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The phrase "a further analysis of" is correct and usable in written English.
It can be used when discussing an additional examination or investigation of a particular subject or topic.
Example: "In this paper, we will conduct a further analysis of the data collected during the experiment."
Alternatives: "an additional examination of" or "a more in-depth study of".
Exact(60)
A further analysis of statewide results reflects a similar trend.
Today's report is based on a further analysis of the data from the Women's Health Initiative.
Today's report is a further analysis of the findings on bone loss.
In a further analysis of this English preference for putting action before thought, Arnold distinguishes two forces which he describes as "Hebraism" and "Hellenism".
A further analysis of the IFRF semi-industrial-scale experiments on flameless (mild) combustion of natural gas is carried out.
This hierarchical approach combines statistical methods with GIS techniques, enabling instant visualisation and a further analysis of the results obtained.
A further analysis of the derived dynamic model provides information on the interaction of the dominant structures in the flow.
A second set of modified criteria were also used to conduct a further analysis of the results.
A further analysis of micrographs revealed, for both S. aureus and E. coli O157 H7, the initial stage of bacterial adhesion process followed a power-law behavior in the case of the hydrophilic substrates with a positive zeta potential.
It has now shifted gears and is working on replacing or repairing some of the lake's 32 huge culverts and conducting a further analysis of the dike.
A further analysis of 31 beef products including cottage pie, beef curry pie and lasagne showed that 21, two-thirds, contained pig DNA.
More suggestions(23)
following a further analysis of the relocation
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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