응답 집계

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 8 819 8 16 92 962 46 89 20 937 12 12 24 42 878 236 28 946 37 33 55 944 89 39
6 18 49 10 903 49 16 34 534 920 22 285 902 44 85 50 50 917 21 69 855 125 32 45 825
992 43 29 975 72 167 14 71 372 42 26 682 42 33 750 49 29 31 19 866 40 56 13 844 105
1 934 106 10 12 695 11 852 8 21 18 24 47 902 126 26 688 27 17 31 75 767 14 25 34
%
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 82 1 2 9 96 5 9 2 93 1 1 2 4 88 24 3 94 4 3 5 94 9 4
1 2 5 1 90 5 2 3 53 92 2 28 90 4 8 5 5 91 2 7 85 12 3 4 82
99 4 3 97 7 17 1 7 37 4 3 68 4 3 75 5 3 3 2 86 4 6 1 84 10
0 93 11 1 1 69 1 85 1 2 2 2 5 90 13 3 69 3 2 3 7 76 1 2 3

막대그래프

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

barplot

## quartz_off_screen 
##                 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 R R R W R R W R R W R R R R R R R R R R
R R R R R R R W R W R W W W R W W R W W W W R R W
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
R R R R R W 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 R 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 R R R R R R R R R

학생별 점수 산출

88, 52, 92, 88, 100, 96, 84, 100, 92, 88, 96, 92, 92, 88, 92, 88, 88, 100, 100, 96, 84, 92, 92, 96, 36, 88, 96, 72, 80, 96, 40, 80, 84, 88, 96, 92, 96, 92, 88, 100, 100, 96, 96, 100, 84, 96, 100, 100, 84, 88, 88, 96, 84, 76, 88, 84, 88, 96, 80, 96, 80, 100, 92, 76, 88, 84, 92, 84, 96, 92, 100, 96, 80, 40, 68, 88, 92, 88, 88, 92, 96, 84, 80, 100, 100, 96, 88, 100, 92, 100, 92, 84, 92, 96, 68, 96, 96, 88, 68, 88, 88, 88, 84, 80, 96, 88, 92, 60, 96, 100, 64, 96, 92, 92, 68, 92, 84, 80, 100, 92, 96, 92, 96, 100, 44, 80, 92, 92, 60, 84, 92, 52, 100, 84, 96, 72, 88, 72, 88, 80, 88, 84, 88, 100, 100, 96, 88, 88, 88, 84, 88, 12, 48, 88, 100, 72, 76, 96, 96, 92, 48, 88, 88, 80, 80, 88, 80, 76, 88, 84, 76, 92, 100, 92, 64, 100, 96, 88, 84, 48, 88, 72, 92, 92, 96, 88, 88, 96, 72, 84, 96, 92, 84, 68, 92, 88, 32, 92, 96, 96, 84, 96, 88, 88, 96, 88, 100, 96, 96, 88, 96, 84, 56, 92, 96, 100, 100, 64, 88, 80, 88, 96, 92, 96, 36, 88, 80, 96, 100, 88, 92, 84, 52, 96, 56, 100, 96, 92, 88, 96, 80, 44, 88, 92, 80, 88, 88, 44, 96, 64, 84, 60, 52, 92, 84, 72, 100, 80, 72, 88, 68, 100, 92, 88, 92, 92, 88, 96, 100, 96, 96, 88, 84, 96, 84, 100, 88, 96, 88, 88, 88, 76, 92, 84, 96, 92, 100, 44, 92, 96, 96, 92, 96, 96, 88, 80, 96, 88, 92, 100, 80, 92, 80, 100, 92, 100, 88, 92, 92, 96, 100, 80, 88, 76, 88, 72, 92, 40, 44, 40, 40, 24, 68, 92, 88, 96, 96, 84, 92, 92, 88, 92, 76, 92, 80, 100, 96, 96, 92, 100, 72, 88, 72, 76, 84, 96, 96, 32, 76, 84, 92, 92, 96, 80, 84, 96, 88, 88, 88, 96, 84, 88, 80, 92, 84, 64, 88, 72, 72, 92, 100, 96, 92, 84, 92, 96, 88, 84, 72, 92, 80, 88, 92, 92, 44, 88, 84, 68, 96, 96, 96, 96, 64, 92, 92, 92, 96, 96, 92, 84, 84, 88, 84, 88, 88, 72, 80, 88, 84, 92, 60, 84, 92, 100, 56, 80, 100, 92, 64, 80, 88, 48, 72, 96, 80, 92, 92, 96, 60, 80, 92, 72, 88, 88, 92, 84, 96, 92, 96, 88, 88, 88, 92, 92, 36, 80, 92, 96, 24, 84, 84, 92, 92, 96, 76, 56, 92, 88, 76, 88, 36, 92, 80, 84, 80, 84, 72, 100, 92, 96, 88, 88, 88, 92, 92, 96, 84, 88, 96, 84, 88, 84, 100, 88, 96, 96, 60, 96, 92, 88, 68, 100, 92, 76, 92, 92, 32, 88, 88, 92, 52, 100, 40, 100, 92, 88, 84, 80, 92, 72, 100, 28, 92, 76, 96, 92, 28, 100, 96, 96, 100, 52, 28, 88, 88, 76, 96, 28, 92, 80, 84, 88, 92, 100, 96, 84, 92, 96, 44, 40, 28, 84, 96, 76, 84, 100, 76, 84, 60, 24, 88, 76, 92, 84, 92, 52, 92, 96, 56, 96, 88, 100, 92, 80, 92, 88, 84, 92, 88, 72, 96, 100, 92, 72, 84, 76, 88, 88, 48, 60, 96, 92, 88, 92, 84, 92, 84, 96, 88, 76, 80, 100, 80, 80, 84, 60, 84, 84, 84, 64, 92, 80, 68, 96, 100, 84, 92, 88, 88, 96, 92, 92, 96, 96, 88, 88, 92, 100, 68, 68, 88, 72, 80, 100, 88, 100, 92, 96, 100, 72, 84, 88, 88, 92, 96, 84, 88, 84, 92, 72, 96, 88, 84, 92, 80, 92, 96, 76, 80, 92, 96, 88, 96, 80, 88, 100, 84, 88, 88, 36, 84, 80, 96, 84, 96, 84, 80, 76, 60, 88, 56, 80, 100, 92, 84, 96, 80, 80, 56, 100, 84, 92, 76, 96, 96, 100, 80, 100, 92, 76, 96, 80, 96, 80, 32, 84, 64, 80, 96, 72, 84, 84, 96, 80, 52, 96, 72, 92, 88, 88, 84, 84, 92, 88, 92, 76, 88, 68, 96, 100, 84, 40, 88, 64, 88, 96, 68, 88, 64, 80, 96, 72, 52, 92, 96, 76, 88, 100, 92, 96, 24, 96, 28, 84, 84, 92, 92, 92, 72, 88, 96, 80, 52, 72, 92, 76, 100, 88, 68, 84, 88, 100, 88, 84, 96, 84, 100, 92, 84, 68, 84, 84, 32, 84, 92, 96, 92, 84, 84, 84, 84, 88, 96, 56, 84, 84, 76, 88, 88, 84, 96, 84, 96, 52, 52, 56, 88, 52, 64, 84, 76, 84, 72, 92, 40, 92, 32, 96, 84, 68, 48, 84, 76, 96, 88, 96, 68, 92, 84, 84, 92, 80, 84, 84, 100, 96, 88, 92, 84, 88, 88, 80, 80, 76, 48, 84, 56, 56, 88, 92, 96, 96, 92, 28, 84, 88, 76, 88, 88, 28, 92, 84, 80, 84, 80, 96, 32, 96, 60, 100, 96, 100, 84, 92, 92, 52, 92, 96, 72, 92, 96, 32, 52, 32, 84, 28, 68, 84, 88, 92, 76, 84, 92, 88, 100, 96, 96, 92, 32, 64, 92, 96, 96, 84, 96, 100, 96, 96, 96, 96, 96, 96, 96, 100, 92, 88, 92, 100, 92, 92, 80, 92, 92, 36, 96, 88, 100, 92, 72, 92, 92, 84, 84, 96, 80, 92, 100, 76, 96, 88, 72, 100, 100, 96, 88, 96, 92, 84, 100, 88, 92, 100, 88, 84, 88, 100, 96, 40, 40, 92, 96, 92, 96, 100, 76, 96, 100, 92, 68, 88, 96, 96, 88, 96, 92, 92, 72, 88, 100, 88, 92, 88, 92, 96, 96, 92, 96, 100, 92, 68, 84, 84, 64, 92, 92, 80, 92, 48, 92, 84, 96, 88, 64, 88, 100, 92, 76, 84, 100, 76, 76, 40 and 88

Red and Black 비교

  • Red:

    Min. 1st Qu. Median Mean 3rd Qu. Max.
    24 84 88 85.6 96 100

  • Black:

    Min. 1st Qu. Median Mean 3rd Qu. Max.
    12 80 88 83 92 100 
## 
##   The decimal point is 1 digit(s) to the right of the |
## 
##    1 | 2
##    2 | 4444888888888
##    3 | 2222222222666666
##    4 | 000000000000444444488888888
##    5 | 22222222222222266666666666
##    6 | 00000000000444444444444444888888888888888888888
##    7 | 22222222222222222222222222222222226666666666666666666666666666666666
##    8 | 00000000000000000000000000000000000000000000000000000000000000000444+277
##    9 | 22222222222222222222222222222222222222222222222222222222222222222222+273
##   10 | 00000000000000000000000000000000000000000000000000000000000000000000+11
  • Red
score %>%
  `[`(literacy$group == "Red") %>%
  stem(scale = 0.5)
## 
##   The decimal point is 1 digit(s) to the right of the |
## 
##    2 | 4888
##    3 | 222666
##    4 | 0000488888
##    5 | 22222226666
##    6 | 00044444448888888888
##    7 | 222222222222222666666666666666666666
##    8 | 00000000000000000000000000000000000044444444444444444444444444444444+98
##    9 | 22222222222222222222222222222222222222222222222222222222222222222222+104
##   10 | 000000000000000000000000000000000000000000000
  • Black
score %>%
  `[`(literacy$group == "Black") %>%
  stem(scale = 0.5)
## 
##   The decimal point is 1 digit(s) to the right of the |
## 
##    1 | 2
##    2 | 444888888
##    3 | 2222222666
##    4 | 00000000444444888
##    5 | 222222226666666
##    6 | 000000004444444488888888888
##    7 | 222222222222222222266666666666666666
##    8 | 00000000000000000000000000000444444444444444444444444444444444444444+99
##    9 | 22222222222222222222222222222222222222222222222222222222222222222222+89
##   10 | 0000000000000000000000000000000000000000000000

Box Plots

QQ plot

ECDF plot

t test

Red 와 Black으로부터 관찰된 점수들의 평균에 대하여 t test를 적용하였더니 통계적으로 매우매우 유의한 차이가 관찰되었습니다. 뜻밖이지만 이런 일도 관찰될 수 있습니다. 매우 드문 확률의 사건이 발생한 것입니다.

Welch Two Sample t-test: score by .$group
Test statistic df P value Alternative hypothesis mean in group Red mean in group Black
2.652 973.3 0.008124 * * two.sided 85.58 82.97

문해력 등급 판정

카이제곱테스트로 Red와 Black에 들어간 등급별 인원수가 얼마나 닮았는지를 살펴보았지만 t-test에서와 마찬가지로 통계적으로 유의한 차이가 관찰되었습니다.

문해력 등급 분포
I II III IV 계
5 52 107 839 1003
문해력 등급 분포(%)
I II III IV 계
0.5 5.18 10.67 83.65 100
그룹별 문해력 등급 분포
I II III IV 계
Red 1 19 46 428 494
Black 4 33 61 411 509
계 5 52 107 839 1003
Pearson’s Chi-squared test with simulated p-value (based on 2000 replicates): .
Test statistic df P value
6.073 NA 0.04748 *

문항 유형별 점수 분석

유형별 정답률

유형 정답률(%)
문1 사실적 98.9
문2 사실적 93.1
문3 비판적 81.7
문4 사실적 97.2
문5 추론적 90.0
문6 추론적 69.3
문7 추론적 95.9
문8 사실적 84.9
문9 추론적 37.1
문10 추론적 91.7
문11 사실적 93.4
문12 사실적 68.0
문13 사실적 89.9
문14 추론적 89.9
문15 사실적 74.8
문16 사실적 87.5
문17 추론적 68.6
문18 비판적 91.4
문19 사실적 94.3
문20 사실적 86.3
문21 사실적 85.2
문22 비판적 76.5
문23 추론적 94.1
문24 사실적 84.1
문25 추론적 82.3

어려운 문제?

정답률 80% 이하

문6 문9 문12 문15 문17 문22
정답률 69.3 37.1 68 74.8 68.6 76.5

정답률 70% 이하

문6 문9 문12 문17
정답률 69.3 37.1 68 68.6

정답률 60% 이하

문9
정답률 37.1

정답률 50% 이하

문9
정답률 37.1

정답률이 낮은 문제들

문6.

문9.

문12.

문15.

문17.

문22.