Inequality in top performance: an examination of cross-country variation in excellence gaps across different levels of parental socioeconomic status

Figures & data

Table 1. Overview of country-specific characteristics for each country (N = 31).

	Early tracking	Educational standardisation	Proportion of private schools
Australia	−1.043	0.81	0.40
Austria	1.817	0.00	0.13
Belgium	1.018	0.00	0.70
Canada	−1.321	0.51	0.08
Czech Republic	1.621	1.00	0.04
Denmark	−0.870	1.00	0.23
Finland	−0.870	1.00	0.04
Germany	1.862	0.44	0.05
Greece	−0.474	0.00	0.05
Hungary	1.421	1.00	0.13
Iceland	−0.805	1.00	0.01
Ireland	−0.302	1.00	0.62
Israel	−0.063	1.00	0.18
Italy	0.166	1.00	0.06
Japan	−0.474	1.00	0.29
Korea	0.072	1.00	0.37
Latvia	−0.576	1.00	0.01
Luxembourg	0.700	1.00	0.15
Netherlands	0.937	1.00	0.66
New Zealand	−0.419	1.00	0.06
Norway	−1.043	1.00	0.01
Poland	−0.083	1.00	0.02
Portugal	−0.327	0.00	0.15
Slovak Republic	1.621	1.00	0.09
Slovenia	0.117	1.00	0.03
Spain	−1.020	0.00	0.34
Sweden	−0.870	0.00	0.10
Switzerland	−0.138	0.00	0.06
Turkey	1.201	1.00	0.01
United Kingdom	−1.043	1.00	0.06
United States	−1.321	0.09	0.09

Table 2. Descriptive statistics of all variables analysed.

	Mean/proportion	Minimum	Maximum	SD
Dependent variables
Top performance Reading
Plausible value 1	0.086	0	1
Plausible value 2	0.087	0	1
Plausible value 3	0.086	0	1
Plausible value 4	0.086	0	1
Plausible value 5	0.086	0	1
Plausible value 6	0.086	0	1
Plausible value 7	0.086	0	1
Plausible value 8	0.086	0	1
Plausible value 9	0.087	0	1
Plausible value 10	0.087	0	1
Top performance Mathematics
Plausible value 1	0.111	0	1
Plausible value 2	0.111	0	1
Plausible value 3	0.112	0	1
Plausible value 4	0.112	0	1
Plausible value 5	0.113	0	1
Plausible value 6	0.112	0	1
Plausible value 7	0.113	0	1
Plausible value 8	0.112	0	1
Plausible value 9	0.113	0	1
Plausible value 10	0.112	0	1
Main independent variable
Low parental SES (scale)	0	−4.183	7.053	1
Country-level variables
Early tracking	0.0	−1.187	1.982	1.0
Educational standardisation	0.0	−1.657	0.746	1.0
Proportion of private schools	0.0	−0.871	2.678	1.0
Control variables
Female	0.498	0	1
Age	15.778	15.170	16.420	0.290
Ethnicity
Native	0.936	0	1
Migrant	0.064	0	1
Repeated a year
Not a repeater	0.954	0	1
Repeater	0.046	0	1
Private school	0.351	0	1	0.144
School size	762.257	0	7.000	490.489
Availability of school materials	2.022	0	3	0.591
School location
Village	0.082	0	1
Small town	0.218	0	1
Town	0.336	0	1
City	0.246	0	1
Large city	0.118	0	1
GDP per capita	0.0	−1.487	3.174	1.0

Source: PISA 2015; 216,980 students; 8,390 schools; 31 countries.

Figure 1. The percentage of top-performing students in reading within each category of parental SES (N = 31).

Source: PISA 2015.

Figure 2. The percentage of top-performing students in mathematics within each category of parental SES (N = 31).

Source: PISA 2015.

Table 3. Logistic multilevel regression analysis of the probability to be a top-performing student in reading.

	Model 1		Model 2		Model 3		Model 4		Model 5		Model 6		Model 7
	B	SE	B	SE	B	SE	B	SE	B	SE	B	SE	B	SE
Individual level
Intercept	−9.355***	0.619	−9.331***	0.618	−9.336***	0.619	−9.339***	0.619	−9.334***	0.620	−9.336***	0.619	−9.338***	0.619
Low parental SES	−0.632***	0.013	−0.632***	0.013	−0.648***	0.026	−0.649***	0.026	−0.648***	0.026	−0.648***	0.026	−0.649***	0.025
Country level
Early tracking			−0.249∼	0.140	−0.257∼	0.133	−0.226	0.143	−0.256∼	0.133	−0.257∼	0.133	−0.222	0.142
Educational standardisation			0.106	0.128	0.148	0.124	0.146	0.124	0.100	0.130	0.148	0.124	0.097	0.130
Proportion of private schools			0.100	0.134	0.089	0.128	0.089	0.129	0.089	0.128	0.092	0.137	0.086	0.136
Cross-level interaction
Early tracking*low parental SES							0.016	0.026					0.017	0.026
Educational standardisation*low parental SES									−0.023	0.024			−0.024	0.024
Proportion of private schools*low parental SES											0.001	0.026	−0.003	0.026
Control variables
Female	0.385***	0.023	0.385***	0.023	0.384***	0.023	0.384***	0.023	0.384***	0.023	0.384***	0.023	0.384***	0.023
Age	0.354***	0.038	0.354***	0.038	0.354***	0.038	0.354***	0.038	0.354***	0.038	0.354***	0.038	0.354***	0.038
Ethnicity
Native	ref.		ref.		ref.		ref.		ref.		ref.		ref.
Migrant	−0.284***	0.046	−0.284***	0.046	−0.289***	0.045	−0.289***	0.045	−0.289***	0.045	−0.289***	0.045	−0.289***	0.045
Repeated a year
Not a repeater	ref.		ref.			ref.		ref.		ref.		ref.		ref.
Repeater	−1.855***	0.133	−1.854***	0.133	−1.861***	0.134	−1.861***	0.134	−1.862***	0.134	−1.861***	0.134	−1.862***	0.134
Private school	0.243***	0.048	0.242***	0.048	0.238***	0.048	0.238***	0.048	0.239***	0.048	0.238***	0.048	0.239***	0.048
School size	0.000***	0.000	0.000***	0.000	0.000***	0.000	0.000***	0.000	0.000***	0.000	0.000***	0.000	0.000***	0.000
Availability of school materials	0.165***	0.031	0.165***	0.031	0.165***	0.031	0.165***	0.031	0.165***	0.031	0.165***	0.031	0.165***	0.031
School location
Village	ref.		ref.		ref.		ref.		ref.		ref.		ref.
Small town	0.027	0.075	0.027	0.075	0.020	0.075	0.020	0.075	0.019	0.075	0.020	0.075	0.019	0.075
Town	0.106	0.071	0.106	0.071	0.099	0.071	0.099	0.072	0.099	0.071	0.099	0.072	0.099	0.072
City	0.193*	0.074	0.194*	0.074	0.186*	0.074	0.186*	0.074	0.186*	0.074	0.186*	0.074	0.186*	0.074
Large city	0.291**	0.094	0.291**	0.094	0.285**	0.094	0.285**	0.094	0.285**	0.094	0.285**	0.094	0.285**	0.094
GDP per capita	0.185	0.128	0.120	0.127	0.148	0.120	0.148	0.120	0.147	0.120	0.148	0.120	0.148	0.120
Variance statistics
Country variance	0.585		0.517
School variance	0.811		0.811		0.815		0.816		0.815		0.815		0.816
Slope low parental SES					0.014		0.014		0.014		0.014		0.013

Source: PISA 2015; 216,980 students; 8,390 schools; 31 countries.

Logistic multilevel regression models, GlmmPQL in R. ∼p < 0.10; *p < 0.05; **p < 0.01; ***p < 0.001.

Table 4. Logistic multilevel regression analysis of the probability to be a top-performing student in mathematics.

	Model 1		Model 2		Model 3		Model 4		Model 5		Model 6		Model 7
	B	SE	B	SE	B	SE	B	SE	B	SE	B	SE	B	SE
Individual level
Intercept	−8.147***	0.613	−8.136***	0.612	−8.096***	0.616	−8.115***	0.615	−8.094***	0.615	−8.094***	0.616	−8.112***	0.615
Low parental SES	−0.622***	0.014	−0.622***	0.014	−0.652***	0.033	−0.660***	0.030	−0.651***	0.033	−0.651***	0.033	−0.660***	0.029
Country level
Early tracking			−0.103	0.158	−0.209	0.155	−0.044	0.160	−0.208	0.155	−0.208	0.155	−0.042	0.160
Educational standardisation			0.113	0.144	0.153	0.137	0.149	0.138	0.115	0.149	0.153	0.137	0.107	0.146
Proportion of private schools			0.126	0.151	0.099	0.144	0.103	0.145	0.099	0.144	0.137	0.156	0.122	0.154
Cross-level interaction
Early tracking*low parental SES							0.086**	0.030					0.087**	0.030
Educational standardisation*low parental SES									−0.020	0.033			−0.023	0.029
Proportion of private schools*low parental SES											0.018	0.034	0.009	0.030
Control variables
Female	−0.508***	0.020	−0.508***	0.020	−0.510***	0.020	−0.510***	0.020	−0.510***	0.020	−0.510***	0.020	−0.510***	0.020
Age	0.322***	0.037	0.322***	0.037	0.320***	0.037	0.320***	0.037	0.320***	0.037	0.320***	0.037	0.320***	0.037
Ethnicity
Native	ref.		ref.		ref.		ref.		ref.		ref.		ref.
Migrant	−0.212***	0.046	−0.212***	0.046	−0.218***	0.047	−0.218***	0.047	−0.218***	0.047	−0.218***	0.047	−0.218***	0.047
Repeated a year
Not a repeater	ref.		ref.		ref.		ref.		ref.		ref.		ref.
Repeater	−2.002***	0.109	−2.001***	0.109	−2.010***	0.108	−2.010***	0.108	−2.011***	0.108	−2.011***	0.108	−2.010***	0.108
Private school	0.243***	0.045	0.242***	0.045	0.233***	0.045	0.233***	0.045	0.233***	0.045	0.233***	0.045	0.233***	0.045
School size	0.000***	0.000	0.000***	0.000	0.000***	0.000	0.000***	0.000	0.000***	0.000	0.000***	0.000	0.000***	0.000
Availability of school materials	0.202***	0.030	0.202***	0.030	0.199***	0.030	0.199***	0.030	0.199***	0.030	0.199***	0.030	0.199***	0.030
School location
Village	ref.		ref.		ref.		ref.		ref.		ref.		ref.
Small town	0.045	0.068	0.045	0.068	0.034	0.069	0.034	0.069	0.034	0.069	0.034	0.069	0.034	0.069
Town	0.047	0.063	0.047	0.063	0.038	0.064	0.038	0.064	0.038	0.064	0.038	0.064	0.038	0.064
City	0.113∼	0.065	0.113∼	0.065	0.104	0.066	0.104	0.066	0.104	0.066	0.104	0.066	0.104	0.066
Large city	0.254**	0.081	0.253**	0.081	0.247**	0.083	0.247**	0.083	0.246**	0.083	0.246**	0.083	0.247**	0.083
GDP per capita	0.119	0.137	0.086	0.142	0.127	0.136	0.127	0.137	0.126	0.135	0.126	0.135	0.127	0.137
Variance statistics
Country variance	0.688		0.656
School variance	0.920		0.920		0.929		0.930		0.929		0.929		0.930
Slope low parental SES					0.028		0.021		0.028		0.028		0.020

Source: PISA 2015; 216,980 students; 8,390 schools; 31 countries.

Logistic multilevel regression models, GlmmPQL in R. ∼p < 0.10; *p < 0.05; **p < 0.01; ***p < 0.001.