Transformation of Rasch model logits for enhanced interpretability

Table 1 Raw total ESS scores, linear logit locations and transformations to different score ranges

Columns:
A	B		C		D		E		F		G		H
			Linear logit transformations^a
			0-24 range (s = 2.79)		0-10 range (s = 1.16)		0-100 range (s = 11.64)		LMD (s = 4.00)		SEM (s = 1.96)		LSD (s = 1.40)
Raw total score	Logit location	Logit SE	New location	New SE	New location	New SE	New location	New SE	New location	New SE	New location	New SE	New location	New SE
0^b	-4.323	1.28	0	3.6	0	1.5	0	14.9	0	5.1	0	2.5	0	1.8
1	-3.428	0.91	3	2.5	1	1.1	10	10.6	4	3.6	2	1.8	1	1.3
2	-2.805	0.73	4	2.0	2	0.8	18	8.5	6	2.9	3	1.4	2	1.0
3	-2.373	0.63	5	1.8	2	0.7	23	7.4	8	2.5	4	1.2	3	0.9
4	-2.029	0.58	6	1.6	3	0.7	27	6.7	9	2.3	4	1.1	3	0.8
5	-1.732	0.54	7	1.5	3	0.6	30	6.3	10	2.2	5	1.1	4	0.8
6	-1.462	0.52	8	1.5	3	0.6	33	6.0	11	2.1	6	1.0	4	0.7
7	-1.210	0.50	9	1.4	4	0.6	36	5.9	12	2.0	6	1.0	4	0.7
8	-0.971	0.49	9	1.4	4	0.6	39	5.7	13	2.0	7	1.0	5	0.7
9	-0.740	0.49	10	1.4	4	0.6	42	5.6	14	1.9	7	1.0	5	0.7
10	-0.514	0.48	11	1.3	4	0.6	44	5.6	15	1.9	7	0.9	5	0.7
11	-0.289	0.48	11	1.3	5	0.6	47	5.6	16	1.9	8	0.9	6	0.7
12	-0.060	0.49	12	1.4	5	0.6	50	5.7	17	1.9	8	1.0	6	0.7
13	0.175	0.49	13	1.4	5	0.6	52	5.7	18	2.0	9	1.0	6	0.7
14	0.420	0.50	13	1.4	6	0.6	55	5.8	19	2.0	9	1.0	7	0.7
15	0.676	0.51	14	1.4	6	0.6	58	5.9	20	2.0	10	1.0	7	0.7
16	0.941	0.52	15	1.5	6	0.6	61	6.0	21	2.1	10	1.0	7	0.7
17	1.213	0.53	15	1.5	6	0.6	64	6.2	22	2.1	11	1.0	8	0.7
18	1.492	0.54	16	1.5	7	0.6	68	6.3	23	2.2	11	1.1	8	0.8
19	1.785	0.56	17	1.6	7	0.7	71	6.6	24	2.3	12	1.1	9	0.8
20	2.103	0.60	18	1.7	7	0.7	75	6.9	26	2.4	13	1.2	9	0.8
21	2.466	0.65	19	1.8	8	0.8	79	7.5	27	2.6	13	1.3	10	0.9
22	2.902	0.73	20	2.0	8	0.8	84	8.5	29	2.9	14	1.4	10	1.0
23	3.485	0.89	22	2.5	9	1.0	91	10.4	31	3.6	15	1.7	11	1.2
24^c	4.265	1.22	24	3.4	10	1.4	100	14.2	34	4.9	17	2.4	12	1.7

ESS Epworth Sleepiness Scale, SE standard error, s spacing factor, LMD least measurable difference, SEM standard error of measurement, LSD least significant difference
^aSee Equations 4-8 for transformation formulae
^bEstimated based on a hypothetical raw score of 0.185 (RUMM2030 Professional Edition, version 5.4)
^cEstimated based on a hypothetical raw score of 23.795 (RUMM2030 Professional Edition, version 5.4)

ISSN: 1471-2288