Take the example of mean scores for items X & Z, with the HB scores scaled to sum to 100 in both cases:

• For group A, the mean importance scores are X[12] and Z[3]

• For group B, the mean importance scores are X[12] and Z[6]

My understanding is that I can argue that

1. for A: X is 4 times more important than Z

2. for B: X is 2 times more important than Z

What about comparisons between groups A and B?

Can I infer that:

3. Z is more important for B than for A?

4. Z is twice as important for B than for A?

Although in both samples/models the scores are scaled to sum to 100, the scale factor could be different in the 2 samples which suggests I can’t make comparisons 3 or 4 - I can compare ratios between models, but not absolute values. Or is that overly cautious?

Can anyone advise on (in)appropriate inference?

thanks

Dan