Data

Search for Best Configuration

M1 <- 1
M2 <- 100000
Xsum <- numeric(0)
Values_mat <- numeric(0)
for(k in M1:M2){
  set.seed(k)
  N <- nrow(class_roll) 
  class_roll$group <- 
    sample(1:N) %%
    2 %>%
    factor(levels = c(0, 1), labels = c("Red", "Black"))
  Xsum <- c(Xsum, red_and_black(class_roll)$Xsum)
  Values_mat <- rbind(Values_mat, red_and_black(class_roll)$Values)
}
colnames(Values_mat) <- paste0("X", 1:6)
# Values_mat
# pairs(Values_mat)
cor(Values_mat) %>%
  round(4)
##         X1      X2      X3      X4      X5      X6
## X1  1.0000  0.0014  0.0423 -0.0037  0.0020  0.0057
## X2  0.0014  1.0000 -0.0032  0.0045  0.0036  0.0079
## X3  0.0423 -0.0032  1.0000 -0.0027  0.0122 -0.0021
## X4 -0.0037  0.0045 -0.0027  1.0000 -0.0031 -0.0001
## X5  0.0020  0.0036  0.0122 -0.0031  1.0000 -0.0007
## X6  0.0057  0.0079 -0.0021 -0.0001 -0.0007  1.0000
names(Xsum) <- M1:M2
Xsum %>%
  summary %>%
  round(2) 
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    3.19   16.39   20.35   21.05   24.98   58.49
Xsum %>%
  sd %>%
  round(2)
## [1] 6.51
Xsum %>%
  `<=`(6) %>%
  which %>%
  `[`(Xsum, .) %>%
  round(2)
##   872  2832  3337  4099  5107  6991  7338  9831 10980 12184 15650 17357 17776 
##  5.45  5.77  5.41  5.88  5.45  5.92  5.96  4.35  5.64  4.87  5.88  4.58  5.53 
## 19485 19855 20177 20361 20778 23621 24079 27357 31520 34490 34968 36427 37132 
##  5.71  4.90  3.21  5.15  5.33  6.00  5.62  6.00  5.95  5.66  3.19  5.95  4.60 
## 39741 40971 41478 42450 46976 47397 48006 48363 49392 64430 70277 71340 74234 
##  5.86  4.95  5.65  5.99  5.13  5.39  5.69  4.81  5.96  5.42  5.53  5.73  5.72 
## 74386 74757 78449 80843 83023 84851 85469 92774 94529 96544 97580 
##  3.90  5.22  5.78  5.69  5.26  4.98  4.98  4.28  4.03  4.25  5.95
Xmin <- names(Xsum[which(Xsum == min(Xsum))])
Xmin
## [1] "34968"

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), 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(class_roll)
## $Values
## [1] 1.35857076 0.05849150 0.07386091 0.43684501 0.75846495 0.50086257
## 
## $Xsum
## [1] 3.187096

학번

class_roll$id_2 <-
  class_roll$id %>%
  ifelse(. <= 2015, "2015", .)
tbl1 <- class_roll %$%
  table(.$group, .$id_2 %>% substr(1, 4)) %>%
  `colnames<-`(c("2015 이전", 2016:2021)) 
tbl1 %>%
  pander
  2015 이전 2016 2017 2018 2019 2020 2021
Red 19 26 28 55 19 46 115
Black 18 32 27 53 19 52 107 
X1min <- tbl1 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X1min
## X-squared 
##  1.358571

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 151 157
Black 148 160 
X2min <- tbl2 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X2min
## X-squared 
## 0.0584915

학적 상태

tbl3 <- class_roll$status %>%
  table(class_roll$group, .) 
tbl3 %>%
  pander
  학생 휴학
Red 279 29
Black 277 31 
X3min <- tbl3 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X3min
##  X-squared 
## 0.07386091

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 262 46
Black 256 52 
X4min <- tbl4 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X4min
## X-squared 
##  0.436845

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 23 29 34 28 24 32 28 38 38 34
Black 24 33 34 25 27 32 27 36 38 32 
X5min <- tbl5 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X5min
## X-squared 
##  0.758465

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 63 45 24 176
Black 65 50 25 168 
X6min <- tbl6 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X6min
## X-squared 
## 0.5008626

Sum of Chi_Squares

Xsum_min <- X1min + X2min + X3min + X4min + X5min + X6min
Xsum_min
## X-squared 
##  3.187096