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The phrase "a further layer of analysis" is correct and usable in written English.
It can be used when discussing the need for additional examination or scrutiny of a subject or data.
Example: "To fully understand the implications of the results, we must apply a further layer of analysis."
Alternatives: "an additional level of analysis" or "a deeper level of analysis".
Exact(4)
Once it's imported code into a vulnerable application, CodePhage can provide a further layer of analysis that guarantees that the bug has been repaired.
Neural investigation adds a further layer of analysis to scientific understanding of the nature of perception.
For that purpose, researchers have applied a further layer of analysis to the results of clustering, making use of additional data containing annotations of genes being analyzed.
This combined report seeks to provide an overview assessment across the development and humanitarian sectors, drawing on the findings and conclusions of the two reports, while adding a further layer of analysis to reflect on UNICEF as one organization engaging in these different spheres.
Similar(56)
There is a further layer of complexity to this.
That it is the NPG that is hosting the show adds a further layer of complexity.
To men case-hardened by work they added a further layer of political hardening.
Revealing how the mechanics work can also be a double bluff, a further layer of illusion.
Moves to protect depositors in bail-ins add a further layer of complexity.
The problem has a further layer of irony because – to simplify for a moment – GCHQ actually invented computers.
In addition, transactions on Monero go through mixers to add a further layer of anonymity.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com