During encoding, participants were presented 50 (short version) or 100 (long version) color images of unknown male and female faces from a large database (presentation time: 2000 ms; no inter-item interval).
The cognitive diversity between each pair of scoring systems, P and Q, is measured by the diversity function d(P,Q), as shown in equation (3), where m is the number of items (intervals) to be scored; in this case m is 63, indicating the number of intervals in the common visual space.
Person separation index indicates replicability of person ordering while item separation index indicates replicability of item placement on an interval scale (Bond and Fox 2015).
Test-retest and inter-rater reliability was assessed by using the intraclass correlation coefficient (ICC) for items with interval data or those with ordinal data where the intervals between measurements were assumed as equivalent (item 7 and total scores).
Although individual Likert items are ordinal in character, we support the position that Likert scales (collections of Likert items) produce interval data, and that it is appropriate to summarize the ratings generated from Likert scales using means and standard deviations, and to use parametric statistics to analyze the scales [ 68].
This analysis provides reassurance that the promotion of the items to interval measurement assumptions did not deviate from the pattern of factor coefficients compared with a less constrained distributional item profile.
Another perspective applies a polytomous Rasch model to infer that the Likert items are interval level estimates on a continuum, and thus that statements reflect increasing levels of an attitude or trait – e.g., as might be used in grading in educational assessment, and scoring of performances by judges.
Briefly, the Rasch model shows what should be expected in response to ordinal items if interval scaling is to be achieved.
Therefore, there is a trend toward using Rasch analysis, a modern statistical method that can transform the ordinal scores of polytomous items into interval scores for the purpose of psychometric evaluation [ 16].
We were also able to transform the ordinal data (constrained to a 0-50 range for each item) to an interval scale through fit to the Rasch model.
