Does educational leadership enhance instructional quality and student achievement? The case of Austrian primary school leaders

Figures & data

Figure 1. Conceptual framework used in this study.

Table 1. Psychometric properties of the leadership and instructional variables

Model	# Items	# Par	Chi^2	df	Chi^2/df	CFI	TLI	RMSEA	SRMR	Mean	SD	Alpha	Omega
School leadership
Setting directions	4	32	28.43	12	2.37	.984	.964	.015	.026	2.912	0.611	0.774	0.800
Managing instructional processes	4									2.748	0.523	0.683	0.680
Instructional quality
Practical orientation	4	22	10.73	2	5.37	1.000	.999	.008	.015	1.49	1.27	0.792	0.960
Cognitive activation – elaboration	4	22	19.81	2	9.91	1.000	.998	.011	.024	1.34	1.06	0.698	0.888
Differentiation	3	15	0.00	0	-	1.000	1.000	.000	.000	0.82	1.87	0.869	0.960
Perceived clarity	3	15	0.01	0	-	1.000	1.000	.000	.001	1.74	1.22	0.636	0.889
Cognitive activation – problem solving^a	3	15	0.00	0	-	1.000	1.000	.000	.000	1.50	1.84	0.884	0.985
Support of meta-cognition	3	15	0.00	0	-	1.000	1.000	.000	.000	1.30	1.77	0.893	0.984
Support of motivation^a	3	15	0.00	0	-	1.000	1.000	.000	.000	1.63	1.42	0.742	0.949
Consideration of students’ voice	4	22	172.99	2	86.50	.999	.994	.034	.022	1.17	1.87	0.908	0.967
Perceived discipline	3	14	1.80	1	1.80	1.000	1.000	.003	.002	1.45	1.60	0.878	0.986
Perceived pace of teaching	2	22	10.73	2	5.37	1.000	.999	.008	.015	1.91	1.73	0.874	0.991

^aError variance of one indicator item was fixed to zero for convergence reasons. While alpha assumes a) that each indicator variable contributes equally to the factor, i.e. same loadings (tau-equivalence) and b) that the error variances of the indicators are uncorrelated, omega is based on neither assumption. Omega represents a (hierarchical) coefficient that gives the proportion of variance in scale scores accounted for by a factor (McDonald, 1999). Regardless of whether alpha or omega is used, low values indicate that it makes no sense to compute a sum score.

Table 2. Model fit indices

	Models without control variables								Models controlling for the social composition of the student body
Model	# Par	Chi^2	df	Chi^2/df	CFI	TLI	RMSEA	SRMR L2	# Par	Chi^2	df	Chi^2/df	CFI	TLI	RMSEA	SRMR L2
1	64	1445.58	55	26.28	.986	.977	.019	.030	104	1845.60	119	15.51	.983	.972	.014	.028
2	64	3677.55	55	66.86	.942	.907	.030	.037	104	4455.30	119	37.44	.931	.889	.022	.041
3	55	1876.15	45	41.69	.984	.974	.023	.025	95	2173.15	101	21.52	.982	.970	.017	.021
4	55	3282.01	45	72.93	.916	.866	.031	.054	95	3790.52	101	37.53	.910	.850	.022	.045
5	55	1519.65	45	33.77	.988	.981	.021	.024	95	1865.31	101	18.47	.986	.977	.015	.018
6	55	2039.83	45	45.33	.985	.976	.025	.026	97	2353.35	99	23.77	.983	.972	.018	.021
7	55	1975.35	45	43.90	.970	.952	.024	.035	95	2355.00	101	23.32	.967	.944	.017	.026
8	64	1795.04	55	32.64	.991	.986	.021	.023	104	2077.85	119	17.46	.990	.984	.015	.018
9	53	1425.29	47	30.33	.987	.981	.020	.025	93	1616.98	103	15.70	.987	.979	.014	.017
10	49	2541.72	34	74.76	.965	.941	.032	.029	89	2762.64	82	33.69	.965	.937	.021	.019

Models 1 to 10 differ only with respect to the mediator variable: 1 practical orientation, 2 cognitive activation – elaboration, 3 differentiation, 4 perceived clarity, 5 cognitive activation – problem solving, 6 support of meta-cognition, 7 support of motivation, 8 consideration of students’ voice, 9 perceived discipline, 10 perceived pace of teaching. # Par = number of parameters, Chi² = chi square value, df = degrees of freedom, CFI = comparative fit index, TLI = Tucker–Lewis index, RMSEA = root mean square error of approximation, SRMR = standardized root mean square residual, L2 = level 2 (here, class level).

Table 3. Standardized direct effects (β) of the three school leadership factors and instructional quality on students’ mathematics achievement

	Models without control variables								Models controlling for the social composition of the student body
Model	Global	p	SetDir	p	InstPro	p	InstQua	p	Global	p	SetDir	p	InstPro	p	InstQua	p
1	.059	.007	−.001	.961	−.101	.000	.143	.000	.019	.264	.009	.686	−.043	.079	.090	.000
2	.060	.007	.001	.980	−.106	.000	.128	.000	.019	.263	.009	.669	−.044	.069	.106	.000
3	.049	.022	.002	.936	−.099	.001	.220	.000	.015	.382	.013	.566	−.043	.077	.106	.000
4	.058	.008	−.002	.927	−.092	.002	.210	.000	.019	.261	.008	.732	−.038	.120	.136	.000
5	.059	.006	−.009	.709	−.089	.002	.318	.000	.027	.106	−.002	.923	−.041	.091	.193	.000
6	.058	.008	−.002	.952	−.103	.000	.178	.000	.018	.289	.010	.657	−.044	.072	.101	.000
7	.055	.010	.002	.941	−.073	.013	.341	.000	.019	.264	.011	.616	−.031	.209	.188	.000
8	.050	.019	.000	.988	−.098	.001	.246	.000	.023	.165	−.002	.900	−.046	.060	.118	.000
9	.066	.001	−.018	.347	−.027	.164	.384	.000	.027	.103	−.003	.851	−.001	.924	.241	.000
10	.066	.002	−.023	.240	−.031	.124	.430	.000	.027	.101	−.002	.915	−.006	.715	.239	.000

Models 1 to 10 differ only with respect to the mediator variable: 1 practical orientation, 2 cognitive activation – elaboration, 3 differentiation, 4 perceived clarity, 5 cognitive activation – problem solving, 6 support of meta-cognition, 7 support of motivation, 8 consideration of students’ voice, 9 perceived discipline, 10 perceived pace of teaching. Global = global school leader factor, SetDir = specific school leader factor ‘setting directions’, InstPro = specific school leader factor ‘managing instructional processes’, InstQua = instructional quality, p = p value.

Table 4. Standardized effects (β) of the three school leadership factors on instructional quality in mathematics

	Models without control variables						Models controlling for the social composition of the student body
Model	Global	p	SetDir	p	InstPro	p	Global	p	SetDir	p	InstPro	p
1	−.003	.915	.035	.243	−.046	.216	−.019	.450	.047	.149	−.028	.448
2	−.009	.766	.018	.586	−.008	.855	−.017	.533	.031	.396	.000	.999
3	.047	.063	.005	.853	−.038	.281	.030	.228	−.001	.985	−.017	.630
4	.002	.944	.029	.396	−.077	.057	−.015	.586	.040	.270	−.055	.168
5	.001	.960	.039	.153	−.060	.091	.001	.984	−.018	.524	−.043	.281
6	.009	.744	.026	.360	−.028	.433	−.003	.892	.029	.368	−.012	.730
7	.015	.596	.002	.957	−.104	.006	−.006	.825	.007	.842	−.076	.040
8	.039	.116	.014	.614	−.040	.251	.031	.179	−.022	.378	−.017	.639
9	.021	.408	−.006	.796	−.086	.000	−.002	.942	−.015	.558	−.071	.001
10	.017	.532	.007	.760	−.069	.010	−.005	.848	−.024	.376	−.054	.028

Models 1 to 10 differ only with respect to the mediator variable: 1 practical orientation, 2 cognitive activation – elaboration, 3 differentiation, 4 perceived clarity, 5 cognitive activation – problem solving, 6 support of meta-cognition, 7 support of motivation, 8 consideration of students’ voice, 9 perceived discipline, 10 perceived pace of teaching. Global = global school leader factor, SetDir = specific school leader factor ‘setting directions’, InstPro = specific school leader factor ‘managing instructional processes’. p = p value.

Table 5. Unstandardized indirect effects (b) of the three school leadership factors via instructional quality on students’ mathematics achievement

	Models without control variables						Models controlling for the social composition of the student body
Model	Global	p	SetDir	p	InstPro	p	Global	p	SetDir	p	InstPro	p
1	.000	.915	.000	.260	.000	.223	−.001	.455	.002	.180	−.001	.453
2	.000	.766	.000	.588	.000	.856	−.001	.535	.002	.405	.000	.998
3	.010	.067	.000	.853	.000	.279	.002	.239	.000	.985	−.001	.629
4	.000	.944	.000	.401	−.010	.061	−.001	.588	.003	.285	−.004	.181
5	.000	.960	.010	.157	−.010	.090	.000	.984	−.002	.526	−.004	.280
6	.000	.744	.000	.366	.000	.431	.000	.893	.001	.374	−.001	.730
7	.000	.596	.000	.957	−.020	.006	−.001	.825	.001	.842	−.007	.045
8	.010	.119	.000	.615	−.010	.248	.002	.186	−.001	.384	−.001	.638
9	.000	.408	.000	.795	−.020	.001	.000	.942	−.002	.559	−.008	.002
10	.000	.532	.000	.760	−.010	.011	−.001	.848	−.003	.378	−.006	.032

Models 1 to 10 differ only with respect to the mediator variable: 1 practical orientation, 2 cognitive activation – elaboration, 3 differentiation, 4 perceived clarity, 5 cognitive activation – problem solving, 6 support of meta-cognition, 7 support of motivation, 8 consideration of students’ voice, 9 perceived discipline, 10 perceived pace of teaching. Global = global school leader factor, SetDir = specific school leader factor ‘setting directions’, InstPro = specific school leader factor ‘managing instructional processes’. p = p value. Control variables are GPA, highest parental occupational status, books at home, migration background, and language spoken at home.

McDonald, R. P. (1999). Test theory: A unified treatment. Lawrence Erlbaum.

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