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The phrase "approximately the same proportion" is correct and usable in written English.
It can be used when discussing quantities or ratios that are similar but not exactly equal.
Example: "The survey results indicated that approximately the same proportion of participants preferred option A over option B."
Alternatives: "roughly the same ratio" or "about the same percentage".
Exact(45)
Nitrogen and phosphorus are incorporated into the tissues of marine organisms in approximately a 16:1 ratio and are eventually returned to solution in approximately the same proportion.
Some two-fifths of the country's population is engaged in agricultural production (working as independent producers or salaried farm labourers), and agriculture accounts for approximately the same proportion of the country's gross domestic product.
Secondly, for a constant R tot ¯, if we decrease η, then λ will decrease in approximately the same proportion.
Firstly, for a constant λ, if we increase η, then R tot ¯ will increase in approximately the same proportion.
A quarter of participants (24.8%) described severe headache, and approximately the same proportion (22.9%) reported that their daily activities were reduced to nil by HY (Table 2).
In stratified V-fold cross-validation the output variable is first stratified and the dataset is pseudo randomly split into V folds making sure that each fold contains approximately the same proportion of different strata.
Similar(15)
Men and women experienced housing nonpayment, having utilities turned-off, and eviction in approximately the same proportions.
In a study of adolescents using questionnaires and interviews, approximately the same proportions of students reported mild or moderate headache intensity (43.1 and 46.6%, respectively), and considerably fewer (10.3%) had severe headaches [32].
Deferred reproduction occurred at all four translocation sites in approximately the same proportions.
For the mouse orthologs, the top 15 categories are the same and occur in approximately the same proportions.
Moreover, the authors showed that each of the different cell subpopulations could give rise to all three lineages in approximately the same proportions observed in the unsorted population.
More suggestions(15)
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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