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The phrase "a two way interaction" is correct and usable in written English.
It can be used to describe a situation where communication or exchange occurs in both directions between two parties.
Example: "Effective communication requires a two way interaction between the speaker and the listener to ensure understanding."
Alternatives: "a reciprocal interaction" or "a bidirectional exchange".
Exact(3)
The results establish a two way interaction in the long-run, so that higher housing prices lead to a credit expansion, which in turn puts an upward pressure on prices.
Additionally, results from a two way interaction term indicated that intervention and control groups were similar in the effect of the exposure on early neonatal death.
To examine possible moderation effect of type of pre-test counselling upon the intention-behaviour relationship, a two way interaction term between intention and type of pre-test counselling was added to the regression model and tested for statistical significance.
Similar(57)
An interaction between two factors (a two-way interaction) is present if the effects of the factors are not independent.
Interactions between the SNPs and physical activity (four categories), sex or age were tested by including a two-way interaction term (SNP*physical activity, SNP*sex or SNP*age) into the main effects model.
"It's a two-way interaction," she says.
In addition, there may be a two-way interaction between health conditions and insurance status.
The FlexRAN API enables a two-way interaction between agents and the master controller.
The results revealed a two-way interaction between post-lesion behavioral testing time and memory demands.
In particular, a two-way interaction between adherence to policy and type of compensation was found.
This type of models allows for a two-way interaction between high-frequency waves (inertial-gravity waves, Kelvin waves) and MJO.
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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