How Much Difference Does It Make? Notes on Understanding, Using, and Calculating Effect Sizes for Schools - Tables

Publication Details

A good way of presenting differences between groups or changes over time in test scores or other measures is by ‘effect sizes’, which allow us to compare things happening in different classes, schools or subjects regardless of how they are measured. This booklet is designed to help school staff to understand and use effect sizes, and includes handy tips and warnings as well as useful tables to calculate effect size values from change scores on standardised tests.

Author(s): Ian Schagen, Research Division [Ministry of Education], Edith Hodgen [NZCER]

Date Published: March 2009

Tables

Links to:

• Table 1: Effect sizes for PAT scores
• Table 2: Effect sizes for STAR test scores
  
• Table 3: Effect sizes for asTTle Mathematics scores
  
• Table 4: Effect sizes for asTTle Reading scores
  
• Table 5: Effect sizes for asTTle Writing scores
  
• Table 6: Standard error of effect size estimates: two independent samples (different students in the two tests)
• Table 7: Standard error of effect size estimates: two dependent samples (matched students in the two tests)
  

Table 1: Effect sizes for PAT scores

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.
				PAT Mathematics							PAT Reading Comprehension							PAT Reading Vocabulary
Current year level		4	5	6	7	8	9	10	4	5	6	7	8	9	10	4	5	6	7	8	9	10
Mean PAT score		31.8	40.3	46.4	50.9	55.5	62.6	66.6	28.8	35.8	45.0	53.2	60.4	67.0	76.5	32.4	40.9	48.7	55.0	60.1	65.7	70.5
SD of PAT score		13.1	13.2	12.4	11.8	12.3	11.3	11.6	15.2	13.2	12.7	12.6	12.3	12.2	12.4	16.0	15.8	15.0	14.3	14.8	14.7	14.8
Difference between mean scores	7.0	-0.11	-0.11	0.07	0.21	0.20	-0.01	0.26	0.00	0.00	-0.17	-0.10	-0.02	0.03	-0.20	-0.09	-0.09	-0.05	0.05	0.13	0.10	0.15
	7.5	-0.08	-0.08	0.11	0.25	0.24	0.04	0.30	0.03	0.04	-0.13	-0.06	0.02	0.07	-0.16	-0.06	-0.06	-0.02	0.08	0.16	0.13	0.18
	8.0	-0.04	-0.04	0.15	0.30	0.28	0.08	0.34	0.07	0.08	-0.09	-0.02	0.07	0.11	-0.12	-0.03	-0.03	0.01	0.12	0.20	0.16	0.22
	8.5	0.00	0.00	0.19	0.34	0.32	0.12	0.39	0.10	0.11	-0.06	0.02	0.11	0.16	-0.08	0.00	0.00	0.05	0.15	0.23	0.20	0.25
	9.0	0.04	0.04	0.23	0.38	0.36	0.17	0.43	0.13	0.15	-0.02	0.06	0.15	0.20	-0.04	0.03	0.03	0.08	0.19	0.26	0.23	0.28
	9.5	0.08	0.08	0.27	0.42	0.40	0.21	0.47	0.16	0.19	0.02	0.10	0.19	0.24	0.00	0.06	0.06	0.11	0.22	0.30	0.27	0.32
	10.0	0.11	0.11	0.31	0.47	0.44	0.26	0.52	0.20	0.23	0.06	0.14	0.23	0.28	0.04	0.09	0.09	0.15	0.26	0.33	0.30	0.35
	10.5	0.15	0.15	0.35	0.51	0.48	0.30	0.56	0.23	0.27	0.10	0.18	0.27	0.32	0.08	0.13	0.13	0.18	0.29	0.36	0.33	0.39
	11.0	0.19	0.19	0.40	0.55	0.52	0.35	0.60	0.26	0.30	0.14	0.22	0.31	0.36	0.12	0.16	0.16	0.21	0.33	0.40	0.37	0.42
	11.5	0.23	0.23	0.44	0.59	0.56	0.39	0.65	0.30	0.34	0.18	0.26	0.35	0.40	0.16	0.19	0.19	0.25	0.36	0.43	0.40	0.45
	12.0	0.27	0.27	0.48	0.64	0.60	0.43	0.69	0.33	0.38	0.22	0.30	0.39	0.44	0.20	0.22	0.22	0.28	0.40	0.47	0.44	0.49
	12.5	0.30	0.30	0.52	0.68	0.64	0.48	0.73	0.36	0.42	0.26	0.34	0.43	0.48	0.24	0.25	0.25	0.31	0.43	0.50	0.47	0.52
	13.0	0.34	0.34	0.56	0.72	0.68	0.52	0.78	0.39	0.45	0.30	0.38	0.47	0.52	0.28	0.28	0.28	0.35	0.47	0.53	0.50	0.55
	13.5	0.38	0.38	0.60	0.76	0.72	0.57	0.82	0.43	0.49	0.34	0.42	0.51	0.57	0.32	0.31	0.32	0.38	0.50	0.57	0.54	0.59
	14.0	0.42	0.42	0.64	0.81	0.76	0.61	0.86	0.46	0.53	0.38	0.46	0.55	0.61	0.36	0.34	0.35	0.41	0.54	0.60	0.57	0.62
	14.5	0.45	0.45	0.68	0.85	0.80	0.65	0.91	0.49	0.57	0.42	0.50	0.59	0.65	0.40	0.38	0.38	0.45	0.57	0.64	0.61	0.66
	15.0	0.49	0.49	0.72	0.89	0.85	0.70	0.95	0.53	0.61	0.46	0.54	0.63	0.69	0.44	0.41	0.41	0.48	0.61	0.67	0.64	0.69
	15.5	0.53	0.53	0.76	0.93	0.89	0.74	0.99	0.56	0.64	0.50	0.58	0.67	0.73	0.48	0.44	0.44	0.51	0.64	0.70	0.67	0.72
	16.0	0.57	0.57	0.80	0.97	0.93	0.79	1.03	0.59	0.68	0.54	0.62	0.72	0.77	0.52	0.47	0.47	0.55	0.68	0.74	0.71	0.76
	16.5	0.61	0.61	0.84	1.02	0.97	0.83	1.08	0.63	0.72	0.57	0.66	0.76	0.81	0.56	0.50	0.51	0.58	0.71	0.77	0.74	0.79
	17.0	0.64	0.64	0.88	1.06	1.01	0.88	1.12	0.66	0.76	0.61	0.70	0.80	0.85	0.60	0.53	0.54	0.61	0.75	0.80	0.78	0.82
	17.5	0.68	0.68	0.92	1.10	1.05	0.92	1.16	0.69	0.80	0.65	0.74	0.84	0.89	0.65	0.56	0.57	0.65	0.78	0.84	0.81	0.86
	18.0	0.72	0.72	0.96	1.14	1.09	0.96	1.21	0.72	0.83	0.69	0.78	0.88	0.93	0.69	0.59	0.60	0.68	0.82	0.87	0.84	0.89
	18.5	0.76	0.76	1.00	1.19	1.13	1.01	1.25	0.76	0.87	0.73	0.82	0.92	0.98	0.73	0.63	0.63	0.71	0.85	0.91	0.88	0.93
	19.0	0.80	0.80	1.04	1.23	1.17	1.05	1.29	0.79	0.91	0.77	0.86	0.96	1.02	0.77	0.66	0.66	0.75	0.89	0.94	0.91	0.96
	19.5	0.83	0.83	1.08	1.27	1.21	1.10	1.34	0.82	0.95	0.81	0.90	1.00	1.06	0.81	0.69	0.70	0.78	0.92	0.97	0.95	0.99
	20.0	0.87	0.87	1.12	1.31	1.25	1.14	1.38	0.86	0.98	0.85	0.94	1.04	1.10	0.85	0.72	0.73	0.81	0.96	1.01	0.98	1.03
	20.5	0.91	0.91	1.16	1.36	1.29	1.19	1.42	0.89	1.02	0.89	0.98	1.08	1.14	0.89	0.75	0.76	0.85	0.99	1.04	1.01	1.06
	21.0	0.95	0.95	1.20	1.40	1.33	1.23	1.47	0.92	1.06	0.93	1.02	1.12	1.18	0.93	0.78	0.79	0.88	1.03	1.07	1.05	1.09
	21.5	0.98	0.98	1.24	1.44	1.37	1.27	1.51	0.95	1.10	0.97	1.06	1.16	1.22	0.97	0.81	0.82	0.91	1.06	1.11	1.08	1.13
	22.0	1.02	1.02	1.28	1.48	1.41	1.32	1.55	0.99	1.14	1.01	1.10	1.20	1.26	1.01	0.84	0.85	0.95	1.10	1.14	1.12	1.16
	22.5	1.06	1.06	1.32	1.53	1.46	1.36	1.59	1.02	1.17	1.05	1.13	1.24	1.30	1.05	0.88	0.89	0.98	1.13	1.18	1.15	1.20
	23.0	1.10	1.10	1.36	1.57	1.50	1.41	1.64	1.05	1.21	1.09	1.17	1.28	1.34	1.09	0.91	0.92	1.01	1.17	1.21	1.18	1.23
	23.5	1.14	1.14	1.40	1.61	1.54	1.45	1.68	1.09	1.25	1.13	1.21	1.33	1.39	1.13	0.94	0.95	1.05	1.20	1.24	1.22	1.26
	24.0	1.17	1.17	1.44	1.65	1.58	1.50	1.72	1.12	1.29	1.17	1.25	1.37	1.43	1.17	0.97	0.98	1.08	1.24	1.28	1.25	1.30
	24.5	1.21	1.21	1.48	1.69	1.62	1.54	1.77	1.15	1.33	1.20	1.29	1.41	1.47	1.21	1.00	1.01	1.11	1.27	1.31	1.29	1.33
	25.0	1.25	1.25	1.52	1.74	1.66	1.58	1.81	1.18	1.36	1.24	1.33	1.45	1.51	1.25	1.03	1.04	1.15	1.31	1.34	1.32	1.36
	25.5	1.29	1.29	1.56	1.78	1.70	1.63	1.85	1.22	1.40	1.28	1.37	1.49	1.55	1.29	1.06	1.08	1.18	1.34	1.38	1.35	1.40
	26.0	1.33	1.33	1.60	1.82	1.74	1.67	1.90	1.25	1.44	1.32	1.41	1.53	1.59	1.33	1.09	1.11	1.21	1.38	1.41	1.39	1.43
	26.5	1.36	1.36	1.65	1.86	1.78	1.72	1.94	1.28	1.48	1.36	1.45	1.57	1.63	1.37	1.13	1.14	1.25	1.41	1.45	1.42	1.47
	27.0	1.40	1.40	1.69	1.91	1.82	1.76	1.98	1.32	1.52	1.40	1.49	1.61	1.67	1.41	1.16	1.17	1.28	1.45	1.48	1.46	1.50
	27.5	1.44	1.44	1.73	1.95	1.86	1.81	2.03	1.35	1.55	1.44	1.53	1.65	1.71	1.45	1.19	1.20	1.31	1.48	1.51	1.49	1.53
	28.0	1.48	1.48	1.77	1.99	1.90	1.85	2.07	1.38	1.59	1.48	1.57	1.69	1.75	1.49	1.22	1.23	1.35	1.52	1.55	1.52	1.57
	28.5	1.52	1.52	1.81	2.03	1.94	1.89	2.11	1.41	1.63	1.52	1.61	1.73	1.80	1.53	1.25	1.27	1.38	1.55	1.58	1.56	1.60
	29.0	1.55	1.55	1.85	2.08	1.98	1.94	2.16	1.45	1.67	1.56	1.65	1.77	1.84	1.57	1.28	1.30	1.41	1.59	1.61	1.59	1.64
	29.5	1.59	1.59	1.89	2.12	2.02	1.98	2.20	1.48	1.70	1.60	1.69	1.81	1.88	1.61	1.31	1.33	1.45	1.62	1.65	1.63	1.67
	30.0	1.63	1.63	1.93	2.16	2.07	2.03	2.24	1.51	1.74	1.64	1.73	1.85	1.92	1.65	1.34	1.36	1.48	1.66	1.68	1.66	1.70
	30.5	1.67	1.67	1.97	2.20	2.11	2.07	2.28	1.55	1.78	1.68	1.77	1.89	1.96	1.69	1.38	1.39	1.51	1.69	1.72	1.69	1.74
	31.0	1.70	1.70	2.01	2.25	2.15	2.12	2.33	1.58	1.82	1.72	1.81	1.93	2.00	1.73	1.41	1.42	1.55	1.73	1.75	1.73	1.77
	31.5	1.74	1.74	2.05	2.29	2.19	2.16	2.37	1.61	1.86	1.76	1.85	1.98	2.04	1.77	1.44	1.46	1.58	1.76	1.78	1.76	1.80
	32.0	1.78	1.78	2.09	2.33	2.23	2.20	2.41	1.64	1.89	1.80	1.89	2.02	2.08	1.81	1.47	1.49	1.61	1.80	1.82	1.80	1.84
	32.5	1.82	1.82	2.13	2.37	2.27	2.25	2.46	1.68	1.93	1.83	1.93	2.06	2.12	1.85	1.50	1.52	1.65	1.83	1.85	1.83	1.87
	33.0	1.86	1.86	2.17	2.42	2.31	2.29	2.50	1.71	1.97	1.87	1.97	2.10	2.16	1.90	1.53	1.55	1.68	1.87	1.89	1.86	1.91

Table 2: Effect sizes for STAR test scores

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

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

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

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 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)

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