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The phrase "a second study of" is correct and usable in written English.
It can be used when referring to an additional examination or analysis of a particular subject or topic that has already been studied.
Example: "The researchers conducted a second study of the effects of sleep deprivation on cognitive performance."
Alternatives: "a follow-up study on" or "an additional analysis of".
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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.
Separately, a second study of tens of thousands of British people's daily eating habits shows that meat lovers' diets cause double the climate-warming emissions of vegetarian diets.
A second study of people with diabetes showed that reducing dietary fat by replacing five typical high-fat foods with versions made with less fat significantly lowered the participants' consumption of cholesterol and saturated fat.
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.
In a second study, of 5,995 men 65 and older, bone mineral density was 3.9percentt lower at the hip and 5.9percentt lower at the lumbar spine in men who used the drugs compared with those who did not.
Frye's other critical works The Well-Tempered Critic (1963), The Secular Scripture: A Study of the Structure of Romance (1976), Northrop Frye on Shakespeare (1986), and Words with Power: Being a Second Study of "The Bible and Literature" (1990)—similarly emphasize symbols and group myths in literature and the systematic classification of literary symbols, genres, and criticism.
In a second study of callers contacting alumni who donated more frequently to the university, the performance effects following a visit from a scholarship recipient were even more striking: A month later, the callers had on average more than doubled their calls per hour and had achieved average weekly revenue increases of more than 400%, from $411.74 to $2,083.52.
In a multicenter study reported last year of 4,498 people with arthritic knees and a second study of 2,907 people with arthritis, improvements in the quality of patients' lives following knee replacement surgery were less than had been previously reported.
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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