Table 3 Performance on each task compared with that expected under the substantial-risk benchmark for each instructional year (prior distribution)

Task	Year	Prior distribution	Mean point estimate and the 95% HDI of the posterior distribution		Substantial-risk benchmarks
Task	Year	Prior distribution	Predicted mean for the average subskill score	Effect size	Substantial-risk benchmarks
Letter name identification (correct letter names per minute)	1	Normal(35,5)	22.43 [17.79, 26.93]	−0.74 [−1.15, −0.36]	25, 37, 42 M = 34.7
	2	Normal(53,5)	31.61 [28.23, 34.93]	−0.96 [−1.18, −0.76]	42, 57, 59 M = 52.7
Letter sound identification (correct letter sounds per minute)	1	Normal(20,7)	9.07 [6.85, 11.35]	−1.42 [−2.00, −0.92]	9, 25, 31 M = 21.7
	2	Normal(45,7)	15.80 [13.83, 17.76]	−2.71 [−3.32, −2.09]	30, 52, 55 M = 45.7
	3	Normal(60,8)	14.38 [12.24, 16.57]	−5.30 [−6.68, −3.97]	50, 68, 76 M = 64.7
Non-word reading (correct non-words per minute)	1	Normal(3,1.5)	0.48 [0.10, 1.16]	−5.25 [−9.44, −0.42]	1, 3, 7 M = 3.7
	2	Normal(10,5)	7.66 [6.68, 8.63]	−0.49 [−0.65, −0.34]	5, 14, 15 M = 11.3
	3	Normal(18,0.7)	16.27 [15.22, 17.37]	−0.24 [−0.34, −0.14]	15, 20, 22 M = 19
Oral reading fluency (correct words per minute)	2	Normal(23,8)	10.32 [8.56, 12.17]	−1.28 [−1.64, −0.91]	10, 21, 39 M = 23.3
Oral reading fluency (correct words per minute)	3	Normal(73,13)	22.50 [20.23, 24.69]	−2.71 [−2.99, −2.44]	49, 78, 94 M = 73.7

For each parameter, the prior was defined using the normal distribution (mean and s.d. are indicated in parentheses) and the results columns show the mean point estimate (top row) and the 95% HDI (bottom row) of the posterior distribution. The effect size is Cohen’s d¹⁹ computed from the posterior distribution, with the mean representing the mean standardized distance between performance expected under the substantial-risk benchmark and that achieved by the pupils, and the 95% HDI describing the uncertainty associated with this mean point estimate. The substantial-risk benchmark for each task and instructional year is reported in the rightmost column, with the top row showing the cut-off scores for the beginning, middle and end of each year, respectively, and the bottom row showing the average (M) score across these three time points.

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