Magnitude Comparison - 2025

1. Probe description

The Magnitude Comparison probe assesses students’ ability to identify the larger of two numbers.

In 2025 there are two main forms used in the screening:

  • Magnitude Comparison 0-20 (MC0-20) - Foundation
  • Magnitude Comparison 0-100 (MC0-100) - Year 1

Both forms are administered at BOY (Term 1), MOY (Term 3), and EOY (Term 4).

Examples

Download Foundation student data (wide format)

Download Year 1 student data (wide format)

2. Overview of test results

Term Test name Test ID Students Median items attempted Median accuracy (%)* Median correct / min
1 Magnitude Comparison 0-100 MC0-100_2025 2424 16/60 92.9 17.14
1 Magnitude Comparison 0 - 20 MC0-20_2025 2486 16/60 92.6 17.31
3 Magnitude Comparison 0-100 MC0-100_2025 1496 19/60 95.5 22.35
3 Magnitude Comparison 0 - 20 MC0-20_2025 1433 19/60 95.7 22.17
4 Magnitude Comparison 0-100 MC0-100_2025 1067 21/60 96.3 25.20
4 Magnitude Comparison 0 - 20 MC0-20_2025 1092 22/60 96.3 25.20
* Accuracy is calculated after removing non-attempted items.

3. Accuracy distribution

4. Response time distribution

Warning: Removed 500 rows containing non-finite outside the scale range
(`stat_ydensity()`).
Warning: Removed 500 rows containing non-finite outside the scale range
(`stat_boxplot()`).

5. Fluency distribution

Fluency distribution

Term Students 25th percentile Median 75th percentile
Term 1 2424 11.76 17.14 23.75
Term 3 1496 15.60 22.35 28.75
Term 4 1067 18.41 25.20 32.55

Bottom quartile vs rest

Term Group Students 25th percentile Median 75th percentile
Term 1 Bottom 25% 613 6.43 8.89 10.38
Term 1 Rest 1811 15.92 20.00 26.09
Term 3 Bottom 25% 376 8.57 11.75 13.85
Term 3 Rest 1120 20.82 25.53 31.30
Term 4 Bottom 25% 267 11.11 14.18 16.36
Term 4 Rest 800 23.61 28.72 35.22

Fluency distribution

Term Students 25th percentile Median 75th percentile
Term 1 2486 11.16 17.31 22.50
Term 3 1433 16.47 22.17 28.16
Term 4 1092 19.59 25.20 31.91

Bottom quartile vs rest

Term Group Students 25th percentile Median 75th percentile
Term 1 Bottom 25% 623 5.51 7.64 9.64
Term 1 Rest 1863 16.00 20.00 24.49
Term 3 Bottom 25% 365 8.73 12.24 15.00
Term 3 Rest 1068 20.82 24.78 30.61
Term 4 Bottom 25% 276 11.76 15.58 17.90
Term 4 Rest 816 23.75 28.28 34.29

6. Question type performance

This section shows performance grouped by different question characteristics.

Performance by Ratio

Question type labels:

  • ≥2:1 ratio - The larger number is at least twice the smaller number
  • <2:1 ratio - The larger number is less than twice the smaller number
Correct response time (sec)
Question type Avg items attempted No. response % Correct Median RT 95th RT
Term 1 – Magnitude Comparison 0-100 (MC0-100_2025)
<2:1 ratio 9.9/33 23835 88.1 2 6
≥2:1 ratio 7/27 16995 87.1 2 8
Term 3 – Magnitude Comparison 0-100 (MC0-100_2025)
<2:1 ratio 11.2/33 16737 92.2 2 5
≥2:1 ratio 8.2/27 12197 91.8 2 6
Term 4 – Magnitude Comparison 0-100 (MC0-100_2025)
<2:1 ratio 12/33 12856 94.1 2 5
≥2:1 ratio 9/27 9551 94.3 2 5
Term 1 – Magnitude Comparison 0 - 20 (MC0-20_2025)
<2:1 ratio 8.7/32 21446 82.3 2 7
≥2:1 ratio 7.6/28 18956 93.9 2 7
Term 3 – Magnitude Comparison 0 - 20 (MC0-20_2025)
<2:1 ratio 10.2/32 14589 89.1 2 5
≥2:1 ratio 9.1/28 13012 96.1 2 6
Term 4 – Magnitude Comparison 0 - 20 (MC0-20_2025)
<2:1 ratio 11.3/32 12203 90.5 2 5
≥2:1 ratio 10.2/28 11085 96.8 2 5

Does the size difference between numbers affect accuracy?

Larger ratios mean one number is much bigger than the other (e.g., 8 vs 2 = ratio of 4), making it easier to spot the larger number. Smaller ratios (e.g., 9 vs 8 = ratio of 1.13) are harder because the numbers are closer together.

`geom_smooth()` using formula = 'y ~ x'
Warning: Removed 25 rows containing missing values or values outside the scale range
(`geom_smooth()`).

Performance by Congruence

Question type labels:

  • C (Congruent) - Ones digit in larger number is equal to or larger than ones digit in smaller number
  • I (Incongruent) - Ones digit in larger number is smaller than ones digit in smaller number
Correct response time (sec)
Question type Avg items attempted No. response % Correct Median RT 95th RT
Term 1 – Magnitude Comparison 0-100 (MC0-100_2025)
C 7.7/28 18576 90.1 2 7
I 9.2/32 22254 85.7 2 7
Term 3 – Magnitude Comparison 0-100 (MC0-100_2025)
C 8.9/28 13231 93.7 2 6
I 10.5/32 15703 90.6 2 5
Term 4 – Magnitude Comparison 0-100 (MC0-100_2025)
C 9.7/28 10327 95.4 2 5
I 11.3/32 12080 93.1 2 5
Term 1 – Magnitude Comparison 0 - 20 (MC0-20_2025)
C 10.8/41 26887 86.4 2 8
I 5.5/19 13515 90.3 2 6
Term 3 – Magnitude Comparison 0 - 20 (MC0-20_2025)
C 12.7/41 18201 91.0 2 6
I 6.6/19 9400 95.1 2 4
Term 4 – Magnitude Comparison 0 - 20 (MC0-20_2025)
C 13.9/41 15195 92.0 2 5
I 7.5/19 8093 96.2 2 4

Performance by Decade

Question type labels:

  • Y (Same decade) - Compared numbers have the same tens digit
  • N (Different decade) - Compared numbers do not have the same tens digit
Correct response time (sec)
Question type Avg items attempted No. response % Correct Median RT 95th RT
Term 1 – Magnitude Comparison 0-100 (MC0-100_2025)
N 15.2/54 36880 87.3 2 7
Y 1.7/6 3950 91.3 2 5
Term 3 – Magnitude Comparison 0-100 (MC0-100_2025)
N 17.5/54 26127 91.9 2 5
Y 1.9/6 2807 93.7 2 5
Term 4 – Magnitude Comparison 0-100 (MC0-100_2025)
N 18.9/54 20216 94.1 2 5
Y 2.1/6 2191 94.5 2 5
Term 1 – Magnitude Comparison 0 - 20 (MC0-20_2025)
N 9.5/35 23653 92.3 2 6
Y 6.7/25 16749 81.3 3 9
Term 3 – Magnitude Comparison 0 - 20 (MC0-20_2025)
N 11.3/35 16129 95.7 2 4
Y 8/25 11472 87.7 2 7
Term 4 – Magnitude Comparison 0 - 20 (MC0-20_2025)
N 12.6/35 13671 96.7 2 4
Y 8.8/25 9617 88.8 2 6

7. Item statistics

NoteItem discrimination

Item discrimination (point-biserial) measures how well an item separates higher-ability from lower-ability students. Values above ~0.3 are typically “good”, below ~0.2 “weak”. In timed tests, late items can look artificially strong because only fast/able students reach them.

Download item stats (CSV)

Correct response time (sec)
Question No.  Question No. response % Correct Median RT 95th RT Item discrim.
Term 1
1 68 vs 14 2397 96.5 4.0 14.00 0.05
2 25 vs 52 2399 85.7 2.0 10.00 0.32
3 60 vs 83 2372 71.0 3.0 9.00 0.25
4 82 vs 33 2373 87.3 2.0 7.00 0.34
5 83 vs 92 2358 84.1 2.0 8.00 0.26
6 17 vs 13 2345 94.5 2.0 6.00 0.15
7 99 vs 66 2326 94.2 2.0 5.00 0.18
8 34 vs 62 2271 88.4 3.0 7.00 0.29
9 87 vs 72 2231 91.0 3.0 7.00 0.16
10 15 vs 41 2085 57.6 3.0 8.00 0.37
11 32 vs 10 2077 96.7 2.0 5.00 0.14
12 96 vs 39 1962 93.7 2.0 6.00 0.25
13 20 vs 30 1847 92.7 2.0 4.00 0.25
14 80 vs 19 1701 92.1 2.0 4.00 0.26
15 94 vs 56 1539 85.3 2.0 5.00 0.28
16 8 vs 7 1387 86.7 2.0 5.00 0.18
17 42 vs 92 1209 88.4 2.0 4.00 0.37
18 18 vs 26 1066 91.2 2.0 4.00 0.35
19 43 vs 33 920 87.3 2.0 4.00 0.36
20 26 vs 55 807 92.1 2.0 3.00 0.39
21 15 vs 48 698 93.3 2.0 3.00 0.41
22 38 vs 19 580 93.1 1.0 3.00 0.33
23 46 vs 56 471 90.9 2.0 3.00 0.42
24 39 vs 97 371 89.2 1.0 3.00 0.54
25 90 vs 86 279 84.2 2.0 3.00 0.34
26 55 vs 51 212 86.8 2.0 3.00 0.32
27 22 vs 74 160 90.6 1.0 3.00 0.56
28 89 vs 94 125 76.8 1.0 3.00 0.44
29 31 vs 21 88 81.8 1.0 3.00 0.47
30 51 vs 15 59 84.7 1.0 3.00 0.36
31 30 vs 87 38 81.6 1.0 2.50 0.45
32 44 vs 90 24 83.3 1.0 2.10 0.75
33 46 vs 76 15 80.0 1.0 2.45 NA
34 64 vs 25 8 87.5 1.0 2.00 NA
35 79 vs 83 6 50.0 1.0 3.70 NA
36 62 vs 67 5 60.0 2.0 3.80 NA
37 27 vs 58 4 50.0 3.0 3.90 NA
38 16 vs 9 3 100.0 1.0 2.80 NA
39 68 vs 70 2 50.0 2.0 2.00 NA
40 23 vs 82 1 100.0 2.0 2.00 NA
41 71 vs 21 1 100.0 2.0 2.00 NA
42 45 vs 8 1 100.0 2.0 2.00 NA
43 23 vs 33 1 100.0 2.0 2.00 NA
44 93 vs 28 1 100.0 2.0 2.00 NA
45 37 vs 42 1 100.0 3.0 3.00 NA
46 98 vs 91 1 100.0 3.0 3.00 NA
47 38 vs 13 1 100.0 3.0 3.00 NA
48 67 vs 82 1 100.0 2.0 2.00 NA
49 30 vs 40 1 100.0 3.0 3.00 NA
Term 3
1 68 vs 14 1475 98.9 3.0 14.00 0.13
2 25 vs 52 1483 92.0 2.0 7.00 0.36
3 60 vs 83 1453 80.4 2.0 7.00 0.24
4 82 vs 33 1475 92.7 2.0 6.00 0.32
5 83 vs 92 1473 89.5 2.0 6.00 0.26
6 17 vs 13 1468 95.7 2.0 5.00 0.18
7 99 vs 66 1463 96.7 2.0 4.00 0.16
8 34 vs 62 1435 93.7 2.0 5.80 0.32
9 87 vs 72 1418 93.4 2.0 6.00 0.20
10 15 vs 41 1367 65.7 3.0 6.15 0.36
11 32 vs 10 1374 97.4 2.0 4.15 0.18
12 96 vs 39 1337 95.5 2.0 5.00 0.25
13 20 vs 30 1288 94.6 2.0 4.00 0.28
14 80 vs 19 1254 96.2 2.0 4.00 0.24
15 94 vs 56 1177 90.4 2.0 5.00 0.18
16 8 vs 7 1094 91.0 2.0 5.00 0.16
17 42 vs 92 1007 93.2 2.0 4.00 0.29
18 18 vs 26 937 94.9 2.0 4.00 0.26
19 43 vs 33 854 92.6 2.0 4.00 0.34
20 26 vs 55 757 96.4 2.0 3.00 0.33
21 15 vs 48 664 96.8 2.0 3.00 0.35
22 38 vs 19 589 95.2 1.0 3.00 0.33
23 46 vs 56 488 95.3 2.0 3.00 0.41
24 39 vs 97 403 92.1 2.0 3.00 0.27
25 90 vs 86 326 88.3 2.0 3.00 0.24
26 55 vs 51 241 93.4 2.0 3.00 0.28
27 22 vs 74 188 95.2 1.0 2.00 0.46
28 89 vs 94 137 80.3 2.0 3.00 0.35
29 31 vs 21 96 89.6 1.0 3.00 0.27
30 51 vs 15 63 88.9 1.0 2.00 0.60
31 30 vs 87 40 92.5 1.0 2.00 0.62
32 44 vs 90 34 91.2 1.0 2.00 0.53
33 46 vs 76 30 93.3 1.0 2.00 0.49
34 64 vs 25 20 80.0 1.0 3.25 0.36
35 79 vs 83 12 50.0 1.5 2.75 NA
36 62 vs 67 4 100.0 1.5 2.00 NA
37 27 vs 58 4 100.0 1.0 1.00 NA
38 16 vs 9 4 75.0 1.0 1.00 NA
39 68 vs 70 2 100.0 1.5 1.95 NA
Term 4
1 68 vs 14 1058 99.1 3.0 11.00 0.11
2 25 vs 52 1052 94.2 2.0 5.00 0.29
3 60 vs 83 1042 84.4 2.0 7.00 0.28
4 82 vs 33 1049 95.5 2.0 5.00 0.28
5 83 vs 92 1045 92.9 2.0 6.00 0.19
6 17 vs 13 1053 96.7 2.0 5.00 0.16
7 99 vs 66 1045 97.7 2.0 4.00 0.15
8 34 vs 62 1045 95.5 2.0 5.00 0.24
9 87 vs 72 1035 95.6 2.0 5.00 0.19
10 15 vs 41 988 74.5 2.0 7.00 0.32
11 32 vs 10 1006 98.5 2.0 4.50 0.20
12 96 vs 39 997 96.0 2.0 4.00 0.16
13 20 vs 30 969 97.2 2.0 3.00 0.20
14 80 vs 19 943 96.4 2.0 4.00 0.26
15 94 vs 56 899 89.8 2.0 5.00 0.15
16 8 vs 7 861 92.2 2.0 5.00 0.14
17 42 vs 92 820 94.8 2.0 4.00 0.27
18 18 vs 26 759 97.5 2.0 4.00 0.19
19 43 vs 33 701 95.6 2.0 3.00 0.26
20 26 vs 55 644 96.3 1.0 3.00 0.27
21 15 vs 48 591 98.3 1.0 3.00 0.24
22 38 vs 19 541 97.6 1.0 2.00 0.25
23 46 vs 56 459 97.8 1.0 3.00 0.24
24 39 vs 97 401 95.3 1.0 3.00 0.36
25 90 vs 86 328 90.5 2.0 4.00 0.17
26 55 vs 51 272 93.0 2.0 3.00 0.09
27 22 vs 74 217 96.8 1.0 2.00 0.45
28 89 vs 94 165 87.9 1.0 3.80 0.39
29 31 vs 21 121 95.0 1.0 3.00 0.25
30 51 vs 15 94 94.7 1.0 2.00 0.52
31 30 vs 87 67 94.0 1.0 2.00 0.43
32 44 vs 90 52 90.4 1.0 2.00 0.23
33 46 vs 76 38 97.4 1.0 2.00 0.66
34 64 vs 25 26 96.2 1.0 1.80 -0.02
35 79 vs 83 17 70.6 1.0 2.45 NA
36 62 vs 67 5 100.0 1.0 1.80 NA
37 27 vs 58 2 100.0 1.0 1.00 NA
Correct response time (sec)
Question No.  Question No. response % Correct Median RT 95th RT Item discrim.
Term 1
1 3 vs 6 2439 95.4 4.0 16.00 0.20
2 14 vs 2 2441 95.4 3.0 8.00 0.21
3 12 vs 9 2440 87.5 3.0 8.00 0.22
4 5 vs 17 2412 94.3 2.0 6.00 0.27
5 19 vs 10 2416 78.8 3.0 9.00 0.28
6 7 vs 10 2387 89.3 2.0 6.00 0.25
7 17 vs 13 2331 69.8 3.0 10.00 0.21
8 19 vs 18 2271 59.4 3.0 8.00 0.17
9 5 vs 13 2200 91.6 2.0 5.00 0.29
10 20 vs 11 2119 87.1 2.0 6.00 0.26
11 8 vs 4 2022 89.9 3.0 6.00 0.20
12 5 vs 16 1939 94.9 2.0 4.00 0.28
13 17 vs 9 1829 93.9 2.0 4.00 0.27
14 3 vs 14 1717 95.6 2.0 4.00 0.25
15 11 vs 15 1579 89.9 2.0 4.00 0.24
16 8 vs 5 1368 90.2 2.0 4.00 0.26
17 4 vs 14 1265 95.1 2.0 4.00 0.34
18 8 vs 7 1080 83.9 2.0 5.00 0.38
19 5 vs 20 874 96.2 2.0 3.00 0.33
20 10 vs 18 732 85.2 2.0 4.00 0.22
21 10 vs 5 595 91.6 2.0 3.00 0.45
22 1 vs 10 492 94.5 1.0 3.00 0.38
23 11 vs 7 385 87.5 2.0 3.00 0.48
24 18 vs 6 303 89.4 1.0 2.00 0.49
25 15 vs 19 212 83.5 2.0 3.00 0.26
26 3 vs 5 144 88.9 2.0 3.65 0.41
27 5 vs 12 108 92.6 1.0 2.05 0.39
28 13 vs 11 74 74.3 1.0 2.00 0.31
29 8 vs 17 56 89.3 1.0 2.00 0.51
30 19 vs 13 39 64.1 1.0 2.00 0.38
31 3 vs 7 28 78.6 1.0 2.95 0.58
32 6 vs 18 23 91.3 1.0 2.00 0.38
33 9 vs 15 15 93.3 1.0 2.00 NA
34 17 vs 2 15 93.3 1.0 1.35 NA
35 3 vs 16 11 90.9 1.0 2.00 NA
36 10 vs 6 7 85.7 1.0 1.75 NA
37 2 vs 15 7 100.0 1.0 1.00 NA
38 12 vs 14 6 100.0 1.0 1.00 NA
39 16 vs 9 4 100.0 1.0 1.00 NA
40 17 vs 12 4 50.0 1.0 1.00 NA
41 4 vs 9 4 100.0 1.5 3.70 NA
42 19 vs 2 4 100.0 1.0 1.85 NA
43 8 vs 13 4 100.0 1.0 1.85 NA
44 20 vs 10 1 100.0 1.0 1.00 NA
Term 3
1 3 vs 6 1405 96.7 4.0 14.00 0.23
2 14 vs 2 1415 96.1 2.0 6.00 0.26
3 12 vs 9 1414 92.1 2.0 6.00 0.26
4 5 vs 17 1407 95.7 2.0 5.00 0.31
5 19 vs 10 1405 86.0 2.0 7.00 0.25
6 7 vs 10 1402 94.2 2.0 5.00 0.33
7 17 vs 13 1393 84.8 2.0 7.00 0.25
8 19 vs 18 1376 69.6 3.0 8.00 0.17
9 5 vs 13 1364 95.7 2.0 5.00 0.29
10 20 vs 11 1343 94.1 2.0 5.00 0.29
11 8 vs 4 1312 91.6 2.0 5.00 0.22
12 5 vs 16 1277 96.7 2.0 4.00 0.33
13 17 vs 9 1255 96.3 2.0 4.00 0.34
14 3 vs 14 1206 97.6 2.0 3.00 0.34
15 11 vs 15 1159 93.2 2.0 4.00 0.18
16 8 vs 5 1086 91.7 2.0 4.00 0.25
17 4 vs 14 1014 97.5 2.0 3.00 0.35
18 8 vs 7 910 91.0 2.0 5.00 0.28
19 5 vs 20 815 98.0 1.0 3.00 0.37
20 10 vs 18 716 83.9 2.0 4.00 0.14
21 10 vs 5 592 96.3 2.0 3.00 0.32
22 1 vs 10 508 97.4 1.0 3.00 0.46
23 11 vs 7 441 96.1 2.0 3.00 0.30
24 18 vs 6 361 96.1 1.0 2.00 0.45
25 15 vs 19 279 90.3 2.0 3.00 0.46
26 3 vs 5 210 91.4 2.0 3.00 0.25
27 5 vs 12 158 94.9 1.0 2.00 0.65
28 13 vs 11 116 90.5 1.0 2.00 0.21
29 8 vs 17 88 96.6 1.0 2.00 0.61
30 19 vs 13 62 90.3 1.0 3.00 0.22
31 3 vs 7 41 92.7 1.5 3.00 0.31
32 6 vs 18 25 96.0 1.0 2.00 0.77
33 9 vs 15 13 84.6 1.0 2.00 NA
34 17 vs 2 11 90.9 1.0 1.55 NA
35 3 vs 16 9 100.0 1.0 1.00 NA
36 10 vs 6 7 85.7 1.0 1.00 NA
37 2 vs 15 4 100.0 1.0 1.00 NA
38 12 vs 14 2 50.0 1.0 1.00 NA
Term 4
1 3 vs 6 1067 97.0 4.0 14.00 0.24
2 14 vs 2 1077 98.0 2.0 5.00 0.24
3 12 vs 9 1073 93.9 2.0 5.00 0.20
4 5 vs 17 1069 97.8 1.0 3.00 0.21
5 19 vs 10 1067 85.8 2.0 5.00 0.21
6 7 vs 10 1068 96.1 2.0 4.00 0.26
7 17 vs 13 1058 89.1 2.0 6.00 0.22
8 19 vs 18 1053 73.7 2.0 7.00 0.14
9 5 vs 13 1055 96.1 2.0 5.00 0.20
10 20 vs 11 1055 95.7 2.0 4.00 0.26
11 8 vs 4 1039 92.6 2.0 5.00 0.14
12 5 vs 16 1023 97.2 2.0 3.00 0.21
13 17 vs 9 1009 97.1 1.0 3.00 0.27
14 3 vs 14 987 98.0 1.0 3.00 0.24
15 11 vs 15 957 92.2 2.0 4.00 0.16
16 8 vs 5 920 92.6 2.0 4.00 0.14
17 4 vs 14 878 98.2 2.0 3.00 0.24
18 8 vs 7 808 89.9 2.0 5.00 0.24
19 5 vs 20 762 98.3 1.0 3.00 0.25
20 10 vs 18 682 85.8 2.0 4.00 0.09
21 10 vs 5 610 96.4 1.0 3.00 0.28
22 1 vs 10 552 98.0 1.0 2.00 0.29
23 11 vs 7 490 95.3 1.0 2.00 0.23
24 18 vs 6 417 96.2 1.0 3.00 0.30
25 15 vs 19 342 88.9 1.0 3.00 0.39
26 3 vs 5 273 90.8 2.0 3.00 0.29
27 5 vs 12 222 95.9 1.0 2.00 0.25
28 13 vs 11 168 90.5 1.0 3.00 0.28
29 8 vs 17 131 96.9 1.0 2.00 0.37
30 19 vs 13 102 92.2 1.0 2.00 0.47
31 3 vs 7 67 85.1 1.0 2.20 0.74
32 6 vs 18 52 92.3 1.0 1.65 0.32
33 9 vs 15 41 90.2 1.0 1.20 0.76
34 17 vs 2 32 87.5 1.0 1.65 0.71
35 3 vs 16 28 89.3 1.0 1.00 0.65
36 10 vs 6 18 100.0 1.0 1.15 NA
37 2 vs 15 12 100.0 1.0 1.45 NA
38 12 vs 14 9 77.8 1.0 1.70 NA
39 16 vs 9 5 100.0 1.0 1.00 NA
40 17 vs 12 3 66.7 1.5 1.95 NA
41 4 vs 9 2 50.0 1.0 1.00 NA
42 19 vs 2 2 50.0 1.0 1.00 NA
43 8 vs 13 2 50.0 1.0 1.00 NA
44 20 vs 10 1 100.0 1.0 1.00 NA

8. Item correct response time

Term 1

Term 3

Term 4

Term 1

Term 3

Term 4