I see that the issue of splitting a variable into two categories has been discussed on this forum and I understand pros, cons as well as some ways of performing it. The issue that I am interested and can't seem to find anything on splitting a variable into three points.
For this to make sense let me briefly explain my data. I have used a psychographic scale (5 Point Likert) which consists of eight items where low scores indicate one trait and high scores indicate a different one. Theoretically, most people should fall into the mid group, with much smaller extreme groups which show clear tendencies for certain behaviour. Thus, I used this scale with an intention of grouping my respondents into low, middle, and high groups. This classification into three groups is supported conceptually by previous research but no study discloses how groups are split.
I tried using a composite score for the scale and e.g. correlate with a dependent variable. However, because extreme groups are relatively small the result for the whole sample indicates asssociation in the expected direction albeit very low. I have considered dichotomising but individuals with top or low scores on the eight variables get muddled up with middle scores that conceptually do not indicate any distinct group.
Having looked into graphical representation of the scale I can conclude that distribution is normal and indeed most people score in the middle. Thus, visually I can identify the cut-off points which seems to make sense, it produces group sizes supported theoretically and any further tests show significant differences between groups on dependent variables of interest. However, I understand that cutting data this way is very arbitrary. Is there any way I can actually justify doing this based on conceptual support for groups? Is there anything else anyone can suggest as I have run out of ideas. Any help will be much appreciated.
Many thanks in advance.