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"was primarily based on" is correct and usable in written English.
You can use it to talk about the origin of something, often in the form of "The decision was primarily based on [reason]." For example, "The company's decision to reduce costs was primarily based on the economic downturn."
Exact(60)
Hand hygiene was primarily based on alcohol-based hand rubs.
Therefore, the patient-based analysis was primarily based on the heterogeneity of response over all lesions, with the identification of the least responsive lesion being predictive for PFS.
Clinton's stand, he says, was primarily based on fund-raising.
The investigation was primarily based on hospital records, including posthumous X-rays.
Agriculture was primarily based on slash-and-burn techniques, and there was extensive trade, mainly by canoe along the coast.
Mr Justice Gillen said the case against them, which was primarily based on mobile phone evidence, was "overwhelming".
Assessment of candidate models was primarily based on statistical criteria.
The diagnosis of extensor tenosynovitis was primarily based on the symptoms of pain, swelling, tenderness, and dorsal crepitus.
Behavioural responses showed that recognition and matching of these hybrid faces was primarily based on their surface properties.
From the 1970s onward, this form of prognostics, which was primarily based on differential equation systems, benefited from the excessive improvement in the computing power of computers [35].
In Strasbourg, the transition decision was primarily based on the grade point average (GPA) of the students during lower-secondary education (collège).
More suggestions(17)
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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