Following the post here, I am wondering if reporting the mean and standard deviation is appropriate when describing a composite score.
My composite score is the total of responses on several likert scale items and count variables.
I have made sure that all are on a five point scale, based on their level of importance, so as to preserve variability.
This is the weighting system I have used to assign the scores:
- 0 = of no importance
- 1 = of some importance
- 2 = of medium importance
- 3 = of high importance
- 4 = of absolute importance
I have then added all scores together to arrive at the composite score. As such, this is based on a formative measurement model framework.
I am aware of issues relating to the purity of scales and I am hoping my logic of using "level of importance" as the weighing criterion would provide the necessary meaning I need to interpret the composite score. For example, if I get a composite score of 3, I know it is of high importance.
(I apologise for my non-statistical language.)
Best Answer
This is certainly done a lot, and I don't see it as problematic. I think concerns about it are related to an over-reliance on Steven's scale of measurement. Steven's scale is useful, but it's not etched in stone.
Briefly, someone who takes the notion of ordinality literally will object to adding the scores. But if you can add the scores, then you can find the mean and sd and so on. Adding the scores implies that the Likert scale itself is interval, rather than ordinal.
I wrote more about this in this article