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'empirically examine' is a correct and usable phrase in written English.
You could use this phrase to describe a research process that involves gathering data to support a hypothesis or draw a conclusion. For example, "Researchers empirically examined the connection between poverty and education levels in a particular neighborhood."
Exact(60)
They empirically examine wages among industries and conclude that labor bears about 60 percent of the corporate tax burden.
"The idea of using the exhibition data to empirically examine this idea was exceptionally creative, and the analysis was well executed," said Professor Sokoloff, a professor of economics at the University of California at Los Angeles.
In order to empirically examine this, I estimate various simple probit models.
We, therefore, attempted to empirically examine the role of liberalization on capital inflow.
Our study is the first to empirically examine possible antecedents and consequences of territoriality.
We call for future research to theoretically and empirically examine other potential mediators.
Such interrelated and complex relationships do not often empirically examine in connection to perceived innovativeness.
To empirically examine this question, we integrate different measures of sentiment into a portfolio optimization procedure.
We empirically examine these three patterns by conducting two exploratory case studies.
A Rasch rating scale model was applied to empirically examine the hierarchical structure.
I use the Cox proportional hazard model to empirically examine the determinants of return migration of Mexican immigrants.
More suggestions(15)
empirically ascertain
constructively examine
empirically analyze
empirically identify
realistically examine
specifically examine
empirically addresses
empirically addressing
actually examine
empirically test
practically examine
empirically evaluating
empirically address
empirically examined
empirically investigated
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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