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The phrase "a weak effect of" is correct and usable in written English.
It can be used when discussing the impact or influence of a variable or factor in a study or analysis, particularly when that impact is minimal.
Example: "The research indicated a weak effect of the new policy on employee productivity."
Alternatives: "a minor impact of" or "a limited influence of".
Exact(45)
There was only a weak effect of prior training.
It is shown that high temperature fatigue crack growth is predominantly loading time dependent with a weak effect of stress cycles.
Earlier studies were restricted to the thermodynamic phase plane and have found a weak effect of the transfer hypothesis on state variables.
A weak effect of economic growth on energy consumption is noted for the lower quantiles of economic growth in China, India, Germany and France, which suggests that energy as an input has less importance at low levels of economic growth.
Wetland occupancy was also temporally dynamic, with only a weak effect of connectivity on the probability of extinction, but a strong positive influence of connectivity on the probability of colonisation.
This behavior is attributed to (i) the lower stress for dislocation generation compared with cyclic flow stresses and (ii) heterogeneous deformation at low strain amplitudes that results in a weak effect of local latent hardening.
Similar(15)
A weaker effect of particle size on their burn time is predicted for smaller particles, in qualitative agreement with recent experiments.
Thus, this result predicts a weaker effect of a recession at entry on subsequent wages for women than for men.
The latter could have facilitated the maintenance of a higher number of integrated elements observed in the chimpanzee genome, because of a weaker effect of genetic drift, although the wide HPD values caution against over-interpretation.
A signal on chr3p26 was observed but only reached significance when the three population samples were combined to increase the power, which suggests a weaker effect of this QTL.
We noted a weaker effect of exposure on hospitalization for all respiratory conditions, and no effect on hospitalization for nonrespiratory conditions.
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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