Hello Vy,

If the questionnaire has previously been used and there are extant recommendations (whether clinical, normative, or other basis) for interpreting scores, you'd be best advised to use them.

However, the big question here is, is it essential to abandon a lot of the relative information about score differences by collapsing scores into three groups? If so, how did you arrive at these proposed cut points?

Assuming you are absolutely, positively convinced that you must have score categories, what are methods for collapsing scores into groups for such a scale? Here are some options:

1. Ask clinical experts how many score categories make sense for this specific questionnaire, show them the obtained score distribution, and follow their suggestions for cut points.

2. Measure "normal" persons and persons having clinically elevated fear symptoms (as diagnosed by qualified mental health professionals) to see what their respective score distributions on your questionnaire might be. Choose a cut score that maximizes your preferred mix of specificity and sensitivity (e.g., minimizes misclassification).

3. Choose cut scores based on a normative definition. Perhaps mean + 1 SD or higher would define "elevated" scores; and mean - 1SD or lower would define "low" scores; the middle set would be "typical" scores.

4. Choose cut scores to yield an equal proportion of cases in each group.

Note that all four methods (or others) can and most often will yield thresholds that differ.

Good luck with your work.

Good Day, Vỹ Ngô

For R.Likert scales, one should recommend to use an odd number of alternatives: 3-, 5-, 7-point scale, because “... In general, it would seem desirable to have each statement so worded that the modal reaction to it is approximately in the middle of possible responses” [Likert, R. (1932). A technique for the measurement of attitudes. Archives of Psychology, 22(140), P. 45. https://legacy.voteview.com/pdf/Likert_1932.pdf]

I hope that using 6-point scale is not a problem but you should think how to reason these 6-point scales.

And concerning to cutoff scores we would like to use quartiles for decision rules: less than Q1 - low, more than Q3 - high, between Q1 and Q3 - normal level.

Reasons: (1) using Q1 and Q3 we do not need a normal distribution, (2) we have more high-level and low-level respondents (23-25% in each group) comparative to ± SD (14-17% in each group)

By the way, you may argue your own cutoffs, for example P10 and P90, or P30 and P70, but (1) they should rely on data distribution and (2) use Q1 and Q3 (P25, P75) or ±SD (≈P16, ≈P84) are common practice.

And may be you will find something interesting here:

1. https://en.wikipedia.org/wiki/Norm-referenced_test

2. https://en.wikipedia.org/wiki/Criterion-referenced_test

Hi Vy

There have been some great answers here so far. I'll just add my thoughts-

If my calculations are correct, which they may not be, you have 42 items and you've added the scores together to represent variability in fear. One issue is that the 42 items may no all be measuring the same thing, fear, to the same degree. So some factor analysis may be a good starting point.

In the unlikely case that all the items do measure one construct you could see if there are any unobservable 'clumps' of participants that represent naturally occurring groups with different levels of fear. Mixture models can do this, even with just one variable. I remember, many years ago, reading a paper where the researchers had found different subpopulations using just the age of onset of a psychological disorder. I was amazed that such a thing could be done! Mixture models could also be used to identify latent/unobservable groups based on more items - this would probably be better.

However, I'm not sure why you want groups rather than scores. As David says this is one way to destroy valuable information. You can get everything and more from continuous scores compared to the categorized version of the same data.

Mark