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The phrase "a large sample of each" is correct and usable in written English.
It can be used when discussing research, data collection, or analysis where multiple groups or categories are involved.
Example: "In our study, we collected a large sample of each demographic group to ensure our findings were representative."
Alternatives: "a significant sample from each" or "an ample sample of every".
Exact(1)
To create Wolbachia cured replicas of LHM and LHM-bw, a large sample of each of these populations was treated with tetracycline over two generations following the protocol of Hoffman et al. [24].
Similar(59)
The samples were selected as part of an ongoing study of dyslexia from a large sample of families, each with at least two siblings who show symptoms of dyslexia (28, 29).
However, it is important to appreciate that our sampling scheme involving many loci provides a large sample of the deeper coalescent history of each population because, by definition the coalescent histories of unlinked loci are independent.
The economists David Neumark and Andrew Postlewaite examined the behavior of a large sample of pairs of American sisters, each containing a sister who did not work outside the home.
They each involved taking a large sample of data from digital music listeners and analysing patterns in how their preferences matched their demographic groups.
It examined a large sample of corporations.
A classic study provided a large sample of children with the lesson that their maths ability was not fixed.
One study that examined a large sample of dual-class firms from 1994 to 2001 found that they notably underperformed the market.
A similar study of a large sample of elderly people in Finland put a more precise figure on the impact of wartime evacuation.
He starts by canvassing views from a large sample of people.
This paper investigates a large sample of sloshing pressure measurements.
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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