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The phrase "a small study of" is correct and usable in written English.
It can be used when referring to a limited research project or investigation focused on a specific topic or subject matter.
Example: "The researchers conducted a small study of the effects of sleep deprivation on cognitive performance."
Alternatives: "a brief analysis of" or "a limited examination of".
Exact(60)
"I have made a small study of tattoo marks".
To be clear, this is a small study of only one sport.
A small study of a different small part of the system could yield entirely different results.
A small study of heart patients found that just a few treatments with an experimental drug reversed years of plaque in coronary arteries.
From a small study of 40 parents with 57 adopted children, 40% reported that their books were good or excellent – but a third said they were terrible.
Likewise, in a small study of the two UK pilot hospitals, participants reported benefits for their day-to-day care of patients and a strengthening of team work.
In a small study of monkeys by the Defense Department, Cipro had been shown to prevent inhalation anthrax at doses comparable to what people would take.
A daily capsule of probiotic bacteria may help people cope with mild anxiety and memory problems, according to a small study of healthy men.
A small study of children with attention deficit hyperactivity disorder last year found that walks outdoors appeared to improve scores on tests of attention and concentration.
One piece was kept out of Göring's reach: a small study of a girl attributed, by Goudstikker, to the Impressionist Berthe Morisot.
In a small study of 19 randomly selected preparers in 2014, he noted, the Government Accountability Office found "significant" errors in returns.
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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