# How to find the upper and lower quartiles of the Ryff scale?

I received this question via email and thought the answer might be sufficiently general to be worth posting here.

I have used the Ryff scale in my research . Actually I am confused about the scoring. The minimum possible score is 54 and the maximum score 324. I calculated this after reversing the negatively worded items. The author of the scale mailed me saying the scale has no cut-off points score you have to consider the upper 25% as higher level of psychological well-being and the scores in the lower 25% as poor psychological well-being.

How would I find the upper and lower 25% (I guess called as Quartile) from just the minimum and maximum score on the scale?

Obtaining the quartiles: Typically you obtain quartiles from the data. Thus, you would have sample data (either your dataset or another dataset), and you can use software to give you .25 and .75 percentiles (or alternatively, you can get such values fairly straightforwardly by rank ordering the data).

Of course, you might be referring to a slightly different notion to quartiles. You might be thinking about low and high scores relative to the scale range. So for example, the mid point of 1 to 5 scale is 3. Therefore, you could say that a mean below 3 suggests that people are below the midpoint on a scale. This idea can readily be extended to other percentiles of the scale range.

The basic equation could be expressed as follows:

min + percentile * (max - min)


where min is the scale minimum and max is the scale maximum and percentile is the percentile of interest (e.g., .25 and .75 in your case or say .5 for the midpoint).

Applying this you get

54 + .25 * (324 - 54) = 121.5
54 + .75 * (324-54) = 256.5


for your low and high cutoffs.

Of course, there's all sorts of discussion you could have about whether this whole process is reasonable, and in general you should try to use the continuous scale for your analyses.