How much difference does it make? Notes on understanding, using, and calculating effect sizes for schools

Publication Details

Author(s): Ian Schagen, Research Division, Ministry of Education and Edith Hodgen, New Zealand Council for Educational Research.

Date Published: March 2009

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Data Tables

Page Index
  • :  Effect sizes for PAT Mathematics scores
  • :  Effect sizes for PAT Reading Comprehension scores
  • :  Effect sizes for PAT Reading Vocabulary scores
  • :     Effect sizes for STAR test scores
  • :     Effect sizes for asTTle Mathematics scores
  • :     Effect sizes for asTTle Reading scores
  • :     Effect sizes for asTTle Writing scores
  • :     Standard error of effect size estimates: two independent samples (different students in the two tests)
  • :     Standard error of effect size estimates: two dependent samples (matched students in the two tests)

Table 1A: Effect sizes for PAT Mathematics scores
PAT Mathematics
Note:
  1. The figures in the body of the table are the effect sizes for the achieved mean difference, at each year level and for each of the three tests, taking into account expected growth over one year. Where the difference is less than expected, the effect size is negative. The expected difference at each year level can be calculated from the mean PAT scores for two year levels. For example, from Year 4 to Year 5 in mathematics, the expected growth is 40.3 – 31.8 = 8.5.
Current Year Level 4 5 6 7 8 9 10
Mean PAT Score 31.8 40.3 46.4 50.9 55.5 62.6 66.6
SD of PAT Score 13.1 13.2 12.4 11.8 12.3 11.3 11.6
Difference Between Mean Scores:
7.0 -0.11 -0.11 0.07 0.21 0.20 -0.01 0.26
7.5 -0.08 -0.08 0.11 0.25 0.24 0.04 0.30
8.0 -0.04 -0.04 0.15 0.30 0.28 0.08 0.34
8.5 0.00 0.00 0.19 0.34 0.32 0.12 0.39
9.0 0.04 0.04 0.23 0.38 0.36 0.17 0.43
9.5 0.08 0.08 0.27 0.42 0.40 0.21 0.47
10.0 0.11 0.11 0.31 0.47 0.44 0.26 0.52
10.5 0.15 0.15 0.35 0.51 0.48 0.30 0.56
11.0 0.19 0.19 0.40 0.55 0.52 0.35 0.60
11.5 0.23 0.23 0.44 0.59 0.56 0.39 0.65
12.0 0.27 0.27 0.48 0.64 0.60 0.43 0.69
12.5 0.30 0.30 0.52 0.68 0.64 0.48 0.73
13.0 0.34 0.34 0.56 0.72 0.68 0.52 0.78
13.5 0.38 0.38 0.60 0.76 0.72 0.57 0.82
14.0 0.42 0.42 0.64 0.81 0.76 0.61 0.86
14.5 0.45 0.45 0.68 0.85 0.80 0.65 0.91
15.0 0.49 0.49 0.72 0.89 0.85 0.70 0.95
15.5 0.53 0.53 0.76 0.93 0.89 0.74 0.99
16.0 0.57 0.57 0.80 0.97 0.93 0.79 1.03
16.5 0.61 0.61 0.84 1.02 0.97 0.83 1.08
17.0 0.64 0.64 0.88 1.06 1.01 0.88 1.12
17.5 0.68 0.68 0.92 1.10 1.05 0.92 1.16
18.0 0.72 0.72 0.96 1.14 1.09 0.96 1.21
18.5 0.76 0.76 1.00 1.19 1.13 1.01 1.25
19.0 0.80 0.80 1.04 1.23 1.17 1.05 1.29
19.5 0.83 0.83 1.08 1.27 1.21 1.10 1.34
20.0 0.87 0.87 1.12 1.31 1.25 1.14 1.38
20.5 0.91 0.91 1.16 1.36 1.29 1.19 1.42
21.0 0.95 0.95 1.20 1.40 1.33 1.23 1.47
21.5 0.98 0.98 1.24 1.44 1.37 1.27 1.51
22.0 1.02 1.02 1.28 1.48 1.41 1.32 1.55
22.5 1.06 1.06 1.32 1.53 1.46 1.36 1.59
23.0 1.10 1.10 1.36 1.57 1.50 1.41 1.64
23.5 1.14 1.14 1.40 1.61 1.54 1.45 1.68
24.0 1.17 1.17 1.44 1.65 1.58 1.50 1.72
24.5 1.21 1.21 1.48 1.69 1.62 1.54 1.77
25.0 1.25 1.25 1.52 1.74 1.66 1.58 1.81
25.5 1.29 1.29 1.56 1.78 1.70 1.63 1.85
26.0 1.33 1.33 1.60 1.82 1.74 1.67 1.90
26.5 1.36 1.36 1.65 1.86 1.78 1.72 1.94
27.0 1.40 1.40 1.69 1.91 1.82 1.76 1.98
27.5 1.44 1.44 1.73 1.95 1.86 1.81 2.03
28.0 1.48 1.48 1.77 1.99 1.90 1.85 2.07
28.5 1.52 1.52 1.81 2.03 1.94 1.89 2.11
29.0 1.55 1.55 1.85 2.08 1.98 1.94 2.16
29.5 1.59 1.59 1.89 2.12 2.02 1.98 2.20
30.0 1.63 1.63 1.93 2.16 2.07 2.03 2.24
30.5 1.67 1.67 1.97 2.20 2.11 2.07 2.28
31.0 1.70 1.70 2.01 2.25 2.15 2.12 2.33
31.5 1.74 1.74 2.05 2.29 2.19 2.16 2.37
32.0 1.78 1.78 2.09 2.33 2.23 2.20 2.41
32.5 1.82 1.82 2.13 2.37 2.27 2.25 2.46
33.0 1.86 1.86 2.17 2.42 2.31 2.29 2.50

Table 1B: Effect sizes for PAT Reading Comprehension scores
PAT Reading Comprehension
Note:
  1. The figures in the body of the table are the effect sizes for the achieved mean difference, at each year level and for each of the three tests, taking into account expected growth over one year. Where the difference is less than expected, the effect size is negative. The expected difference at each year level can be calculated from the mean PAT scores for two year levels. For example, from Year 4 to Year 5 in mathematics, the expected growth is 40.3 – 31.8 = 8.5.
Current Year Level 4 5 6 7 8 9 10
Mean PAT Score 28.8 35.8 45.0 53.2 60.4 67.0 76.5
SD of PAT Score 15.2 13.2 12.7 12.6 12.3 12.2 12.4
Difference Between Mean Scores:
7.0 0.00 0.00 -0.17 -0.10 -0.02 0.03 -0.20
7.5 0.03 0.04 -0.13 -0.06 0.02 0.07 -0.16
8.0 0.07 0.08 -0.09 -0.02 0.07 0.11 -0.12
8.5 0.10 0.11 -0.06 0.02 0.11 0.16 -0.08
9.0 0.13 0.15 -0.02 0.06 0.15 0.20 -0.04
9.5 0.16 0.19 0.02 0.10 0.19 0.24 0.00
10.0 0.20 0.23 0.06 0.14 0.23 0.28 0.04
10.5 0.23 0.27 0.10 0.18 0.27 0.32 0.08
11.0 0.26 0.30 0.14 0.22 0.31 0.36 0.12
11.5 0.30 0.34 0.18 0.26 0.35 0.40 0.16
12.0 0.33 0.38 0.22 0.30 0.39 0.44 0.20
12.5 0.36 0.42 0.26 0.34 0.43 0.48 0.24
13.0 0.39 0.45 0.30 0.38 0.47 0.52 0.28
13.5 0.43 0.49 0.34 0.42 0.51 0.57 0.32
14.0 0.46 0.53 0.38 0.46 0.55 0.61 0.36
14.5 0.49 0.57 0.42 0.50 0.59 0.65 0.40
15.0 0.53 0.61 0.46 0.54 0.63 0.69 0.44
15.5 0.56 0.64 0.50 0.58 0.67 0.73 0.48
16.0 0.59 0.68 0.54 0.62 0.72 0.77 0.52
16.5 0.63 0.72 0.57 0.66 0.76 0.81 0.56
17.0 0.66 0.76 0.61 0.70 0.80 0.85 0.60
17.5 0.69 0.80 0.65 0.74 0.84 0.89 0.65
18.0 0.72 0.83 0.69 0.78 0.88 0.93 0.69
18.5 0.76 0.87 0.73 0.82 0.92 0.98 0.73
19.0 0.79 0.91 0.77 0.86 0.96 1.02 0.77
19.5 0.82 0.95 0.81 0.90 1.00 1.06 0.81
20.0 0.86 0.98 0.85 0.94 1.04 1.10 0.85
20.5 0.89 1.02 0.89 0.98 1.08 1.14 0.89
21.0 0.92 1.06 0.93 1.02 1.12 1.18 0.93
21.5 0.95 1.10 0.97 1.06 1.16 1.22 0.97
22.0 0.99 1.14 1.01 1.10 1.20 1.26 1.01
22.5 1.02 1.17 1.05 1.13 1.24 1.30 1.05
23.0 1.05 1.21 1.09 1.17 1.28 1.34 1.09
23.5 1.09 1.25 1.13 1.21 1.33 1.39 1.13
24.0 1.12 1.29 1.17 1.25 1.37 1.43 1.17
24.5 1.15 1.33 1.20 1.29 1.41 1.47 1.21
25.0 1.18 1.36 1.24 1.33 1.45 1.51 1.25
25.5 1.22 1.40 1.28 1.37 1.49 1.55 1.29
26.0 1.25 1.44 1.32 1.41 1.53 1.59 1.33
26.5 1.28 1.48 1.36 1.45 1.57 1.63 1.37
27.0 1.32 1.52 1.40 1.49 1.61 1.67 1.41
27.5 1.35 1.55 1.44 1.53 1.65 1.71 1.45
28.0 1.38 1.59 1.48 1.57 1.69 1.75 1.49
28.5 1.41 1.63 1.52 1.61 1.73 1.80 1.53
29.0 1.45 1.67 1.56 1.65 1.77 1.84 1.57
29.5 1.48 1.70 1.60 1.69 1.81 1.88 1.61
30.0 1.51 1.74 1.64 1.73 1.85 1.92 1.65
30.5 1.55 1.78 1.68 1.77 1.89 1.96 1.69
31.0 1.58 1.82 1.72 1.81 1.93 2.00 1.73
31.5 1.61 1.86 1.76 1.85 1.98 2.04 1.77
32.0 1.64 1.89 1.80 1.89 2.02 2.08 1.81
32.5 1.68 1.93 1.83 1.93 2.06 2.12 1.85
33.0 1.71 1.97 1.87 1.97 2.10 2.16 1.90

Table 1C: Effect sizes for PAT Reading Vocabulary scores
PAT Reading Vocabulary
Note:
  1. The figures in the body of the table are the effect sizes for the achieved mean difference, at each year level and for each of the three tests, taking into account expected growth over one year. Where the difference is less than expected, the effect size is negative. The expected difference at each year level can be calculated from the mean PAT scores for two year levels. For example, from Year 4 to Year 5 in mathematics, the expected growth is 40.3 – 31.8 = 8.5.
Current Year Level 4 5 6 7 8 9 10
Mean PAT Score 32.4 40.9 48.7 55.0 60.1 65.7 70.5
SD of PAT Score 16.0 15.8 15.0 14.3 14.8 14.7 14.8
Difference Between Mean Scores:
7.0 -0.09 -0.09 -0.05 0.05 0.13 0.10 0.15
7.5 -0.06 -0.06 -0.02 0.08 0.16 0.13 0.18
8.0 -0.03 -0.03 0.01 0.12 0.20 0.16 0.22
8.5 0.00 0.00 0.05 0.15 0.23 0.20 0.25
9.0 0.03 0.03 0.08 0.19 0.26 0.23 0.28
9.5 0.06 0.06 0.11 0.22 0.30 0.27 0.32
10.0 0.09 0.09 0.15 0.26 0.33 0.30 0.35
10.5 0.13 0.13 0.18 0.29 0.36 0.33 0.39
11.0 0.16 0.16 0.21 0.33 0.40 0.37 0.42
11.5 0.19 0.19 0.25 0.36 0.43 0.40 0.45
12.0 0.22 0.22 0.28 0.40 0.47 0.44 0.49
12.5 0.25 0.25 0.31 0.43 0.50 0.47 0.52
13.0 0.28 0.28 0.35 0.47 0.53 0.50 0.55
13.5 0.31 0.32 0.38 0.50 0.57 0.54 0.59
14.0 0.34 0.35 0.41 0.54 0.60 0.57 0.62
14.5 0.38 0.38 0.45 0.57 0.64 0.61 0.66
15.0 0.41 0.41 0.48 0.61 0.67 0.64 0.69
15.5 0.44 0.44 0.51 0.64 0.70 0.67 0.72
16.0 0.47 0.47 0.55 0.68 0.74 0.71 0.76
16.5 0.50 0.51 0.58 0.71 0.77 0.74 0.79
17.0 0.53 0.54 0.61 0.75 0.80 0.78 0.82
17.5 0.56 0.57 0.65 0.78 0.84 0.81 0.86
18.0 0.59 0.60 0.68 0.82 0.87 0.84 0.89
18.5 0.63 0.63 0.71 0.85 0.91 0.88 0.93
19.0 0.66 0.66 0.75 0.89 0.94 0.91 0.96
19.5 0.69 0.70 0.78 0.92 0.97 0.95 0.99
20.0 0.72 0.73 0.81 0.96 1.01 0.98 1.03
20.5 0.75 0.76 0.85 0.99 1.04 1.01 1.06
21.0 0.78 0.79 0.88 1.03 1.07 1.05 1.09
21.5 0.81 0.82 0.91 1.06 1.11 1.08 1.13
22.0 0.84 0.85 0.95 1.10 1.14 1.12 1.16
22.5 0.88 0.89 0.98 1.13 1.18 1.15 1.20
23.0 0.91 0.92 1.01 1.17 1.21 1.18 1.23
23.5 0.94 0.95 1.05 1.20 1.24 1.22 1.26
24.0 0.97 0.98 1.08 1.24 1.28 1.25 1.30
24.5 1.00 1.01 1.11 1.27 1.31 1.29 1.33
25.0 1.03 1.04 1.15 1.31 1.34 1.32 1.36
25.5 1.06 1.08 1.18 1.34 1.38 1.35 1.40
26.0 1.09 1.11 1.21 1.38 1.41 1.39 1.43
26.5 1.13 1.14 1.25 1.41 1.45 1.42 1.47
27.0 1.16 1.17 1.28 1.45 1.48 1.46 1.50
27.5 1.19 1.20 1.31 1.48 1.51 1.49 1.53
28.0 1.22 1.23 1.35 1.52 1.55 1.52 1.57
28.5 1.25 1.27 1.38 1.55 1.58 1.56 1.60
29.0 1.28 1.30 1.41 1.59 1.61 1.59 1.64
29.5 1.31 1.33 1.45 1.62 1.65 1.63 1.67
30.0 1.34 1.36 1.48 1.66 1.68 1.66 1.70
30.5 1.38 1.39 1.51 1.69 1.72 1.69 1.74
31.0 1.41 1.42 1.55 1.73 1.75 1.73 1.77
31.5 1.44 1.46 1.58 1.76 1.78 1.76 1.80
32.0 1.47 1.49 1.61 1.80 1.82 1.80 1.84
32.5 1.50 1.52 1.65 1.83 1.85 1.83 1.87
33.0 1.53 1.55 1.68 1.87 1.89 1.86 1.91

Table 2: Effect sizes for STAR test scores
Note:
  1. STAR scores are stanines, so the expected change is 0, and standard deviation is 2.
Stanine Difference Effect Size
0.2 0.1
0.4 0.2
0.6 0.3
0.8 0.4
1 0.5
1.2 0.6
1.4 0.7
1.6 0.8
1.8 0.9
2 1
2.2 1.1
2.4 1.2
2.6 1.3
2.8 1.4
3 1.5
3.2 1.6
3.4 1.7
3.6 1.8
3.8 1.9
4 2
4.2 2.1
4.4 2.2
4.6 2.3
4.8 2.4
5 2.5
5.2 2.6

Table 3: Effect sizes for asTTle Mathematics scores
Note:
  1. The effect size values in the table are for differences across one year. The calculations are based on a standard deviation of 100.
asTTle Mathematics
Current Year Level 4 5 6 7 8 9 10 11 12
Mean asTTle Score 410 470 502 541 638 774 807 828 848
Difference Between Mean Scores: 
44.0 -0.16 -0.16 0.12 0.05 -0.53 -0.92 0.11 0.23 0.24
46.0 -0.14 -0.14 0.14 0.07 -0.51 -0.90 0.13 0.25 0.26
48.0 -0.12 -0.12 0.16 0.09 -0.49 -0.88 0.15 0.27 0.28
50.0 -0.10 -0.10 0.18 0.11 -0.47 -0.86 0.17 0.29 0.30
52.0 -0.08 -0.08 0.20 0.13 -0.45 -0.84 0.19 0.31 0.32
54.0 -0.06 -0.06 0.22 0.15 -0.43 -0.82 0.21 0.33 0.34
56.0 -0.04 -0.04 0.24 0.17 -0.41 -0.80 0.23 0.35 0.36
58.0 -0.02 -0.02 0.26 0.19 -0.39 -0.78 0.25 0.37 0.38
60.0 0.00 0.00 0.28 0.21 -0.37 -0.76 0.27 0.39 0.40
62.0 0.02 0.02 0.30 0.23 -0.35 -0.74 0.29 0.41 0.42
64.0 0.04 0.04 0.32 0.25 -0.33 -0.72 0.31 0.43 0.44
66.0 0.06 0.06 0.34 0.27 -0.31 -0.70 0.33 0.45 0.46
68.0 0.08 0.08 0.36 0.29 -0.29 -0.68 0.35 0.47 0.48
70.0 0.10 0.10 0.38 0.31 -0.27 -0.66 0.37 0.49 0.50
72.0 0.12 0.12 0.40 0.33 -0.25 -0.64 0.39 0.51 0.52
74.0 0.14 0.14 0.42 0.35 -0.23 -0.62 0.41 0.53 0.54
76.0 0.16 0.16 0.44 0.37 -0.21 -0.60 0.43 0.55 0.56
78.0 0.18 0.18 0.46 0.39 -0.19 -0.58 0.45 0.57 0.58
80.0 0.20 0.20 0.48 0.41 -0.17 -0.56 0.47 0.59 0.60
82.0 0.22 0.22 0.50 0.43 -0.15 -0.54 0.49 0.61 0.62
84.0 0.24 0.24 0.52 0.45 -0.13 -0.52 0.51 0.63 0.64
86.0 0.26 0.26 0.54 0.47 -0.11 -0.50 0.53 0.65 0.66
88.0 0.28 0.28 0.56 0.49 -0.09 -0.48 0.55 0.67 0.68
90.0 0.30 0.30 0.58 0.51 -0.07 -0.46 0.57 0.69 0.70
92.0 0.32 0.32 0.60 0.53 -0.05 -0.44 0.59 0.71 0.72
94.0 0.34 0.34 0.62 0.55 -0.03 -0.42 0.61 0.73 0.74
96.0 0.36 0.36 0.64 0.57 -0.01 -0.40 0.63 0.75 0.76
98.0 0.38 0.38 0.66 0.59 0.01 -0.38 0.65 0.77 0.78
100.0 0.40 0.40 0.68 0.61 0.03 -0.36 0.67 0.79 0.80
105.0 0.45 0.45 0.73 0.66 0.08 -0.31 0.72 0.84 0.85
110.0 0.50 0.50 0.78 0.71 0.13 -0.26 0.77 0.89 0.90
115.0 0.55 0.55 0.83 0.76 0.18 -0.21 0.82 0.94 0.95
120.0 0.60 0.60 0.88 0.81 0.23 -0.16 0.87 0.99 1.00
125.0 0.65 0.65 0.93 0.86 0.28 -0.11 0.92 1.04 1.05
130.0 0.70 0.70 0.98 0.91 0.33 -0.06 0.97 1.09 1.10
135.0 0.75 0.75 1.03 0.96 0.38 -0.01 1.02 1.14 1.15
140.0 0.80 0.80 1.08 1.01 0.43 0.04 1.07 1.19 1.20
145.0 0.85 0.85 1.13 1.06 0.48 0.09 1.12 1.24 1.25
150.0 0.90 0.90 1.18 1.11 0.53 0.14 1.17 1.29 1.30
155.0 0.95 0.95 1.23 1.16 0.58 0.19 1.22 1.34 1.35
160.0 1.00 1.00 1.28 1.21 0.63 0.24 1.27 1.39 1.40
165.0 1.05 1.05 1.33 1.26 0.68 0.29 1.32 1.44 1.45
170.0 1.10 1.10 1.38 1.31 0.73 0.34 1.37 1.49 1.50
175.0 1.15 1.15 1.43 1.36 0.78 0.39 1.42 1.54 1.55
180.0 1.20 1.20 1.48 1.41 0.83 0.44 1.47 1.59 1.60
185.0 1.25 1.25 1.53 1.46 0.88 0.49 1.52 1.64 1.65
190.0 1.30 1.30 1.58 1.51 0.93 0.54 1.57 1.69 1.70
195.0 1.35 1.35 1.63 1.56 0.98 0.59 1.62 1.74 1.75
200.0 1.40 1.40 1.68 1.61 1.03 0.64 1.67 1.79 1.80
210.0 1.50 1.50 1.78 1.71 1.13 0.74 1.77 1.89 1.90
220.0 1.60 1.60 1.88 1.81 1.23 0.84 1.87 1.99 2.00
230.0 1.70 1.70 1.98 1.91 1.33 0.94 1.97 2.09 2.10
240.0 1.80 1.80 2.08 2.01 1.43 1.04 2.07 2.19 2.20

Table 4: Effect sizes for asTTle Reading scores
Note:
  1. The effect size values in the table are for differences across one year. The calculations are based on a standard deviation of 100.
asTTle Reading
Current Year Level 4 5 6 7 8 9 10 11 12
Mean asTTle Score 412 462 489 508 517 634 728 768 780
Difference Between Mean Scores:
44.0 -0.06 -0.06 0.17 0.25 0.35 -0.73 -0.50 0.04 0.32
46.0 -0.04 -0.04 0.19 0.27 0.37 -0.71 -0.48 0.06 0.34
48.0 -0.02 -0.02 0.21 0.29 0.39 -0.69 -0.46 0.08 0.36
50.0 0.00 0.00 0.23 0.31 0.41 -0.67 -0.44 0.10 0.38
52.0 0.02 0.02 0.25 0.33 0.43 -0.65 -0.42 0.12 0.40
54.0 0.04 0.04 0.27 0.35 0.45 -0.63 -0.40 0.14 0.42
56.0 0.06 0.06 0.29 0.37 0.47 -0.61 -0.38 0.16 0.44
58.0 0.08 0.08 0.31 0.39 0.49 -0.59 -0.36 0.18 0.46
60.0 0.10 0.10 0.33 0.41 0.51 -0.57 -0.34 0.20 0.48
62.0 0.12 0.12 0.35 0.43 0.53 -0.55 -0.32 0.22 0.50
64.0 0.14 0.14 0.37 0.45 0.55 -0.53 -0.30 0.24 0.52
66.0 0.16 0.16 0.39 0.47 0.57 -0.51 -0.28 0.26 0.54
68.0 0.18 0.18 0.41 0.49 0.59 -0.49 -0.26 0.28 0.56
70.0 0.20 0.20 0.43 0.51 0.61 -0.47 -0.24 0.30 0.58
72.0 0.22 0.22 0.45 0.53 0.63 -0.45 -0.22 0.32 0.60
74.0 0.24 0.24 0.47 0.55 0.65 -0.43 -0.20 0.34 0.62
76.0 0.26 0.26 0.49 0.57 0.67 -0.41 -0.18 0.36 0.64
78.0 0.28 0.28 0.51 0.59 0.69 -0.39 -0.16 0.38 0.66
80.0 0.30 0.30 0.53 0.61 0.71 -0.37 -0.14 0.40 0.68
82.0 0.32 0.32 0.55 0.63 0.73 -0.35 -0.12 0.42 0.70
84.0 0.34 0.34 0.57 0.65 0.75 -0.33 -0.10 0.44 0.72
86.0 0.36 0.36 0.59 0.67 0.77 -0.31 -0.08 0.46 0.74
88.0 0.38 0.38 0.61 0.69 0.79 -0.29 -0.06 0.48 0.76
90.0 0.40 0.40 0.63 0.71 0.81 -0.27 -0.04 0.50 0.78
92.0 0.42 0.42 0.65 0.73 0.83 -0.25 -0.02 0.52 0.80
94.0 0.44 0.44 0.67 0.75 0.85 -0.23 0.00 0.54 0.82
96.0 0.46 0.46 0.69 0.77 0.87 -0.21 0.02 0.56 0.84
98.0 0.48 0.48 0.71 0.79 0.89 -0.19 0.04 0.58 0.86
100.0 0.50 0.50 0.73 0.81 0.91 -0.17 0.06 0.60 0.88
105.0 0.55 0.55 0.78 0.86 0.96 -0.12 0.11 0.65 0.93
110.0 0.60 0.60 0.83 0.91 1.01 -0.07 0.16 0.70 0.98
115.0 0.65 0.65 0.88 0.96 1.06 -0.02 0.21 0.75 1.03
120.0 0.70 0.70 0.93 1.01 1.11 0.03 0.26 0.80 1.08
125.0 0.75 0.75 0.98 1.06 1.16 0.08 0.31 0.85 1.13
130.0 0.80 0.80 1.03 1.11 1.21 0.13 0.36 0.90 1.18
135.0 0.85 0.85 1.08 1.16 1.26 0.18 0.41 0.95 1.23
140.0 0.90 0.90 1.13 1.21 1.31 0.23 0.46 1.00 1.28
145.0 0.95 0.95 1.18 1.26 1.36 0.28 0.51 1.05 1.33
150.0 1.00 1.00 1.23 1.31 1.41 0.33 0.56 1.10 1.38
155.0 1.05 1.05 1.28 1.36 1.46 0.38 0.61 1.15 1.43
160.0 1.10 1.10 1.33 1.41 1.51 0.43 0.66 1.20 1.48
165.0 1.15 1.15 1.38 1.46 1.56 0.48 0.71 1.25 1.53
170.0 1.20 1.20 1.43 1.51 1.61 0.53 0.76 1.30 1.58
175.0 1.25 1.25 1.48 1.56 1.66 0.58 0.81 1.35 1.63
180.0 1.30 1.30 1.53 1.61 1.71 0.63 0.86 1.40 1.68
185.0 1.35 1.35 1.58 1.66 1.76 0.68 0.91 1.45 1.73
190.0 1.40 1.40 1.63 1.71 1.81 0.73 0.96 1.50 1.78
195.0 1.45 1.45 1.68 1.76 1.86 0.78 1.01 1.55 1.83
200.0 1.50 1.50 1.73 1.81 1.91 0.83 1.06 1.60 1.88
210.0 1.60 1.60 1.83 1.91 2.01 0.93 1.16 1.70 1.98
220.0 1.70 1.70 1.93 2.01 2.11 1.03 1.26 1.80 2.08
230.0 1.80 1.80 2.03 2.11 2.21 1.13 1.36 1.90 2.18
240.0 1.90 1.90 2.13 2.21 2.31 1.23 1.46 2.00 2.28

Table 5: Effect sizes for asTTle Writing scores
Note:
  1. The effect size values in the table are for differences across one year. The calculations are based on a standard deviation of 100.
asTTle Writing
Current Year Level 4 5 6 7 8 9 10 11 12
Mean asTTle Score 454 482 504 518 536 590 633 639 669
Difference Between Mean Scores:
44.0 0.16 0.16 0.22 0.30 0.26 -0.10 0.01 0.38 0.14
46.0 0.18 0.18 0.24 0.32 0.28 -0.08 0.03 0.40 0.16
48.0 0.20 0.20 0.26 0.34 0.30 -0.06 0.05 0.42 0.18
50.0 0.22 0.22 0.28 0.36 0.32 -0.04 0.07 0.44 0.20
52.0 0.24 0.24 0.30 0.38 0.34 -0.02 0.09 0.46 0.22
54.0 0.26 0.26 0.32 0.40 0.36 0.00 0.11 0.48 0.24
56.0 0.28 0.28 0.34 0.42 0.38 0.02 0.13 0.50 0.26
58.0 0.30 0.30 0.36 0.44 0.40 0.04 0.15 0.52 0.28
60.0 0.32 0.32 0.38 0.46 0.42 0.06 0.17 0.54 0.30
62.0 0.34 0.34 0.40 0.48 0.44 0.08 0.19 0.56 0.32
64.0 0.36 0.36 0.42 0.50 0.46 0.10 0.21 0.58 0.34
66.0 0.38 0.38 0.44 0.52 0.48 0.12 0.23 0.60 0.36
68.0 0.40 0.40 0.46 0.54 0.50 0.14 0.25 0.62 0.38
70.0 0.42 0.42 0.48 0.56 0.52 0.16 0.27 0.64 0.40
72.0 0.44 0.44 0.50 0.58 0.54 0.18 0.29 0.66 0.42
74.0 0.46 0.46 0.52 0.60 0.56 0.20 0.31 0.68 0.44
76.0 0.48 0.48 0.54 0.62 0.58 0.22 0.33 0.70 0.46
78.0 0.50 0.50 0.56 0.64 0.60 0.24 0.35 0.72 0.48
80.0 0.52 0.52 0.58 0.66 0.62 0.26 0.37 0.74 0.50
82.0 0.54 0.54 0.60 0.68 0.64 0.28 0.39 0.76 0.52
84.0 0.56 0.56 0.62 0.70 0.66 0.30 0.41 0.78 0.54
86.0 0.58 0.58 0.64 0.72 0.68 0.32 0.43 0.80 0.56
88.0 0.60 0.60 0.66 0.74 0.70 0.34 0.45 0.82 0.58
90.0 0.62 0.62 0.68 0.76 0.72 0.36 0.47 0.84 0.60
92.0 0.64 0.64 0.70 0.78 0.74 0.38 0.49 0.86 0.62
94.0 0.66 0.66 0.72 0.80 0.76 0.40 0.51 0.88 0.64
96.0 0.68 0.68 0.74 0.82 0.78 0.42 0.53 0.90 0.66
98.0 0.70 0.70 0.76 0.84 0.80 0.44 0.55 0.92 0.68
100.0 0.72 0.72 0.78 0.86 0.82 0.46 0.57 0.94 0.70
105.0 0.77 0.77 0.83 0.91 0.87 0.51 0.62 0.99 0.75
110.0 0.82 0.82 0.88 0.96 0.92 0.56 0.67 1.04 0.80
115.0 0.87 0.87 0.93 1.01 0.97 0.61 0.72 1.09 0.85
120.0 0.92 0.92 0.98 1.06 1.02 0.66 0.77 1.14 0.90
125.0 0.97 0.97 1.03 1.11 1.07 0.71 0.82 1.19 0.95
130.0 1.02 1.02 1.08 1.16 1.12 0.76 0.87 1.24 1.00
135.0 1.07 1.07 1.13 1.21 1.17 0.81 0.92 1.29 1.05
140.0 1.12 1.12 1.18 1.26 1.22 0.86 0.97 1.34 1.10
145.0 1.17 1.17 1.23 1.31 1.27 0.91 1.02 1.39 1.15
150.0 1.22 1.22 1.28 1.36 1.32 0.96 1.07 1.44 1.20
155.0 1.27 1.27 1.33 1.41 1.37 1.01 1.12 1.49 1.25
160.0 1.32 1.32 1.38 1.46 1.42 1.06 1.17 1.54 1.30
165.0 1.37 1.37 1.43 1.51 1.47 1.11 1.22 1.59 1.35
170.0 1.42 1.42 1.48 1.56 1.52 1.16 1.27 1.64 1.40
175.0 1.47 1.47 1.53 1.61 1.57 1.21 1.32 1.69 1.45
180.0 1.52 1.52 1.58 1.66 1.62 1.26 1.37 1.74 1.50
185.0 1.57 1.57 1.63 1.71 1.67 1.31 1.42 1.79 1.55
190.0 1.62 1.62 1.68 1.76 1.72 1.36 1.47 1.84 1.60
195.0 1.67 1.67 1.73 1.81 1.77 1.41 1.52 1.89 1.65
200.0 1.72 1.72 1.78 1.86 1.82 1.46 1.57 1.94 1.70
210.0 1.82 1.82 1.88 1.96 1.92 1.56 1.67 2.04 1.80
220.0 1.92 1.92 1.98 2.06 2.02 1.66 1.77 2.14 1.90
230.0 2.02 2.02 2.08 2.16 2.12 1.76 1.87 2.24 2.00
240.0 2.12 2.12 2.18 2.26 2.22 1.86 1.97 2.34 2.10

Table 6: Standard error of effect size estimates: two independent samples (different students in the two tests)
Note:
  1. Note that it does not matter which sample is regarded as sample 1 and which sample 2; the table is symmetric (the values in the first row equal those in the first column, etc.).
n2 n1

10 15 20 25 30 35 40 50 60 75 100 150 200 250 300 500 1000 2000
10 0.45 0.41 0.39 0.37 0.37 0.36 0.35 0.35 0.34 0.34 0.33 0.33 0.32 0.32 0.32 0.32 0.32 0.32
15 0.41 0.37 0.34 0.33 0.32 0.31 0.30 0.29 0.29 0.28 0.28 0.27 0.27 0.27 0.26 0.26 0.26 0.26
20 0.39 0.34 0.32 0.30 0.29 0.28 0.27 0.26 0.26 0.25 0.24 0.24 0.23 0.23 0.23 0.23 0.23 0.22
25 0.37 0.33 0.30 0.28 0.27 0.26 0.25 0.24 0.24 0.23 0.22 0.22 0.21 0.21 0.21 0.20 0.20 0.20
30 0.37 0.32 0.29 0.27 0.26 0.25 0.24 0.23 0.22 0.22 0.21 0.20 0.20 0.19 0.19 0.19 0.19 0.18
35 0.36 0.31 0.28 0.26 0.25 0.24 0.23 0.22 0.21 0.20 0.20 0.19 0.18 0.18 0.18 0.17 0.17 0.17
40 0.35 0.30 0.27 0.25 0.24 0.23 0.22 0.21 0.20 0.20 0.19 0.18 0.17 0.17 0.17 0.16 0.16 0.16
50 0.35 0.29 0.26 0.24 0.23 0.22 0.21 0.20 0.19 0.18 0.17 0.16 0.16 0.15 0.15 0.15 0.14 0.14
60 0.34 0.29 0.26 0.24 0.22 0.21 0.20 0.19 0.18 0.17 0.16 0.15 0.15 0.14 0.14 0.14 0.13 0.13
75 0.34 0.28 0.25 0.23 0.22 0.20 0.20 0.18 0.17 0.16 0.15 0.14 0.14 0.13 0.13 0.12 0.12 0.12
100 0.33 0.28 0.24 0.22 0.21 0.20 0.19 0.17 0.16 0.15 0.14 0.13 0.12 0.12 0.12 0.11 0.10 0.10
150 0.33 0.27 0.24 0.22 0.20 0.19 0.18 0.16 0.15 0.14 0.13 0.12 0.11 0.10 0.10 0.09 0.09 0.08
200 0.32 0.27 0.23 0.21 0.20 0.18 0.17 0.16 0.15 0.14 0.12 0.11 0.10 0.09 0.09 0.08 0.08 0.07
250 0.32 0.27 0.23 0.21 0.19 0.18 0.17 0.15 0.14 0.13 0.12 0.10 0.09 0.09 0.09 0.08 0.07 0.07
300 0.32 0.26 0.23 0.21 0.19 0.18 0.17 0.15 0.14 0.13 0.12 0.10 0.09 0.09 0.08 0.07 0.07 0.06
500 0.32 0.26 0.23 0.20 0.19 0.17 0.16 0.15 0.14 0.12 0.11 0.09 0.08 0.08 0.07 0.06 0.05 0.05
1000 0.32 0.26 0.23 0.20 0.19 0.17 0.16 0.14 0.13 0.12 0.10 0.09 0.08 0.07 0.07 0.05 0.04 0.04
2000 0.32 0.26 0.22 0.20 0.18 0.17 0.16 0.14 0.13 0.12 0.10 0.08 0.07 0.07 0.06 0.05 0.04 0.03

Table 7: Standard error of effect size estimates: two dependent samples (matched students in the two tests)
Note:
  1. STAR raw scores (and stanine scores) tend to have correlations (r) of between 0.8 and 0.9; PAT scores tend to have correlations of between 0.7 (between Year 3 and Year 4 scores) and 0.9 (all other years); and asTTle scores tend to have correlations between 0.6 and 0.9 (most correlations are in the 0.6 to 0.7 range). Use this information to pick the most appropriate column/s for your data.

r
n 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
10 0.42 0.40 0.37 0.35 0.32 0.28 0.24 0.20 0.14
15 0.35 0.33 0.31 0.28 0.26 0.23 0.20 0.16 0.12
20 0.30 0.28 0.26 0.24 0.22 0.20 0.17 0.14 0.10
25 0.27 0.25 0.24 0.22 0.20 0.18 0.15 0.13 0.09
30 0.24 0.23 0.22 0.20 0.18 0.16 0.14 0.12 0.08
35 0.23 0.21 0.20 0.19 0.17 0.15 0.13 0.11 0.08
40 0.21 0.20 0.19 0.17 0.16 0.14 0.12 0.10 0.07
50 0.19 0.18 0.17 0.15 0.14 0.13 0.11 0.09 0.06
60 0.17 0.16 0.15 0.14 0.13 0.12 0.10 0.08 0.06
75 0.15 0.15 0.14 0.13 0.12 0.10 0.09 0.07 0.05
100 0.13 0.13 0.12 0.11 0.10 0.09 0.08 0.06 0.04
150 0.11 0.10 0.10 0.09 0.08 0.07 0.06 0.05 0.04
200 0.09 0.09 0.08 0.08 0.07 0.06 0.05 0.04 0.03
250 0.08 0.08 0.07 0.07 0.06 0.06 0.05 0.04 0.03
300 0.08 0.07 0.07 0.06 0.06 0.05 0.04 0.04 0.03
500 0.06 0.06 0.05 0.05 0.04 0.04 0.03 0.03 0.02
1000 0.04 0.04 0.04 0.03 0.03 0.03 0.02 0.02 0.01
2000 0.03 0.03 0.03 0.02 0.02 0.02 0.02 0.01 0.01

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