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'strength of influence' is correct and can be used in written English.
This is a phrase commonly used to express the power of ideas, information, or behaviors on people or groups. For example, you could say, "The strength of influence of the media on society is undeniable."
Exact(21)
Mr. Secretary General, The strength of influence of any internation organization rests on the belief of the human environment in which the organization exists and which places its trust in it, once the organization declares that it has been founded to achieve goals important to mankind.
Comparing the results for these two cases, we can estimate the strength of influence of particular adsorbents on the CrO4 2− excited state structure.
This is in line with the work by Bapna and Umyarov (2012) who discovered in an online social music network that the strength of influence decreases with a user's number of friends.
First, the author might try to judge the strength of influence they themselves perceive a financial interest to have.
In order to examine the directional relationship between the two ICs, Granger causality spectral analysis [76], [77] was applied to evaluate the relative strength of influence.
The switching point varies with strength of influence.
Similar(39)
This impact network is based on expert judgments on the direction and strength of influences between alternative developments of system elements.
In the parameter range 0.16 ≤ J ≤ 0.2, all the eigenvalues are influenced by the state variables ∆δ 1, ∆ω 1, ∆δ 2 and ∆ω 2 together and there is little difference between the strengths of influence.
In the parameter range from 90 to 50, all the eigenvalues are influenced by the state variables ∆δ 1, ∆ω 1, ∆δ 2 and ∆ω 2 together and there is little difference between the strengths of influence.
One of the major drawbacks of these qualitative abstractions, however, is the coarse level of representation detail that does not provide for indicating strengths of influences.
"But by having slightly different rules and strengths of influences between the cells they transform into very different final forms".
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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