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The phrase "a previous study on the same" is correct and usable in written English.
It can be used when referring to an earlier research work that addresses a similar topic or question as the current study.
Example: "In light of the findings from a previous study on the same subject, we decided to explore further."
Alternatives: "an earlier study on the same topic" or "a prior study on the same issue".
Exact(23)
Barely a day goes by without the papers reporting a new study that seems to contradict a previous study on the same subject.
These findings replicate and extend those of a previous study on the same 2-day seminar [Top. Stroke Rehabil. 2 (1995) 53.].
The starting point was a previous study on the same subject, which considered that no solute is lost in the vapor phase and a fixed fraction of 2% of the CO2 is lost within the heavy phase.
In a previous study on the same patient cohort, the appropriateness of the ED visits was determined using predefined criteria.
This is coherent with a previous study on the same data set, which finds this pair of neurons dependent through a complete different method [22].
On the other hand, the demonstration of a significant difference between the TPOAbs URLs obtained with the five different automated IMA methods both in males and females, confirms the data of a previous study on the same topic, using indirect methods [15].
Similar(37)
Patients included in the present study were the same as those included in a previous study on the effect of SNS on IBS specific symptoms [ 7].
This was developed in a previous study of the same service, based on interview data, observations and documentary analysis.
The choice for a 15-second interval between asynchrony and the occurrence of arousal was chosen based on one previous study on the same topic [19].
The study presented here is an extension of that previous study on the same community of IDUs.
Related site A previous study on violence, from the same group.
More suggestions(17)
a previous project on the same
a longitudinal study on the same
a previous study on the metabolic
a second study on the same
a previous study on the functional
a previous study on the economic
a later study on the same
a previous experiment on the same
a previous study on the early
a recent study on the same
a previous publication on the same
a previous study on the cold
a retrospective study on the same
a previous article on the same
a previous work on the same
a previous study on the transcriptomic
a previous report on the same
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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