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The phrase "also demonstrated that when" is correct and usable in written English.
It can be used when discussing findings or results in a context where you are adding information about a specific condition or situation.
Example: "The study also demonstrated that when participants received adequate training, their performance improved significantly."
Alternatives: "also showed that when" or "further indicated that when".
Exact(28)
(No one told her that there is no I in E!) The ceremony was intended to show support for the Writers Guild, but it also demonstrated that when it comes to award-show writing, less is more.
We also demonstrated that when using the stateful forwarding property it is easy to implement producer-driven differentiated services.
We also demonstrated that when the country fixed effects were removed from the regression model the effects of home computer use vanished.
Our analytical results also demonstrated that when all the hosts transmit at an equal data rate, 802.11 CSMA/CA can only present fairness on condition of homogeneous link qualities; the presence of diverse link qualities can cause significant unfairness.
Using DMA techniques we also demonstrated that when pure trehalose, a fragile glass-former, was diluted with a small amount of the strong glass-former, glycerol, the overall mixture was strengthened significantly.
Studies have also demonstrated that when people receive a favour from someone, they feel obligated to reciprocate in some way – what social scientists refer to as the "norm of reciprocity".
Similar(32)
It was not just showing people who do not understand her and who do not trust her who she is as a person, or laying out her policy proposals, but also demonstrating that when she represents them on the world stage, she would do so with that hard-to-pin-down aura of leadership and power.
Moreover, Apple's success also demonstrates that when you make women happy, you make everybody happy.
They also demonstrate that, when immigration does affect wages, its effects can be identified by local labor markets comparisons and structural simulations of the national economy.
We also demonstrate that, when mixed with photochromic organic compounds, ILGs display rapid color changes, similar to light-triggered camouflage, on living Musca domestica specimens.
The analytical results also demonstrate that when SS is spread within columns, the system over-strength increases by 30% with respect to the carbon-steel benchmark structure.
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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