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Discover Ludwig"by analysis of" is correct and usable in written English.
It is a prepositional phrase that is used to indicate how you arrived at a conclusion. For example, "By analysis of the data, it appears that sales have increased by 10% over the past year."
Exact(60)
By analysis of the e.s.r.r
Differences were compared by analysis of variance.
Data analyses were performed by analysis of variance.
Figure 4 Database building by analysis of recorded human subject.
The model was validated by analysis of variance (ANOVA).
Hemodynamic and echocardiographic data were analyzed by analysis of variance.
Statistical analysis was done by analysis of variance.
Statistical analysis was by analysis of variance (ANOVA).
Cytotoxicity was assessed by analysis of propidium iodide uptake.
The stability is testified by analysis of phonon dispersion curves.
Multiple groups were compared by analysis of variance (ANOVA).
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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