Data

Search for Best Configuration

M1 <- 1
M2 <- 10000
Xsum <- sapply(M1:M2, red_and_black)
names(Xsum) <- M1:M2
Xsum %>%
  summary %>%
  round(2) 
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    0.70    5.12    7.53    8.19   10.50   26.94
Xsum %>%
  sd %>%
  round(2)
## [1] 4.1
Xsum %>%
  `<=`(2) %>%
  which %>%
  `[`(Xsum, .) %>%
  round(2)
##   58  203  243  351  475  688  752  810  841  878 1038 1049 1066 1157 1401 1406 
## 1.92 1.26 1.64 0.99 1.54 1.65 1.37 1.92 1.92 1.54 0.70 0.70 1.37 1.92 1.54 1.26 
## 1428 1476 1504 1530 1537 1627 1724 1845 1991 2007 2018 2086 2183 2356 2368 2372 
## 1.92 1.65 0.70 1.92 1.37 1.26 1.64 0.70 1.26 1.92 1.54 0.70 0.99 0.99 1.93 1.92 
## 2615 2688 2718 2782 2887 3044 3110 3127 3136 3186 3206 3213 3330 3332 3385 3423 
## 1.54 1.92 1.26 1.26 1.26 1.92 1.64 1.92 1.60 1.71 1.54 1.92 1.92 0.99 0.99 0.99 
## 3510 3573 3591 3723 3753 3761 3770 3805 3883 3893 4010 4126 4186 4208 4334 4371 
## 1.54 1.71 1.26 0.70 0.99 1.65 1.26 1.92 1.37 1.37 0.70 1.54 1.94 1.54 1.54 0.99 
## 4481 4570 4618 4687 4715 4745 4835 4860 5012 5034 5065 5163 5175 5186 5188 5193 
## 1.60 1.54 0.70 1.93 1.54 1.26 0.99 1.54 1.94 1.26 1.65 1.71 1.94 1.92 1.92 1.93 
## 5198 5226 5259 5279 5342 5374 5391 5570 5588 5638 5714 5750 5804 5830 6033 6051 
## 1.92 1.65 1.26 1.94 1.64 1.92 1.92 1.92 1.26 1.60 1.60 0.99 1.26 1.26 1.54 0.70 
## 6060 6075 6078 6104 6151 6271 6353 6394 6420 6426 6471 6496 6505 6533 6553 6644 
## 1.92 1.92 1.65 1.26 1.92 1.71 1.26 1.65 0.99 1.71 1.93 1.65 1.54 1.71 1.65 1.60 
## 6660 6699 7041 7137 7219 7326 7405 7455 7512 7515 7531 7587 7596 7601 7773 7797 
## 0.70 1.93 1.93 1.54 0.70 1.71 0.70 1.26 1.92 0.70 1.26 1.94 1.64 1.60 1.94 1.26 
## 7831 7952 7954 7995 8120 8179 8222 8227 8232 8364 8367 8368 8371 8570 8574 8645 
## 1.92 1.26 0.99 0.70 1.54 1.92 1.71 1.60 1.92 1.65 1.92 0.70 0.70 1.71 1.92 1.92 
## 8660 8698 8722 8763 8783 8784 8787 8847 8893 8945 8987 9003 9013 9129 9164 9172 
## 1.92 0.99 1.26 1.94 1.71 0.99 1.64 1.71 1.26 1.64 1.92 1.26 1.92 1.92 1.54 1.65 
## 9509 9584 9989 
## 1.60 0.99 1.54
Xmin <- names(Xsum[which(Xsum == min(Xsum))])
Xmin
##  [1] "1038" "1049" "1504" "1845" "2086" "3723" "4010" "4618" "6051" "6660"
## [11] "7219" "7405" "7515" "7995" "8368" "8371"

Plot

hist(Xsum, prob = TRUE, nclass = 30, xlim = c(0, 25), ylim = c(0, 0.15))
x <- seq(0, 25, by = 0.1)
lines(x, dchisq(x, df = 8), col = "red")
legend("topright", inset = 0.05, legend = c("Xsum", "Chi-square(8)"), col = c("black", "red"), lty = 1)

plot(density(Xsum), xlim = c(0, 25), ylim = c(0, 0.15), main = "Density Estimation of Xsum")
lines(x, dchisq(x, df = 9), col = "red")

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] 0.7002038

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 9 8
Black 10 7 
X2min <- tbl2 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X2min
## X-squared 
## 0.1192982

출생 시기

tbl3 <- class_roll$yob %>%
    cut(breaks = c(-Inf, 1980, 1995, Inf), 
        labels =c ("X세대", "Y세대", "Z세대" )) %>%
    table(class_roll$group, .) 
tbl3 %>%
  pander
  X세대 Y세대 Z세대
Red 3 7 7
Black 4 7 6 
X3min <- tbl3 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X3min
## X-squared 
## 0.2197802

email 서비스

isp <- class_roll$email %>%
    strsplit("@", fixed = TRUE) %>%
    sapply("[", 2) %>%
    strsplit("[.]", fixed = FALSE) %>%
    sapply("[", 1)
tbl4 <- isp %>%
    `%in%`(c("naver", "gmail")) %>%
    `!` %>%
    ifelse("기타서비스", isp) %>%
    factor(levels = c("naver", "gmail", "기타서비스"),
           labels = c("네이버", "구글", "기타서비스")) %>%
    table(class_roll$group, .) 
tbl4 %>%
  pander
  네이버 구글 기타서비스
Red 9 6 2
Black 9 6 2 
X4min <- tbl4 %>%
    chisq.test(simulate.p.value = TRUE) %>%
    `[[`(1) 
X4min
## X-squared 
##         0

성별

tbl5 <- class_roll$gender %>%
    table(class_roll$group, .) 
tbl5 %>%
  pander
  f m
Red 8 9
Black 9 8 
X5min <- tbl5 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1) 
X5min
## X-squared 
## 0.1176471

성씨 분포

f_name <- class_roll$name %>%
  substring(first = 1, last = 1) 
tbl6 <- f_name %>%
  `%in%`(c("김", "이")) %>%
  ifelse(f_name, "기타") %>%
  factor(levels = c("김", "이", "기타")) %>%
  table(class_roll$group, .) 
tbl6 %>%
  pander
  김 이 기타
Red 3 2 12
Black 3 3 11 
X6min <- tbl6 %>%
  chisq.test(simulate.p.value = TRUE) %>%
  `[[`(1)
X6min
## X-squared 
## 0.2434783

Sum of Chi_Squares

Xsum_min <- X2min + X3min + X4min + X5min + X6min
Xsum_min
## X-squared 
## 0.7002038