APPLICATIONS
OF
PSYCHOLOGY
PAPER 2
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, FORMULAE AND STATISTICAL TABLES
Standard deviation (sample estimate)
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( x − x )2
n −1
Spearman’s rank correlation coefficient
6d2
n (n2 −1)
1−
Critical values for Spearman’s rank
Level of significance for a one-tailed test
0.05 0.025 0.01 0.005 0.0025
Level of significance for a two-tailed test
N 0.10 0.05 0.025 0.01 0.005
5 0.900 1.000 1.000 1.000 1.000
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6 0.829 0.886 0.943 1.000 1.000
7 0.714 0.786 0.893 0.929 0.964
8 0.643 0.738 0.833 0.881 0.905
9 0.600 0.700 0.783 0.833 0.867
10 0.564 0.648 0.745 0.794 0.830
11 0.536 0.618 0.709 0.755 0.800
12 0.503 0.587 0.678 0.727 0.769
13 0.484 0.560 0.648 0.703 0.747
14 0.464 0.538 0.626 0.679 0.723
15 0.446 0.521 0.604 0.654 0.700
16 0.429 0.503 0.582 0.635 0.679
17 0.414 0.485 0.566 0.615 0.662
18 0.401 0.472 0.550 0.600 0.643
19 0.391 0.460 0.535 0.584 0.628
20 0.380 0.447 0.520 0.570 0.612
21 0.370 0.435 0.508 0.556 0.599 DO NOT WRITE IN THIS AREA
22 0.361 0.425 0.496 0.544 0.586
23 0.353 0.415 0.486 0.532 0.573
24 0.344 0.406 0.476 0.521 0.562
25 0.337 0.398 0.466 0.511 0.551
26 0.331 0.390 0.457 0.501 0.541
27 0.324 0.382 0.448 0.491 0.531
28 0.317 0.375 0.440 0.483 0.522
29 0.312 0.368 0.433 0.475 0.513
30 0.306 0.362 0.425 0.467 0.504
The calculated value must be equal to or exceed the critical value in this table for
significance to be shown.
3
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, Chi-squared distribution formula
(O − E )
2
X2 = df = (r −1)(c −1)
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E
Critical values for chi-squared distribution
Level of significance for a one-tailed test
0.10 0.05 0.025 0.01 0.005 0.0005
Level of significance for a two-tailed test
df 0.20 0.10 0.05 0.025 0.01 0.001
1 1.64 2.71 3.84 5.02 6.64 10.83
2 3.22 4.61 5.99 7.38 9.21 13.82
3 4.64 6.25 7.82 9.35 11.35 16.27
4 5.99 7.78 9.49 11.14 13.28 18.47
5 7.29 9.24 11.07 12.83 15.09 20.52
6 8.56 10.65 12.59 14.45 16.81 22.46
7 9.80 12.02 14.07 16.01 18.48 24.32
8 11.03 13.36 15.51 17.54 20.09 26.12
9 12.24 14.68 16.92 19.02 21.67 27.88
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10 13.44 15.99 18.31 20.48 23.21 29.59
11 14.63 17.28 19.68 21.92 24.73 31.26
12 15.81 18.55 21.03 23.34 26.22 32.91
13 16.99 19.81 22.36 24.74 27.69 34.53
14 18.15 21.06 23.69 26.12 29.14 36.12
15 19.31 22.31 25.00 27.49 30.58 37.70
16 20.47 23.54 26.30 28.85 32.00 39.25
17 21.62 24.77 27.59 30.19 33.41 40.79
18 22.76 25.99 28.87 31.53 34.81 42.31
19 23.90 27.20 30.14 32.85 36.19 43.82
20 25.04 28.41 31.41 34.17 37.57 45.32
21 26.17 29.62 32.67 35.48 38.93 46.80
22 27.30 30.81 33.92 36.78 40.29 48.27
23 28.43 32.01 35.17 38.08 41.64 49.73
24 29.55 33.20 36.42 39.36 42.98 51.18
25 30.68 34.38 37.65 40.65 44.31 52.62
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26 31.80 35.56 38.89 41.92 45.64 54.05
27 32.91 36.74 40.11 43.20 46.96 55.48
28 34.03 37.92 41.34 44.46 48.28 56.89
29 35.14 39.09 42.56 45.72 49.59 58.30
30 36.25 40.26 43.77 46.98 50.89 59.70
40 47.27 51.81 55.76 59.34 63.69 73.40
50 58.16 63.17 67.51 71.42 76.15 86.66
60 68.97 74.40 79.08 83.30 88.38 99.61
70 79.72 85.53 90.53 95.02 100.43 112.32
The calculated value must be equal to or exceed the critical value in this table for
significance to be shown.
4
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, Mann-Whitney U test formulae
U = n n + na (na +1) − R
a
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a a b
2
U = n n + nb (nb +1) − R
b a b
2
b
(U is the smaller of Ua and Ub)
Critical values for the Mann-Whitney U test
Nb
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Na
p ≤ 0.05 (one-tailed), p ≤ 0.10 (two-tailed)
5 4 5 6 8 9 11 12 13 15 16 18 19 20 22 23 25
6 5 7 8 10 12 14 16 17 19 21 23 25 26 28 30 32
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7 6 8 11 13 15 17 19 21 24 26 28 30 33 35 37 39
8 8 10 13 15 18 20 23 26 28 31 33 36 39 41 44 47
9 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54
10 11 14 17 20 24 27 31 34 37 41 44 48 51 55 58 62
11 12 16 19 23 27 31 34 38 42 46 50 54 57 61 65 69
12 13 17 21 26 30 34 38 42 47 51 55 60 64 68 72 77
13 15 19 24 28 33 37 42 47 51 56 61 65 70 75 80 84
14 16 21 26 31 36 41 46 51 56 61 66 71 77 82 87 92
15 18 23 28 33 39 44 50 55 61 66 72 77 83 88 94 100
16 19 25 30 36 42 48 54 60 65 71 77 83 89 95 101 107
17 20 26 33 39 45 51 57 64 70 77 83 89 96 102 109 115
18 22 28 35 41 48 55 61 68 75 82 88 95 102 109 116 123 DO NOT WRITE IN THIS AREA
19 23 30 37 44 51 58 65 72 80 87 94 101 109 116 123 130
20 25 32 39 47 54 62 69 77 84 92 100 107 115 123 130 138
5
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OF
PSYCHOLOGY
PAPER 2
Questions and
Answers Latest
Updates 2025 TOP
RATED A+
Advanced
2
■■■■
, FORMULAE AND STATISTICAL TABLES
Standard deviation (sample estimate)
DO NOT WRITE IN THIS AREA
( x − x )2
n −1
Spearman’s rank correlation coefficient
6d2
n (n2 −1)
1−
Critical values for Spearman’s rank
Level of significance for a one-tailed test
0.05 0.025 0.01 0.005 0.0025
Level of significance for a two-tailed test
N 0.10 0.05 0.025 0.01 0.005
5 0.900 1.000 1.000 1.000 1.000
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6 0.829 0.886 0.943 1.000 1.000
7 0.714 0.786 0.893 0.929 0.964
8 0.643 0.738 0.833 0.881 0.905
9 0.600 0.700 0.783 0.833 0.867
10 0.564 0.648 0.745 0.794 0.830
11 0.536 0.618 0.709 0.755 0.800
12 0.503 0.587 0.678 0.727 0.769
13 0.484 0.560 0.648 0.703 0.747
14 0.464 0.538 0.626 0.679 0.723
15 0.446 0.521 0.604 0.654 0.700
16 0.429 0.503 0.582 0.635 0.679
17 0.414 0.485 0.566 0.615 0.662
18 0.401 0.472 0.550 0.600 0.643
19 0.391 0.460 0.535 0.584 0.628
20 0.380 0.447 0.520 0.570 0.612
21 0.370 0.435 0.508 0.556 0.599 DO NOT WRITE IN THIS AREA
22 0.361 0.425 0.496 0.544 0.586
23 0.353 0.415 0.486 0.532 0.573
24 0.344 0.406 0.476 0.521 0.562
25 0.337 0.398 0.466 0.511 0.551
26 0.331 0.390 0.457 0.501 0.541
27 0.324 0.382 0.448 0.491 0.531
28 0.317 0.375 0.440 0.483 0.522
29 0.312 0.368 0.433 0.475 0.513
30 0.306 0.362 0.425 0.467 0.504
The calculated value must be equal to or exceed the critical value in this table for
significance to be shown.
3
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, Chi-squared distribution formula
(O − E )
2
X2 = df = (r −1)(c −1)
DO NOT WRITE IN THIS AREA
E
Critical values for chi-squared distribution
Level of significance for a one-tailed test
0.10 0.05 0.025 0.01 0.005 0.0005
Level of significance for a two-tailed test
df 0.20 0.10 0.05 0.025 0.01 0.001
1 1.64 2.71 3.84 5.02 6.64 10.83
2 3.22 4.61 5.99 7.38 9.21 13.82
3 4.64 6.25 7.82 9.35 11.35 16.27
4 5.99 7.78 9.49 11.14 13.28 18.47
5 7.29 9.24 11.07 12.83 15.09 20.52
6 8.56 10.65 12.59 14.45 16.81 22.46
7 9.80 12.02 14.07 16.01 18.48 24.32
8 11.03 13.36 15.51 17.54 20.09 26.12
9 12.24 14.68 16.92 19.02 21.67 27.88
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10 13.44 15.99 18.31 20.48 23.21 29.59
11 14.63 17.28 19.68 21.92 24.73 31.26
12 15.81 18.55 21.03 23.34 26.22 32.91
13 16.99 19.81 22.36 24.74 27.69 34.53
14 18.15 21.06 23.69 26.12 29.14 36.12
15 19.31 22.31 25.00 27.49 30.58 37.70
16 20.47 23.54 26.30 28.85 32.00 39.25
17 21.62 24.77 27.59 30.19 33.41 40.79
18 22.76 25.99 28.87 31.53 34.81 42.31
19 23.90 27.20 30.14 32.85 36.19 43.82
20 25.04 28.41 31.41 34.17 37.57 45.32
21 26.17 29.62 32.67 35.48 38.93 46.80
22 27.30 30.81 33.92 36.78 40.29 48.27
23 28.43 32.01 35.17 38.08 41.64 49.73
24 29.55 33.20 36.42 39.36 42.98 51.18
25 30.68 34.38 37.65 40.65 44.31 52.62
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26 31.80 35.56 38.89 41.92 45.64 54.05
27 32.91 36.74 40.11 43.20 46.96 55.48
28 34.03 37.92 41.34 44.46 48.28 56.89
29 35.14 39.09 42.56 45.72 49.59 58.30
30 36.25 40.26 43.77 46.98 50.89 59.70
40 47.27 51.81 55.76 59.34 63.69 73.40
50 58.16 63.17 67.51 71.42 76.15 86.66
60 68.97 74.40 79.08 83.30 88.38 99.61
70 79.72 85.53 90.53 95.02 100.43 112.32
The calculated value must be equal to or exceed the critical value in this table for
significance to be shown.
4
■■■■
, Mann-Whitney U test formulae
U = n n + na (na +1) − R
a
DO NOT WRITE IN THIS AREA
a a b
2
U = n n + nb (nb +1) − R
b a b
2
b
(U is the smaller of Ua and Ub)
Critical values for the Mann-Whitney U test
Nb
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Na
p ≤ 0.05 (one-tailed), p ≤ 0.10 (two-tailed)
5 4 5 6 8 9 11 12 13 15 16 18 19 20 22 23 25
6 5 7 8 10 12 14 16 17 19 21 23 25 26 28 30 32
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7 6 8 11 13 15 17 19 21 24 26 28 30 33 35 37 39
8 8 10 13 15 18 20 23 26 28 31 33 36 39 41 44 47
9 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54
10 11 14 17 20 24 27 31 34 37 41 44 48 51 55 58 62
11 12 16 19 23 27 31 34 38 42 46 50 54 57 61 65 69
12 13 17 21 26 30 34 38 42 47 51 55 60 64 68 72 77
13 15 19 24 28 33 37 42 47 51 56 61 65 70 75 80 84
14 16 21 26 31 36 41 46 51 56 61 66 71 77 82 87 92
15 18 23 28 33 39 44 50 55 61 66 72 77 83 88 94 100
16 19 25 30 36 42 48 54 60 65 71 77 83 89 95 101 107
17 20 26 33 39 45 51 57 64 70 77 83 89 96 102 109 115
18 22 28 35 41 48 55 61 68 75 82 88 95 102 109 116 123 DO NOT WRITE IN THIS AREA
19 23 30 37 44 51 58 65 72 80 87 94 101 109 116 123 130
20 25 32 39 47 54 62 69 77 84 92 100 107 115 123 130 138
5
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