A. Data Structure and Diemnsions
[1] 67946 1122[1] 67946 14Classes 'data.table' and 'data.frame': 67946 obs. of 14 variables:
$ cntryid : Factor w/ 80 levels "8","31","32",..: 20 20 20 20 20 20 20 20 20 20 ...
$ cnt : Factor w/ 80 levels "ALB","ARE","ARG",..: 20 20 20 20 20 20 20 20 20 20 ...
$ cntschid : num 21400001 21400001 21400001 21400001 21400001 ...
$ cntstuid : num 21400089 21400095 21400268 21400581 21400680 ...
$ oecd : Factor w/ 2 levels "No","Yes": 1 1 1 1 1 1 1 1 1 1 ...
$ icthome : num 6 4 2 0 4 2 1 1 2 11 ...
$ ictsch : num 6 2 7 1 3 2 1 2 4 10 ...
$ grade : num -1 -1 -2 -1 0 0 0 1 -1 -1 ...
$ paredint : num 16 14.5 12 9 12 6 9 16 12 16 ...
$ wealth : num -1.222 -2.089 -4.318 NA -0.869 ...
$ reading_score : num 272 345 255 249 343 ...
$ math_score : num 298 317 246 294 320 ...
$ science_score : num 276 330 260 291 304 ...
$ student_gender: Factor w/ 2 levels "Female","Male": 2 2 1 1 1 2 2 1 2 2 ...
- attr(*, ".internal.selfref")=<externalptr> B. Variable Descriptions
- cntryid: A categorical variable representing the country ID, where each unique value corresponds to a different country in the dataset.
- cnt: A categorical variable representing the country code as a short identifier, such as “USA” for the United States.
- cntschid: A numeric variable representing the unique international school ID, which identifies each school within a country.
- cntstuid: A numeric variable representing the unique international student ID, which identifies each student within the dataset.
- oecd: A categorical variable indicating whether the country is a member of the Organisation for Economic Co-operation and Development (OECD). It has two levels: “Yes” (OECD member) and “No” (non-OECD member).
- icthome: A numeric variable representing the availability of Information and Communication Technology (ICT) at the student’s home. Higher values indicate greater availability.
- ictsch: A numeric variable representing the availability of Information and Communication Technology (ICT) at the student’s school. Higher values indicate greater availability.
- grade: A numeric variable indicating the student’s grade level compared to the modal grade in their country. Negative values indicate below-modal grades, zero indicates the modal grade, and positive values indicate above-modal grades.
- paredint: A numeric variable representing the highest level of parental education, measured in international years of schooling.
- wealth: A numeric variable representing the family’s wealth index, measured using a weighted likelihood estimate (WLE). Higher values indicate greater wealth.
- student_gender: A categorical variable representing the student’s gender, coded as “Female” or “Male”. It also includes categories for cases like “Valid Skip”, “Not Applicable”, “Invalid”, and “No Response”.
- reading_score: A numeric variable representing the student’s weighted average score in reading, calculated from multiple plausible values.
- math_score: A numeric variable representing the student’s weighted average score in mathematics, calculated from multiple plausible values.
- science_score: A numeric variable representing the student’s weighted average score in science, calculated from multiple plausible values.
C. Missing Value Analysis
The missing value analysis shows that the ictsch (ICT availability at school) and icthome (ICT availability at home) variables have substantial missing data, with 22.83% and 21.77% of values missing, respectively, which could significantly impact the reliability of analyses involving these variables. The paredint (highest parental education) variable has 4.17% missing data, while the wealth (family wealth index) variable has 2.44% missing, both of which are less concerning but still noteworthy.
D. Descriptive Analyiss of Key Variables
i. Summary Statistics for Students’ Reading Scores, Math Scores, Science Scores, Parental Education, and Wealth
# A tibble: 5 × 8
Variable mean median sd min max skewness kurtosis
<chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 reading 456. 454. 113. 147. 810. 0.0405 -0.739
2 math 461. 463. 112. 100. 825. 0.0122 -0.726
3 science 458. 456. 108. 114. 843. 0.0660 -0.733
4 paredint 13.0 14.5 3.30 3 16 -1.22 1.13
5 wealth -0.637 -0.535 1.33 -7.33 4.63 -0.444 1.81 # A tibble: 50 × 7
cnt Variable mean median sd min max
<fct> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
1 DOM reading 345. 338. 78.4 169. 647.
2 DOM math 328. 323. 64.6 100. 594.
3 DOM science 338. 329. 64.9 177. 603.
4 DOM paredint 12.9 12 3.32 3 16
5 DOM wealth -1.69 -1.72 1.20 -6.81 4.13
6 GBR reading 500. 503. 94.6 185. 795.
7 GBR math 495. 496. 81.9 182. 754.
8 GBR science 497. 498. 89.3 205. 780.
9 GBR paredint 14.1 14.5 2.16 3 16
10 GBR wealth 0.444 0.397 0.891 -6.79 4.11
11 HKG reading 527. 537. 93.7 195. 783.
12 HKG math 554. 560. 85.0 237. 792.
13 HKG science 519. 525. 79.0 247. 759.
14 HKG paredint 12.2 12 2.79 3 16
15 HKG wealth -0.467 -0.455 0.831 -5.27 4.04
16 KOR reading 516. 525. 97.9 147. 785.
17 KOR math 528. 532. 93.2 182. 825.
18 KOR science 520. 527. 92.0 184. 843.
19 KOR paredint 14.8 16 1.91 6 16
20 KOR wealth -0.442 -0.448 0.562 -2.87 4.02
21 MAC reading 525. 532. 88.4 192. 749.
22 MAC math 558. 561. 72.4 274. 757.
23 MAC science 544. 548. 77.3 220. 757.
24 MAC paredint 12.1 12 3.11 3 16
25 MAC wealth -0.542 -0.585 0.856 -6.88 3.11
26 MAR reading 358. 353. 71.2 162. 604.
27 MAR math 367. 360. 67.9 162. 625.
28 MAR science 375. 369. 61.5 200. 605.
29 MAR paredint 9.42 9 4.82 3 16
30 MAR wealth -1.90 -1.88 1.38 -7.33 4.63
31 PAN reading 378. 373. 83.3 156. 656.
32 PAN math 355. 351. 70.3 146. 611.
33 PAN science 366. 360. 80.4 114. 656.
34 PAN paredint 12.0 12 3.86 3 16
35 PAN wealth -1.55 -1.50 1.58 -6.93 4.34
36 QAZ reading 389. 389. 70.4 178. 671.
37 QAZ math 420. 418. 80.5 149. 704.
38 QAZ science 398. 395. 67.4 200. 655.
39 QAZ paredint 13.4 14.5 2.17 3 16
40 QAZ wealth -1.16 -1.19 1.02 -6.84 4.14
41 TAP reading 498. 505. 99.0 150. 772.
42 TAP math 527. 533. 93.9 201. 780.
43 TAP science 511. 516. 94.9 124. 777.
44 TAP paredint 13.5 14.5 2.27 3 16
45 TAP wealth -0.506 -0.540 0.893 -6.99 4.42
46 USA reading 501. 505. 105. 157. 810.
47 USA math 473. 474. 86.5 197. 750.
48 USA science 498. 499. 94.6 195. 795.
49 USA paredint 14.0 16 2.58 3 16
50 USA wealth 0.411 0.351 1.04 -6.85 4.26ii. Distribution of Students by Country, Country Code, OECD Membership
# A tibble: 10 × 3
cntryid cnt Observations
<fct> <fct> <int>
1 31 QAZ 6827
2 158 TAP 7243
3 214 DOM 5674
4 344 HKG 6037
5 410 KOR 6650
6 446 MAC 3775
7 504 MAR 6814
8 591 PAN 6270
9 826 GBR 13818
10 840 USA 4838[1] "Number of unique countries: 10"[1] "The OECD variable shows that there are 42640 observations from non-OECD countries and 25306 from OECD countries."[1] "The dataset includes 33591 female students and 34355 male students."iii. Cross-tabulation of Variables
Female Male
DOM 2890 2784
GBR 6996 6822
HKG 2955 3082
KOR 3191 3459
MAC 1862 1913
MAR 3262 3552
PAN 3173 3097
QAZ 3262 3565
TAP 3624 3619
USA 2376 2462iv. Average Scores by Subjects for Top 6 and Bottom 4 Countries
v. Calculate Mean Scores by Group and Gender
vi. Calcualte Mean Scores by Group, Gender, and Wealth (Quartiles)
vii. Scores by Group, Gender, and Parental Education
