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The phrase "analysis depends on" is correct and usable in written English.
It can be used when discussing the factors or conditions that influence the outcome or results of an analysis.
Example: "The accuracy of the results in this study shows that the analysis depends on the quality of the data collected."
Alternatives: "evaluation relies on" or "assessment is contingent upon".
Exact(60)
The dependability of the power analysis depends on the amount of detail that you give the analyser.
The cost-benefit analysis depends on your priorities.
The success of the whole high-level analysis depends on the quality of the design.
The accuracy of the finite element analysis depends on the precise estimation of soil properties.
The computational complexity of kinematic analysis depends on the shapes and motion types of the parts of the mechanism, and is in general intractable.
The accuracy in sensitivity analysis depends on the accuracy in evaluating strains and stresses on the boundary.
The proposed analysis depends on redeveloped simulator which is unique PV-aware simulator for both synchronous and asynchronous NoCs.
Much more pronounced than in the design stage the benefit of fracture mechanics in failure analysis depends on its accuracy.
His introduction is a no-nonsense manifesto about eating that's worth quoting at length: "Good cooking, in the final analysis, depends on two things: common sense and good taste...
It should be noted, however, that the gloomy Moody's analysis depends on a number of assumptions, the most important of which is that the economy is indeed currently operating at full employment.
Even fingerprint analysis depends on a subjective judgment by experts as to how closely two prints match, a conclusion that can be biased by the examiner's knowledge of the suspect or the case.
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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