426 7192253 
##    3.53    4.06    4.52    4.49    4.96    4.11    4.72    3.39    3.41    4.89 
## 7204797 7207568 7208619 7210405 7229166 7230186 7230813 7231563 7238784 7252399 
##    4.77    4.62    3.99    4.92    3.69    4.89    4.48    3.49    4.57    4.46 
## 7255211 7264192 7264864 7266888 7278005 7292810 7298653 7313190 7317888 7318987 
##    4.27    4.45    4.29    4.02    4.95    4.97    4.57    3.34    4.01    4.02 
## 7320944 7334077 7342253 7344773 7363013 7368837 7372308 7378116 7383472 7395274 
##    4.09    3.83    3.28    4.90    4.98    4.98    3.51    4.90    4.01    3.97 
## 7396583 7417245 7436360 7438753 7441999 7442694 7446338 7461952 7464986 7471670 
##    4.75    4.68    4.05    4.98    4.71    4.73    4.05    3.08    3.47    4.45 
## 7471882 7474479 7477581 7479257 7480958 7483900 7490375 7521830 7524851 7525062 
##    4.57    3.69    4.79    4.94    4.17    4.84    4.81    4.96    4.59    4.09 
## 7528997 7534618 7537971 7577509 7582088 7589048 7589396 7595931 7597023 7598298 
##    4.71    3.56    4.83    4.44    5.00    4.79    4.91    4.94    4.95    4.20 
## 7598769 7610001 7616663 7621237 7627352 7652947 7654738 7654806 7655882 7663763 
##    4.72    4.39    4.17    3.91    4.77    4.95    4.59    4.26    4.12    4.56 
## 7671276 7672225 7678652 7680378 7681775 7684991 7687516 7691009 7691825 7696928 
##    4.77    4.84    4.53    4.66    4.95    4.13    3.97    4.98    4.97    4.54 
## 7705846 7708543 7711808 7714596 7716669 7720051 7723433 7733526 7734024 7740426 
##    4.76    3.59    4.00    4.37    4.89    4.83    4.81    4.75    4.80    4.40 
## 7742840 7745721 7756945 7770087 7771078 7785653 7786043 7786759 7795926 7811064 
##    3.59    3.42    4.53    4.68    4.85    4.75    4.35    4.93    4.72    4.99 
## 7815898 7824130 7831160 7844009 7870613 7879033 7881375 7897077 7898866 7909658 
##    4.86    4.89    3.27    4.93    4.89    4.91    4.84    4.87    4.95    4.67 
## 7926512 7948757 7982106 7991513 7991974 
##    2.89    4.44    4.66    3.12    4.58
Xmin <- names(Xsum[which(Xsum == min(Xsum))])
Xmin
## [1] "7926512"

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] 2.890813

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 30 56 69 43 67 226
Black 15 28 56 62 41 69 236 
X1min <- tbl1 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X1min
## X-squared 
## 0.7355059

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 408 98
Black 404 103 
X4min <- tbl4 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X4min
## X-squared 
## 0.1430955

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 43 44 52 56 53 58 58 45 51
Black 47 49 48 48 61 52 58 56 40 48 
X5min <- tbl5 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X5min
## X-squared 
##  1.378298

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 72 36 281
Black 117 70 42 278 
X6min <- tbl6 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X6min
## X-squared 
##  0.504821

Sum of Chi_Squares

Xsum_min <- X1min + X2min + X3min + X4min + X5min + X6min
Xsum_min
## X-squared 
##  2.890813