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

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

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
+ 0.30c
% items with p (DIF)
< 0.05b
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
  1. PSI person separation index, χ2 Chi-square, DIF differential item functioning
  2. aThe high percentages were expected given the large sample size but are still informative when some items are much worse fitting relative to others
  3. 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
  4. 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