Development and validation of a new instrument to measure perceived risks associated with the use of tobacco and nicotine-containing products

Table 5 Rasch Measurement Theory –Summary for PRI Health and Addiction Risk Scales in Surveys 1 and 2

Proposed Scale (# items)	% coverage item threshold distribution	% items with fit residual > \| 2.5 \|^a	% items with p (χ²) < 0.05 ^b	% items with disordered thresholds	% pairs of item residual correlations > 0.30	% pairs of item residual correlations > mean + 0.30^c	% items with p (DIF) < 0.05^b	PSI
Survey 1 Long Form Scales
Health Risk (34)	88	94	21	0	16/595	24/595	50	0.97
Addiction Risk (11)	80	82	18	0	3/49	4/49	9	0.94
Survey 1 Reduced Scales
Health Risk (18)	84	61	0	0	0/153	13/153	0	0.97
Addiction Risk (7)	75	86	0	0	0/18	2/18	0	0.93
Survey 2 Reduced Scales
Health Risk (18)	87	72	0	0	0/153	8/153	0	0.97
Addiction Risk (7)	78	86	0	0	0/18	1/18	0	0.94

PSI person separation index, χ² Chi-square, DIF differential item functioning
^aThe high percentages were expected given the large sample size but are still informative when some items are much worse fitting relative to others
^bIn the statistical assessment the actual n was adjusted to 500 in order to mitigate excessive power and for parallel fit assessment based on a sample size of 500, which is deemed appropriate for the present psychometric analysis
^cThe critical values for residual correlations were 0.268 and 0.188, respectively, for Survey 1 Long Form Scales; 0.146 and 0.058, respectively, for Survey 1 Reduced Scale: and 0.169 and 0.057, respectively, for Survey 2 Reduced Scales

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