Psychological distance between categories in the Likert scale: Comparing different numbers of options
This study review many studies about how many categories are appropriate in Likert scale. Many viewpoints have been used to investigated this question, including various of participant's response, reliability, and cognitive aspect. The author proposed the IRT applied to calculate the scale value of each category for assessing the psychological distance. The formula in page 5 can be illustrated as figure below:
the numerator is f(C2)-f(C1), and the denominator is the area of line drawing.
We can calculate scale value of each category, and then compare with conventional scale score (1, 2, ..., 5). If the difference between scale value and conventional scale score is large, this category design would be demonstrated as a bad design. The result in this study as figure 4 to 7 found that 7-point scale is not necessary.
comment
1) How about the error term of formula in page 5? The Cp estimated in IRT was directly used in this formula. Maybe using plausible value method to calculate this psychological distance is better.
2) This result just told us the 7-point is not appropriate with the Big-Five questionnaire. it can't be generalized to other tests.
3) the result In table 5 showed the category parameter of one item. It is better to show a summary statistic of all items, or he should use rating scale model.
4) the formula in page 4 use the standard normal distribution. I think it is better to use the real distribution of his population.