막대그래프

막대그래프로 답안 분포를 시각적으로 살핀다. 차후 나오는 정답률과 함께 어느 문항에서 어느 답안을 많이 고르는지 파악하는 데 활용한다.

Data

Counts
Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20 Q21 Q22 Q23 Q24 Q25
4 7 669 6 13 44 812 42 75 10 788 18 16 24 36 742 171 20 802 25 19 36 797 58 19
6 11 57 5 766 53 10 31 445 783 27 227 772 29 75 45 39 778 12 54 731 123 23 33 721
830 42 13 820 56 128 12 46 311 36 12 584 22 13 630 34 25 23 12 734 35 35 15 733 74
2 782 103 11 7 617 8 723 11 13 15 13 32 776 101 21 607 21 16 29 57 648 7 18 28
%
Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20 Q21 Q22 Q23 Q24 Q25
0 1 79 1 2 5 96 5 9 1 94 2 2 3 4 88 20 2 95 3 2 4 95 7 2
1 1 7 1 91 6 1 4 53 93 3 27 92 3 9 5 5 92 1 6 87 15 3 4 86
99 5 2 97 7 15 1 5 37 4 1 69 3 2 75 4 3 3 1 87 4 4 2 87 9
0 93 12 1 1 73 1 86 1 2 2 2 4 92 12 2 72 2 2 3 7 77 1 2 3

ggplot

문해력 점수 계산

정답과 대조하여 R(Right)/W(Wrong) 표시

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20 Q21 Q22 Q23 Q24 Q25
R R R R R W R R R R R R R R W R W R R R R R R R R
R R R R R R R R R R R R R R R R W R R R R R R R W
R R R R R R R R W R R R R R R R R R R R W R R R R
R R R R R R R R W R R W R R R R R R R R R R R R R
R R R R R R R R W R R W R R R R R R R R R R R R R
R R R R R R R R W R R R R R R R R R R R R R R R R

학생별 점수 산출

88, 92, 92, 92, 92, 96, 32, 88, 100, 88, 92, 92, 96, 96, 96, 56, 84, 88, 92, 84, 84, 96, 80, 96, 96, 92, 84, 76, 52, 88, 92, 96, 88, 92, 88, 84, 84, 92, 100, 80, 100, 100, 88, 96, 96, 76, 80, 88, 88, 96, 92, 100, 40, 72, 96, 88, 96, 92, 80, 92, 96, 92, 96, 32, 40, 96, 76, 100, 96, 96, 84, 96, 92, 100, 100, 92, 100, 96, 84, 96, 96, 80, 52, 84, 92, 96, 96, 92, 92, 100, 96, 88, 88, 96, 80, 96, 92, 88, 92, 84, 100, 100, 96, 88, 72, 92, 100, 88, 92, 96, 84, 96, 96, 88, 80, 84, 76, 60, 96, 88, 84, 92, 76, 88, 92, 96, 96, 88, 84, 96, 96, 92, 96, 88, 96, 84, 96, 84, 88, 76, 88, 16, 88, 96, 96, 88, 92, 84, 96, 88, 40, 96, 100, 100, 92, 88, 96, 48, 76, 96, 92, 96, 84, 96, 92, 100, 92, 100, 100, 96, 72, 84, 92, 80, 80, 88, 96, 96, 96, 72, 96, 80, 84, 64, 92, 88, 100, 92, 88, 92, 92, 48, 100, 96, 72, 20, 88, 88, 96, 96, 88, 88, 92, 72, 80, 92, 76, 68, 92, 96, 92, 96, 88, 96, 84, 24, 28, 60, 56, 64, 84, 96, 92, 100, 88, 100, 96, 96, 92, 96, 96, 84, 88, 96, 96, 84, 88, 20, 92, 96, 68, 100, 88, 80, 92, 80, 96, 92, 100, 92, 92, 72, 80, 88, 88, 96, 96, 100, 92, 92, 92, 72, 76, 96, 84, 92, 84, 88, 88, 56, 88, 92, 84, 92, 92, 80, 64, 100, 44, 92, 84, 100, 92, 80, 96, 88, 88, 96, 84, 96, 100, 100, 96, 96, 92, 84, 88, 88, 92, 96, 92, 96, 100, 84, 100, 88, 92, 88, 56, 84, 92, 92, 92, 92, 60, 76, 88, 96, 96, 96, 92, 72, 88, 92, 92, 84, 80, 88, 96, 96, 92, 92, 20, 96, 88, 96, 84, 92, 88, 88, 88, 68, 48, 84, 80, 96, 88, 92, 88, 84, 24, 84, 60, 88, 88, 48, 28, 76, 56, 76, 88, 84, 84, 100, 96, 84, 84, 92, 84, 92, 80, 92, 92, 92, 100, 72, 64, 20, 52, 92, 100, 80, 88, 44, 92, 84, 100, 96, 76, 96, 88, 96, 100, 96, 52, 84, 96, 100, 92, 84, 88, 96, 88, 88, 96, 100, 92, 88, 80, 96, 88, 88, 96, 88, 92, 40, 96, 76, 92, 80, 84, 96, 96, 92, 92, 100, 76, 92, 92, 84, 88, 100, 96, 96, 96, 88, 28, 92, 92, 80, 100, 96, 100, 96, 92, 100, 84, 84, 76, 84, 84, 88, 92, 84, 68, 100, 36, 96, 96, 76, 76, 56, 92, 96, 76, 24, 72, 84, 92, 96, 80, 100, 76, 92, 80, 92, 60, 88, 76, 96, 24, 88, 80, 40, 92, 96, 96, 68, 96, 92, 96, 80, 88, 80, 88, 96, 92, 88, 92, 92, 88, 84, 100, 88, 84, 92, 84, 92, 96, 76, 92, 92, 100, 96, 96, 96, 92, 72, 84, 92, 84, 92, 76, 100, 76, 60, 88, 96, 96, 84, 96, 76, 96, 92, 88, 96, 96, 84, 100, 80, 40, 92, 80, 24, 92, 60, 92, 76, 84, 88, 84, 52, 88, 96, 96, 84, 92, 80, 92, 100, 88, 96, 92, 48, 88, 84, 80, 96, 80, 96, 92, 100, 88, 96, 44, 92, 72, 84, 96, 92, 92, 96, 84, 76, 88, 84, 92, 92, 88, 92, 96, 84, 24, 92, 80, 92, 92, 92, 56, 92, 76, 88, 92, 88, 88, 76, 96, 92, 44, 60, 96, 64, 92, 96, 76, 84, 100, 76, 76, 92, 96, 84, 88, 92, 96, 80, 92, 84, 92, 88, 92, 72, 96, 88, 88, 96, 72, 88, 84, 84, 88, 88, 92, 96, 88, 88, 92, 96, 48, 88, 92, 96, 80, 96, 92, 100, 92, 100, 32, 100, 100, 92, 96, 88, 92, 92, 80, 80, 92, 88, 96, 96, 96, 92, 28, 88, 100, 84, 44, 92, 72, 92, 88, 96, 88, 84, 80, 88, 72, 100, 44, 76, 96, 20, 84, 84, 88, 80, 84, 28, 92, 84, 84, 92, 72, 96, 92, 60, 96, 88, 84, 88, 88, 96, 84, 76, 36, 100, 84, 84, 96, 100, 76, 80, 80, 92, 88, 96, 92, 88, 92, 84, 84, 96, 84, 88, 92, 72, 92, 28, 76, 64, 68, 88, 92, 60, 80, 76, 80, 68, 88, 100, 76, 100, 100, 100, 92, 80, 84, 84, 84, 96, 92, 76, 96, 92, 100, 88, 92, 92, 80, 48, 84, 56, 80, 92, 96, 96, 96, 48, 100, 92, 96, 72, 64, 76, 84, 64, 92, 92, 80, 92, 80, 84, 88, 100, 96, 96, 96, 92, 76, 88, 88, 80, 96, 40, 100, 96, 92, 68, 96, 92, 96, 92, 96, 92, 76, 88, 92, 96, 28, 100, 92, 92, 100, 100, 96, 96, 72, 92, 100, 92, 84, 48, 84, 88, 64, 20, 100, 88, 92 and 88

Red and Black 비교

  • Red:

    Min. 1st Qu. Median Mean 3rd Qu. Max.
    20 80 88 85.2 96 100

  • Black:

    Min. 1st Qu. Median Mean 3rd Qu. Max.
    16 84 92 85.4 96 100 
## 
##   The decimal point is 1 digit(s) to the right of the |
## 
##    1 | 6
##    2 | 0000004444448888888
##    3 | 22266
##    4 | 0000000444444888888888
##    5 | 2222266666666
##    6 | 000000000044444444488888888
##    7 | 222222222222222222222666666666666666666666666666666666666666666
##    8 | 00000000000000000000000000000000000000000000000000444444444444444444+191
##    9 | 22222222222222222222222222222222222222222222222222222222222222222222+268
##   10 | 00000000000000000000000000000000000000000000000000000000000000000000
  • Red
score %>%
  `[`(literacy$group == "Red") %>%
  stem(scale = 0.5)
## 
##   The decimal point is 1 digit(s) to the right of the |
## 
##    2 | 04488888
##    3 | 26
##    4 | 004448888
##    5 | 2266666
##    6 | 000000044448888
##    7 | 22222222266666666666666666666666666
##    8 | 00000000000000000000000000000004444444444444444444444444444444444444+65
##    9 | 22222222222222222222222222222222222222222222222222222222222222222222+87
##   10 | 000000000000000000000000000000
  • Black
score %>%
  `[`(literacy$group == "Black") %>%
  stem(scale = 0.5)
## 
##   The decimal point is 1 digit(s) to the right of the |
## 
##    1 | 6
##    2 | 00000444488
##    3 | 226
##    4 | 0000044488888
##    5 | 222666
##    6 | 000444448888
##    7 | 2222222222226666666666666666
##    8 | 00000000000000000004444444444444444444444444444444444444444444888888+46
##    9 | 22222222222222222222222222222222222222222222222222222222222222222222+101
##   10 | 0000000000000000000000000000000000000000000

Box Plots

QQ plot

ECDF plot

t test

Red 와 Black으로부터 관찰된 점수들의 평균에 대하여 t test를 적용하였더니 통계적으로 유의한 차이가 관찰되지 않음.

Welch Two Sample t-test: score by .$group
Test statistic df P value Alternative hypothesis mean in group Red mean in group Black
-0.2125 825.6 0.8318 two.sided 85.19 85.42

문해력 등급 판정

문해력 등급 분포
I II III IV 계
13 34 61 734 842
문해력 등급 분포(%)
I II III IV 계
1.54 4.04 7.24 87.17 99.99
그룹별 문해력 등급 분포
I II III IV 계
Red 3 16 31 368 418
Black 10 18 30 366 424
계 13 34 61 734 842
Pearson’s Chi-squared test with simulated p-value (based on 2000 replicates): .
Test statistic df P value
0.1383 NA 0.953

문항 유형별 점수 분석

유형별 정답률

유형 정답률(%)
문1 사실적 98.6
문2 사실적 92.9
문3 비판적 79.5
문4 사실적 97.4
문5 추론적 91.0
문6 추론적 73.3
문7 추론적 96.4
문8 사실적 85.9
문9 추론적 36.9
문10 추론적 93.0
문11 사실적 93.6
문12 사실적 69.4
문13 사실적 91.7
문14 추론적 92.2
문15 사실적 74.8
문16 사실적 88.1
문17 추론적 72.1
문18 비판적 92.4
문19 사실적 95.2
문20 사실적 87.2
문21 사실적 86.8
문22 비판적 77.0
문23 추론적 94.7
문24 사실적 87.1
문25 추론적 85.6

어려운 문제?

정답률 80% 이하

문3 문6 문9 문12 문15 문17 문22
정답률 79.5 73.3 36.9 69.4 74.8 72.1 77

정답률 70% 이하

문9 문12
정답률 36.9 69.4

정답률 60% 이하

문9
정답률 36.9

정답률 50% 이하

문9
정답률 36.9

정답률이 낮은 문제들

문6.

문9.

문12.

문15.

문17.

문22.