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The phrase "analysis provided that" is not correct in standard written English.
It seems to be an attempt to combine "analysis provided" with a conditional clause, but it lacks clarity and proper structure.
Example: "The results of the study were inconclusive, analysis provided that the sample size was too small."
Alternatives: "analysis given that" or "analysis assuming that".
Exact(22)
18 Patients of the SYNERGY study were considered evaluable for this post hoc analysis, provided that sex was specified.
The stability analysis of controlled system becomes simple Hurwitz stability analysis provided that a parameter is chosen suitably.
Another advantage of single-cell sequencing is that it makes rare cells more accessible to analysis, provided that methods are available to isolate or enrich these cells from their heterogeneous environments.
FT-IR spectroscopy and elemental analysis provided that it is possible to know the amount of Ti (IV) incorporated into the SBA-15 framework.
The Chandra CALDB is the directory and indexing structure that stores and provides access to all calibration files that are required for standard processing and analysis, provided that they have been put into FITS format.
Therefore maps with only partial marker coverage would be suitable for genetic analysis, provided that the parents are previously tested for a large initial sample of markers with good coverage of the genome, allowing identification of the segregating regions of each particular parent or cross.
Similar(38)
Further, EDS analysis provides that the tip of nanowire consists of Ni and Si, indicating that the catalysis Ni is solidified, so that NiSi2 is formed at the tip of silicon nanowire.
All of this would result in the lack of power for detection of gene effects, thus requiring further updated meta-analysis provided that more studies are published in the literature.
The exploratory network analysis provided data that helped inform the later content analysis.
Our gender analysis provided several findings that were inconsistent with the literature on female offenders.
"Genetic analysis provided evidence that these associations were partly causal," the researchers wrote.
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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