Identifying high impact school improvements using conditional mean independent correlations and growth functions

Figures & data

Table

1. Culture and climate (y1)	Perceived school culture and climate
Example item: ‘People at this school are friendly to me.’
2. Belonging (y2)	Perceived sense of belonging
Example item: ‘I fit in with the students at this school.’
3. Safety (y3)	Perceived safety
Example item: ‘Students at this school are not threatened or bullied.’
4. Educator trust (y4)	Students’ trust in their educators (teachers and school principal)
Example item: ‘My teacher really cares about me.’
5. Student-led learning (y5)	Perceived student-led learning experiences, such as goal setting and self-paced learning
Example item: ‘My teacher and I work together to set goals for my learning.’
6. Relevancy of schoolwork (y6)	Perceived relevancy of schoolwork
Example item: ‘I learn about important things.’
7. Teacher interactions (y7)	Perceived prevalence of student-teacher interactions that support learning
Example item: ‘My teacher is available when I need him or her.’
8. Peer interactions (y8)	Perceived prevalence of peer interactions that support learning
Example item: ‘I can ask other students for help.’
9. Usefulness of mobile devices (y9)	Perceived usefulness of mobile devices for Learning
Example item: ‘My [mobile device] supports my learning.’

Table 1. Descriptive statistics of student perceptions on all domains subject to improvement.

Scales and variable names		N	M	SD	Min	Max	Relative Scores	Cronbach’s Alpha
Culture and climate	y1	684	4.34	0.85	1	6^a	72%	0.83
Belonging	y2	684	4.62	0.84	1	6	77%	0.76
Safety	y3	684	3.86	1.21	1	6	64%	0.63
Educator trust	y4	684	4.63	0.75	1	6	77%	0.92
Student-led learning	y5	684	3.26	0.62	1	5^b	65%	0.77
Relevancy of schoolwork	y6	684	3.29	0.79	1	5	66%	0.67
Teacher interactions	y7	684	3.41	0.69	1	5	68%	0.89
Peer interactions	y8	684	3.55	0.58	1	5	71%	0.69
Usefulness of mobile devices	y9	684	3.91	0.82	1	5	78%	0.76

^a Scores are based on a multi-item scale based on a six-point Likert scale varying from strongly disagree to strongly agree.

^b Scores are based on a multi-item scale based on a five-point Likert scale varying from almost never to almost always.

Table 2. Pearson correlation coefficients based on the total scores across domains.

		y1	y2	y3	y4	y5	y6	y7	y8	y9
Culture and climate	y1	1
Belonging	y2	0.60	1
Safety	y3	0.10	0.18	1
Educator trust	y4	0.32	0.53	0.39	1
Student-led learning	y5	0.41	0.34	0.05	0.37	1
Relevancy of schoolwork	y6	0.36	0.28	−0.07	0.22	0.56	1
Student-teacher interactions	y7	0.43	0.36	0.06	0.40	0.69	0.55	1
Student-peer interactions	y8	0.39	0.47	0.18	0.42	0.52	0.40	0.48	1
Usefulness of mobile devices	y9	0.19	0.17	0.15	0.27	0.37	0.29	0.37	0.33	1.00

Figure 1. Estimated conditional mean independent correlations.

Table 3. Estimated Conditional Mean Independent Correlations (CMIC) between domains.

		CMIC for pair $\left\{y_i,y_j\right\}$ (S.E)									R^2
		y1	y2	y3	y4	y5	y6	y7	y8	y9
Culture and climate	y1	1.00									0.48
Belonging	y2	0.72 (0.02)	1.00								0.45
Safety	y3	0.19 (0.03)	−0.20 (0.03)	1.00							0.27
Educator trust	y4	−0.10 (0.03)	0.47 (0.03)	0.40 (0.02)	1.00						0.48
Student-led learning	y5	0.13 (0.03)	−0.18 (0.03)	−0.16 (0.03)	0.12 (0.03)	1.00					0.53
Relevancy of schoolwork	y6	0.05 (0.03)	0.03 (0.03)	−0.11 (0.03)	−0.06 (0.03)	0.37 (0.02)	1.00				0.43
Student-teacher interactions	y7	0.03 (0.03)	−0.05 (0.03)	0.01 (0.02)	0.19 (0.03)	0.49 (0.02)	0.18 (0.02)	1.00			0.54
Student-peer interactions	y8	0.06 (0.03)	0.24 (0.03)	0.07 (0.03)	0.01 (0.03)	0.22 (0.03)	0.17 (0.03)	0.10 (0.03)	1.00		0.43
Usefulness of mobile devices	y9	−0.03 (0.03)	−0.07 (0.02)	0.22 (0.03)	0.09 (0.03)	0.17 (0.02)	0.11 (0.03)	0.08 (0.02)	0.18 (0.02)	1.00	0.20

Figure 2. Estimates and confidence intervals of the unrestricted and restricted Conditional Mean Independent Correlations (CMIC). The x axis represents the direction and strength of the CMIC coefficient between the improvement domain that is written vertically and the domain that is written horizontally on the left side of the graph.

Figure 3. Estimates and confidence intervals of the Conditional Mean Independent Correlations (CMIC) with and without inclusion of observed background characteristics. The x axis represents the direction and strength of the CMIC coefficient between the improvement domain that is written vertically and the domain that is written horizontally on the left side of the graph.

Table 4. Ranking highest impact improvement based on Maximize Growth (MG).

Ranking based on MG	Overall growth score $G_{yi}$
1. Student-led learning	2.16
2. Educator trust	2.10
3. Peer interactions	2.04
4. Culture and climate	2.03
5. Teacher interactions	2.02
6. Belonging	1.97
7. Relevancy of schoolwork	1.75
8. Usefulness of mobile devices	1.71
9. Safety	1.41

Table 5. Ranking highest impact improvement based on Maximize Growth with Preference Weights (MG-PW).

Ranking based on MG-PW	Pref. Prop. (p)	Weight (p*n)	Overall growth score $G_{yi}$
1. Culture and climate	0	0	2.89
2. Relevancy of schoolwork	1/3	3	2.77
3. Belonging	1/3	3	2.50
4. Educator trust	0	0	2.41
5. Safety	1/3	3	2.07
6. Peer interactions	0	0	1.46
7. Usefulness of mobile devices	0	0	0.76
8. Teacher interactions	0	0	0.42
9. Student-led learning	0	0	0.11

Table 6. Ranking highest impact improvement based on Maximize Growth with Inequality Penalty (MG-IP).

Ranking based on MG-IP	Penalty with λ=0.5	Overall growth score $G_{yi}$
1. Educator trust	20%	1.68
2. Culture and climate	27%	1.48
3. Peer interactions	31%	1.41
4. Safety	0%	1.41
5. Teacher interactions	33%	1.35
6. Student-led learning	39%	1.32
7. Usefulness of mobile devices	26%	1.27
8. Belonging	40%	1.18
9. Relevancy of schoolwork	37%	1.10

Figure 4. Rankings of highest impact improvement domains based on CMIC and growth functions and administrators’ reports. The rank-order values are based upon the numbers 1–9.