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The phrase "an almost equal proportion" is correct and usable in written English.
It can be used when discussing quantities or distributions that are nearly the same but not exactly equal.
Example: "In the survey results, the responses were divided into an almost equal proportion of positive and negative feedback."
Alternatives: "a nearly equal share" or "an approximately equal ratio".
Exact(10)
First, there is an almost equal proportion of smokers and non-smokers.
The participants' response rate was 58% (780/1345) with an almost equal proportion from each public healthcare facility.
25 In our laboratory, ARVC is the second most common cardiomyopathy accounting for 13% of the SCDs, with HCM being identified in an almost equal proportion (11%).
We received an almost equal proportion of completed questionnaires from each category of the public healthcare facility, namely health clinics, health offices and hospitals (table 1).
NCAs were tested significantly older (81 ± 10 years) than CAs (73 ± 12 years) with an almost equal proportion of female gender (58 vs. 55%%).
In Vinh Long where the survey only included rural communes, an almost equal proportion of women (47% and 46%) reported using CHSs and private clinics, with 29% visiting the district hospital, and 15% going to the provincial or central hospital for ANC services.
Similar(50)
Unlike in New York City, where 90% of the samples tested were positive for pandemic H1N1 virus [15], both seasonal-A and pandemic H1N1 were represented in almost equal proportion in this study.
But Jefferson Huang, vice president for admission and financial aid, said foreign and domestic applicants are accepted in almost equal proportion.
When it was over, Reyes tipped his cap to the fans, who cheered and booed in almost equal proportion.
There is grace in the almost equal proportion of front and rear deck, and the Targa roof with its basket-handle roll bar.
When the proteins were subjected to SDS-PAGE in non-reduced condition (Fig. 2c), presence of some aggregates was observed in all four FST-type proteins with almost equal proportion at around 50%%.
More suggestions(16)
an almost equal man-to-woman
an almost equal challenge
an almost equal length
an almost equal passion
an almost equal effect
an almost equal transmission
an almost equal part
an almost equal balance
an almost equal potency
an almost equal impact
an almost equal ratio
an almost equal show
an almost equal interest
an almost equal division
an almost equal percentage
an almost implausible proportion
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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