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"empirical dimension" is a correct and usable phrase in written English.
You can use it when referring to "a measurable and quantifiable dimension of a phenomenon that can be observed and studied empirically". For example, "The empirical dimension of this research project is complex and multi-faceted."
Exact(8)
What has been strikingly absent from the conception of public health law has been an empirical dimension.
The empirical dimension explores the theoretical propositions in the context of co-located and distributed sketching.
A conception of history as merely a designer's pattern book is as inadequate as that of history as the empirical dimension of design theory.
The article examines everyday life in Northern Ireland's segregated communities and focus on a neglected empirical dimension of ethnic and social segregation developed within the socio-spatial relations between people and their built environment.
Virtually any question in ethics will have an empirical dimension.
Concerns about the potential for oppression implicit in group rights often have an empirical dimension.
Similar(52)
The empirical dimensions of 'sibling involvement' used in this section, including measures of sibling control and participation, are similar to those used for parental involvement.
Once all normative and empirical dimensions have been carefully considered, one may want to adopt a firm standpoint regarding the need for publicity or secrecy in deliberation and voting in general.
In some cases, these problems also occur due to the application of inaccurate empirical dimensioning methods, without the wide use of computational tools, which would yield a more accurate structural analysis results.
We will continue to engage in those pragmatic and empirical dimensions.
But, as one can see, the individuality of a singular object is not easily (even principally not) describable in its empirical dimensions.
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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