could u help me with a reference support categorize continuous variable as low, moderate and high low (1-2.33), moderate (2.34-3.67) and high (3.68-5).
Hey Yasser, I don't think you need a reference to support the way you have produced terciles. You have just split the 1 to 5 scores into three equally spaced categories, and calling them low/med/high is not unreasonable.
However I suspect that there is more than this. For example, if the 1-5 were actual scores from a Likert scale (or something similar) then labelling them low/med/high is an entirely different story - I would have concerns about that for many reasons.
Mark
It is NOT recommended to cut a continuous variable into categories. This will reduce power and makes the unreasonable assumption, that values close to a cut of point (e.g. 2.33 on your scale) are absolutely the same as the other end within that group (e.g. 1), and maximally different to values close to the cut of, from the other group (e.g. 2.34). This is the case since all values from 1-2.33 will be assigned a dummy code, e.g. 0 and all values 2.34 to 3.67 for example a 1.
It is more reasonable to use the metric variable in a regression and test for interaction with the moderator. Both, predictor and moderator may be continuous. If you find evidence for an interaction, you can do simple slope analyses (also called "probing interaction"), where you estimate the slopes of the predictor at different values of the moderator. Here you can choose several strategies. For example, if you have meaningful values for the moderator, you should use them. Otherwise, you will find approaches like testing the 16th, 50th, and 84th percentile of the moderator. This guarantees that the values are really on the scale of the moderator. In case of a normally distributed moderator, this approach will lead to the same results as the also established +/- 1 SD approach. But the +/- 1SD approach may lead to values outside of the scale of the moderator, in case of skewed distributions.
I agree with Rainer Duesing. Here is a summary of the (many) problems that can arise when you carve a quantitative variable into categories:
- https://discourse.datamethods.org/t/categorizing-continuous-variables/3402
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