Educational achievement in selective and comprehensive local education authorities: a configurational analysis

Figures & data

Table 1. Perfect implication: sufficiency.

‘if A, then O’ expressed in terms of inclusion, sufficient relationship
	O	Not O
A	Present	Excluded
Not A	Possible	Possible

Figure1. Sufficiency.

Table 2. Example: quasi-sufficiency.

Weaker implication, quasi-sufficient relationship: ‘if A, then (nearly always) O’
	O	Not O
A	602	77
Not A	1158	529

Figure2. Necessity.

Table 3. Example with two conditions.

		O	Not O
A	B	151 (98.7%)	2 (1.3%)
	Not B	451 (85.7%)	75 (14.3%)
Not A	B	140 (98.6%)	2 (1.4%)
	Not B	1018 (65.9%)	527 (34.1%)

Table 4. Truth table example.

A	B	Number of cases	O	Consistency
1	1	153	1	0.987
0	1	142	1	0.986
1	0	526	1	0.857
0	0	1545	0	0.659

Table 5. QCA output example.

	Raw coverage	Unique coverage	Consistency
A+	0.342	0.256	0.887
B	0.165	0.080	0.986
solution coverage: 0.422
solution consistency: 0.904

Figure 3. Venn diagram of overlapping conditions.

Table 6. Truth table, outcome ‘at least A-level’.

Row number	Male	Service class	Working class	High ability	In selective LEA	Number of cases	At least A-level	Consistency
1	1	1	0	1	1	76	1	0.908
2	1	1	0	1	0	41	1	0.854
3	0	1	0	1	0	40	1	0.825
4	1	0	0	1	1	40	1	0.825
5	1	0	1	1	1	43	1	0.791
6	0	1	0	1	1	100	1	0.79
7	1	0	0	1	0	21	0	0.667
8	1	0	1	1	0	35	0	0.657
9	0	0	0	1	1	33	0	0.636
10	1	1	0	0	0	95	0	0.548
11	1	1	0	0	1	117	0	0.521
12	0	0	1	1	1	61	0	0.475
13	0	1	0	0	0	82	0	0.451
14	1	0	0	0	1	98	0	0.449
15	0	0	0	1	0	29	0	0.414
16	0	0	0	0	0	69	0	0.377
17	0	1	0	0	1	128	0	0.375
18	1	0	0	0	0	93	0	0.366
19	0	0	1	1	0	42	0	0.357
20	1	0	1	0	1	265	0	0.328
21	1	0	1	0	0	259	0	0.29
22	0	0	0	0	1	103	0	0.214
23	0	0	1	0	1	244	0	0.148
24	0	0	1	0	0	252	0	0.127

Table 7. QCA output ‘A-level’ outcome.

	Raw coverage	Unique coverage	Consistency
CLASS_S^∗HIGH_ABILITY+	0.227	0.227	0.840
MALE^∗class_s^∗HIGH_ABILITY^∗LEATYPE_SELECTIVE	0.070	0.070	0.807
solution coverage: 0.297
solution consistency: 0.832

Table 8. High-ability cases in selective LEAs.

Truth table row		Social class	Number	Consistency/proportion obtaining at least A-level
1	Male	Service	76	0.908
5	Male	Working	43	0.791
6	Female	Service	100	0.79
12	Female	Working	61	0.475

Table 9. High-ability cases in comprehensive LEAs.

Truth table row		Social class	Number	Consistency/proportion obtaining at least A-level
2	Male	Service	41	0.854
3	Female	Service	40	0.825
8	Male	Working	35	0.657
19	Female	Working	42	0.357

Table 10. Truth table, outcome ‘at least O-level’.

Row number	Male	Service class	Working class	Low ability	In selective LEA	Number of cases	At least O-level	Consistency
1	1	1	0	0	1	166	1	0.964
2	1	1	0	0	0	106	1	0.934
3	0	1	0	0	1	207	1	0.928
4	1	0	0	0	1	107	1	0.925
5	0	0	0	0	0	80	1	0.913
6	0	1	0	0	0	109	1	0.899
7	1	0	0	0	0	72	1	0.875
8	1	0	1	0	0	171	1	0.842
9	0	0	0	0	1	107	1	0.832
10	1	0	1	0	1	174	1	0.822
11	0	0	1	0	1	204	0	0.735
12	0	0	1	0	0	176	0	0.727
13	0	1	0	1	0	13	0	0.615
14	1	0	1	1	1	134	0	0.604
15	1	1	0	1	1	27	0	0.593
16	0	1	0	1	1	21	0	0.571
17	1	1	0	1	0	30	0	0.567
18	1	0	0	1	1	31	0	0.548
19	1	0	1	1	0	123	0	0.528
20	0	0	0	1	0	18	0	0.500
21	1	0	0	1	0	42	0	0.429
22	0	0	1	1	0	118	0	0.339
23	0	0	1	1	1	101	0	0.317
24	0	0	0	1	1	29	0	0.241

Table 11. QCA output ‘at least O-level’ outcome (0.8 cut-off).

	Raw coverage	Unique coverage	Consistency
class_w∗low_ability+	0.496	0.404	0.915
MALE∗class_s∗low_ability	0.255	0.163	0.857
solution coverage: 0.659
solution consistency: 0.893