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The phrase "a further analysis for" is correct and usable in written English.
It can be used when discussing the need for additional examination or investigation regarding a specific topic or subject.
Example: "The results of the initial study indicate a need for a further analysis for understanding the long-term effects of the treatment."
Alternatives: "an additional analysis of" or "a more in-depth analysis regarding".
Exact(3)
We then performed a further analysis for the whole period (July 2002 June 2008) by pesticide type: insecticide, herbicide, unknown pesticide and all pesticides (Fig. 4).
Year of diagnosis was categorised as follows: 1968 1977, 1978 1987, 1988–1997, 1998 2010, with a further analysis for acute lymphoblastic leukaemia (ALL) by trial start and finish dates.
Also, off-targeting information against host organisms, including Homo sapiens and a further analysis for protein essentiality provided a final set of 31 druggable, essential and non-host homologous targets, tabulated in table S4, additional file 1.
Similar(57)
The council asked Aleshire to make a further analysis of the proposal for its consideration Tuesday.
That means our analysis can be seen as a preprocessing step for a further analysis of the obtained networks.
But a further analysis undertaken for TfL - Travel in London Report 5 - which looks at annual trends raises questions about that.
To minimize the influence of drug therapy on the development of NAFLD, a further analysis adjusted for anti-hyperlipidemia and diabetic mellitus drugs was performed.
A further analysis shows differences for arousal and dominance for both factors.
A further analysis is prepared for SDB and YJD in the proposed model.
A further analysis will adjust for distance to nearest healthcare centres (public and private) and migration.
For a further analysis, see Leo Herzel and John R. Schmidt, "Shareholders Can Benefit from Sale of 'Crown Jewels,' " Legal Times, October 24, 1983, p. 33.
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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