Data

Search for Best Configuration

M1 <- 2000001
M2 <- 3000000
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   16.35   20.36   21.03   24.97   72.86
Xsum %>%
  sd %>%
  round(2)
## [1] 6.51
Xsum %>%
  `<=`(5) %>%
  which %>%
  `[`(Xsum, .) %>%
  round(2)
## 2008542 2009887 2016026 2018191 2027012 2031288 2032062 2042553 2042593 2043239 
##    4.30    5.00    4.20    4.53    3.19    4.94    2.79    4.71    4.87    4.69 
## 2045409 2050842 2063147 2077520 2086384 2090547 2094189 2096773 2100037 2100061 
##    3.66    4.08    4.47    4.90    4.89    4.38    4.71    4.88    4.60    2.79 
## 2100783 2101190 2122086 2134318 2138988 2139084 2139411 2142418 2146889 2161475 
##    4.81    4.62    4.23    4.77    4.27    4.42    3.56    3.44    4.79    4.77 
## 2191239 2198337 2210948 2213452 2213526 2213527 2232209 2235043 2249349 2255963 
##    4.78    4.25    4.46    4.97    3.86    4.17    4.81    4.95    4.93    4.63 
## 2260427 2268217 2271979 2291853 2292859 2293638 2293801 2294994 2307718 2310514 
##    4.39    3.97    4.75    4.53    2.72    4.86    4.90    4.99    4.99    4.25 
## 2315928 2322875 2323240 2343854 2356223 2357822 2358518 2362574 2384826 2393927 
##    4.47    4.14    3.81    4.10    4.84    4.42    4.80    4.01    4.17    4.10 
## 2397947 2415101 2450142 2454283 2454562 2456378 2461273 2466049 2466423 2472376 
##    4.87    4.69    4.63    4.85    3.38    4.89    4.75    3.28    4.76    3.88 
## 2475452 2488225 2506909 2508300 2527836 2528062 2536468 2562849 2574206 2579032 
##    4.99    3.63    4.95    3.97    4.46    4.65    4.66    4.93    3.92    3.90 
## 2593500 2605944 2616586 2637560 2644387 2645202 2647153 2669902 2671240 2697668 
##    4.59    4.89    4.40    4.77    3.82    4.84    4.96    4.74    4.75    4.62 
## 2701660 2703278 2725618 2728827 2730178 2738546 2747482 2766021 2766798 2775923 
##    4.55    4.92    3.73    4.09    3.99    4.86    4.33    4.19    4.82    4.17 
## 2781054 2787205 2803775 2821305 2821817 2828108 2830495 2833915 2836477 2851055 
##    4.13    4.84    4.89    4.16    4.90    4.33    4.78    3.85    4.14    2.48 
## 2856185 2861025 2866570 2866582 2867286 2870271 2894826 2895761 2904764 2905927 
##    4.91    4.66    4.94    4.76    4.60    4.69    4.91    4.62    4.46    4.59 
## 2913794 2942072 2945523 2946310 2946870 2957198 2957831 2965075 2985837 2993696 
##    4.16    3.79    3.87    4.96    4.15    4.55    3.92    4.42    4.20    4.80
Xmin <- names(Xsum[which(Xsum == min(Xsum))])
Xmin
## [1] "2851055"

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] 2.481618

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 56 66 43 70 229
Black 16 30 56 65 41 66 233 
X1min <- tbl1 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X1min
## X-squared 
## 0.4088438

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 273 233
Black 265 242 
X2min <- tbl2 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X2min
## X-squared 
## 0.2884985

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 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 46 48 53 60 52 60 54 39 48
Black 47 46 44 47 57 53 56 60 46 51 
X5min <- tbl5 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X5min
## X-squared 
##  1.751227

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 70 39 280
Black 117 72 39 279 
X6min <- tbl6 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X6min
##  X-squared 
## 0.02897078

Sum of Chi_Squares

Xsum_min <- X1min + X2min + X3min + X4min + X5min + X6min
Xsum_min
## X-squared 
##  2.481618