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The phrase "assumed based on a" is correct and usable in written English.
It can be used when discussing conclusions or beliefs that are derived from certain information or evidence.
Example: "The results of the experiment were assumed based on a preliminary analysis of the data."
Alternatives: "presumed from a" or "inferred from a".
Exact(10)
We assumed, based on a previous study12, which also used PE, that earthworms might ingest and/or transport microparticles of different sizes to a different extent.
It was assumed, based on a presumed dating of hypothetical biblical sources, that the patriarchal narratives in the Bible were only a projection of the situation and concerns of a much later period (9th 5th century bc) and of dubious historical value.
Because ion molecule cross-sections are not readily available, a constant cross-section (10−20 m2) has been assumed based on a hard-sphere collision model [44].
Because ion molecule cross-sections are not readily available, a constant cross-section (10−20) has been assumed based on a hard-sphere collision model [25].
A priori fault parameters are assumed, based on a model proposed by the Geospatial Information Authority of Japan (GSI, http://www.gsi.go.jp/cais/topic110422-index.html); the resulting fault parameters are listed in Table 1.
While we have assumed, based on a parsimonious fit to the data that TfR efflux occurs as a first order process, a two component model that allows for fast and slow recycling steps can also be proposed [50].
Similar(50)
An intra-cluster correlation coefficient of ρ = 0.13 was assumed based on an earlier study [ 40].
Why would we assume, based on a queen's beauty, that she was loved?
They're just assuming, based on a headline or an excerpt on a blog, that I'm unpatriotic or irreligious or lecherous.
But that isn't to say that the decision was made, as she believes Ms. Badinter assumes, based on "a debilitating false consciousness".
Many viewers assume, based on a tiny clip in the previews for the finale, that the Jennings family is heading north, hoping to grab Henry and escape via Canada.
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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