Table 4.

Letter parameters for IRT and DIF models in the combined sample.

Letter	Stage 2 2PL IRT model		Stage 3 DIF model					Stage 4 2PL IRT model accounting for first initial
	Discrimination	Difficulty	Discrimination	Not first letter of name	First letter of name			Discrimination	Difficulty
				Difficulty	Difficulty	Log odds	p-value
A	1.77	-0.99	1.78	-0.95	-1.33	3.22	.001	1.80	-0.95
B	1.54	-1.06	1.55	-1.04	-2.11	16.63	.005	1.53	-1.04
C	1.81	-0.83	1.950	-0.76	-1.47	10.30	<.001	1.94	-0.76
D	1.80	-0.54	1.87	-0.49	-1.08	6.44	<.001	1.90	-0.49
E	1.76	-0.62	1.86	-0.57	-1.40	13.97	<.001	1.89	-0.57
F	1.98	-0.45	2.00	-0.44	-1.21	13.62	.037	2.01	-0.44
G	1.77	-0.34	1.82	-0.32	-1.66	62.69	<.001	1.82	-0.32
H	1.86	-0.59	1.94	-0.56	-9.92a			1.94	-0.56
I	1.71	-0.31	1.72	-0.30	-0.73	3.49	.154	1.72	-0.30
J	1.67	-0.40	1.80	-0.32	-1.00	8.18	<.001	1.84	-0.31
K	1.73	-0.57	1.87	-0.49	-1.44	20.47	<.001	1.90	-0.49
L	2.13	-0.46	2.23	-0.42	-1.16	16.05	<.001	2.27	-0.42
M	1.54	-0.58	1.63	-0.52	-1.42	12.32	<.001	1.61	-0.51
N	1.82	-0.33	1.88	-0.30	-1.13	14.27	<.001	1.87	-0.30
O	1.83	-1.24	1.82	-1.23	-1.97	9.78	.152	1.80	-1.24
P	2.06	-0.63	2.06	-0.62	-1.08	5.04	.075	2.06	-0.62
Q	1.68	-0.31	1.69	-0.30	-8.96a			1.69	-0.30
R	2.17	-0.56	2.29	-0.51	-1.39	30.52	<.001	2.32	-0.50
S	2.24	-0.66	2.30	-0.62	-1.10	6.54	<.001	2.33	-0.62
T	1.76	-0.60	1.79	-0.56	-1.07	4.69	<.001	1.82	-0.56
U	1.62	-0.15	1.63	-0.14	-7.77a			1.63	-0.14
V	1.86	0.03	1.89	0.04	-1.31	76.71	.012	1.89	0.04
W	1.20	-0.55	1.20	-0.54	-1.21	3.85	.372	1.19	-0.54
X	1.07	-0.66	1.07	-0.65	-1.28	3.13	.375	1.07	-0.65
Y	1.59	-0.42	1.59	-0.41	-8.88a			1.60	-0.41
Z	1.71	-0.43	1.74	-0.41	-1.34	15.63	.005	1.75	-0.41
First letter b								1.56	-1.34

Note.

^aEstimates for these letters were unstable due to lack of variability in the joint distributions.

^bItem coding whether children correctly responded to the first letters of their first names.