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The phrase "a different methodology for" is correct and usable in written English.
It can be used when discussing an alternative approach or method for achieving a specific goal or solving a problem.
Example: "The researchers proposed a different methodology for analyzing the data, which yielded more accurate results."
Alternatives: "an alternative method for" or "a new approach to".
Exact(9)
The Institute for Health Metrics and Evaluation uses a different methodology for tallying malaria deaths and says the global death toll could be double what the WHO reports.
And when there's a different market for pricing players, you've got to introduce a different methodology for building a team".
Three studies [29, 30, 32, 33] used a different methodology for identifying ED versus non-ED invasive lines.
Finally Watanabe et al. in [23] propose a different methodology for identifying 'bottleneck' stations based on passenger flows, volumes of transfer passengers through the stations and on multi-objective optimization with a generic algorithm.
However, we employ a different methodology for the selection of optimal kernel bandwidth as described below.
First, Italy used a different methodology for automatic coding in ICD10 as compared to ICD 9 (ISTAT 2011).
Similar(51)
Each province has been counting the deaths with a different methodology — BC, for example, is the only province that's just counting deaths that occurred in illicit circumstances, while Alberta casts a much wider net that includes people who were prescribed the drug.
This discrepancy may be mostly due to a different methodology used for detecting microvessels in tumour areas.
Quite possibly in the course of writing he came to understand that a different methodology is required for approaching economic issues.
Drawing from the abovementioned bottom-up approach, a different methodology was adopted for successful improvement of the traditional cookstove and its commercialization in Gawand wadi.
Addison et al. (2014), using a different methodology and controlling for employee heterogeneity, report a smaller 'wage gap' in Germany of 3 4percentt during the first half of the 2000s.
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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