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The phrase "associated with the largest" is correct and usable in written English.
It can be used when discussing relationships or connections with something that is the biggest or most significant in a particular context.
Example: "The study focused on the factors associated with the largest increase in productivity among employees."
Alternatives: "linked to the highest" or "connected to the most significant".
Exact(60)
This paper demonstrates that these lower domain scores are often associated with the largest treatment-associated changes towards improvement.
Many of the years associated with the largest late-stage errors in the polling, like 1968 and 1980, were also associated with third-party candidates.
Therefore, the first subset represents the basis associated with the largest absolute value of the coefficients.
In their framework (see footnote 19), prior skilled work was associated with the largest earnings advantage.
Having handguns in the home was associated with the largest effect estimates.
After 168 h, butyrate and H2S were associated with the largest quantity of sulfate removed.
The second column of U, u 2, is associated with the largest subordinate root, and so on.
To project the matrix in the new base, we have selected the eigenvectors associated with the largest eigenvalues.
The dextral offset was ca. 20 cm after the mainshock, almost half of which was associated with the largest foreshock.
This gravity profile is associated with the largest chromite deposit found in the province (Davis et al. 1957).
It is not surprising, since SLE is the autoimmune disease associated with the largest number of autoantibodies [21].
More suggestions(16)
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relationship with the largest
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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