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The phrase "a third study of" is correct and usable in written English.
It can be used when referring to the examination or analysis of a particular subject or topic that has been studied previously, indicating that this is the third instance of such a study.
Example: "The researchers conducted a third study of the effects of sleep deprivation on cognitive performance."
Alternatives: "the third analysis of" or "a third examination of".
Exact(30)
"I've made two studies of falling leaves in an avenue of poplars and a third study of this whole avenue, entirely yellow".
A third study of single-parent homes found boys were less likely than girls to enroll in college.
In a third study of pair feeding, aluminum (0.20%) in severe calcium deficiency (0.02%) had an adverse effect on bone calcium.
A third study of the composer, Bach: A Musical Biography, was completed just before Williams fell ill with leukaemia in September 2015, and is due to be published in May.
A third study of this area was carried out by McCaffrey (2005).
Data from a third study of the open field (Brown1; unpublished) showed that the duplication was associated with less activity and a greater number of fecal boli (r = 0.73; p<0.01, r = 0.67, p<0.013, respectively).
Similar(30)
A second study of the drug in people with autism is also underway.
Also includes an untitled draft of a second study of Sweden.
A second study, of more than 5,000 students undertaken at about the same time, came to similar conclusions.
A second study, of a hundred and seventy-five salespeople, found the relationship to hold for sales numbers as well: sales were higher in environments with moderate rules, while environments with too few or too many rules suffered.
A second study of 51 first-years did the same reading and colouring tasks but different psychological tests, which found they showed better creative thinking and visual attention afterwards.
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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