Adverbs describing Adverbs

Question

We have a similar question here, but I think my examples are a bit different and I would love to understand how this is done correctly.

Let's say we are talking about

significantly higher thicknesses in some group

When I see this right, then significantly describes higher, while high is the description of the thicknesses. Now, I would like to say that the differences are statistically significant, but it just won't sound right to me

1. statistically significant higher thicknesses in some group
2. statistically significantly higher thicknesses in some group

What is the correct form to say this and why?

A very relevant example is

Seven clinically highly relevant publications

Is this correct, because both, clinically and highly describe the adjective relevant? I'm a bit lost and I would really like to understand the rules behind this.

Answer 1

By definition, an adverb can describe another adverb, so your #2 statement is technically correct. It could be considered rather ambiguous, with no commas, whether the adverb is describing the other adverb, or the adjective.

To make it clearer, you could re-work the phrase as

significantly higher thicknesses, statistically, in some group

to wrap the phrase significantly higher thicknesses in another adverb

or

statistically far higher thicknesses in some group

to add the emphasis you need to higher