"showed that when" is correct and usable in written English.
For example: The research showed that when people spend time out in nature, they experience lower levels of stress.
Iraq showed that when, never forget, many European nations supported our action.
"He showed that when things are clicking he can make some nice throws," Hambrick said.
Woodward himself showed that when his thesis altered because the government's standing had altered (drastically).
She showed that when given young plasma, old mice regained their stamina.
We showed that when we are behind we are a side that can go forward.
Ranieri's success showed that when the ingredients are right, anything is possible.
This campaign showed that, when we work in unity, we can be as effective as anyone".
It showed that when the playing field is level, the organization can come up short".
Studying a particular lesson, the Stanford researchers showed that when the order was reversed, students' performances improved substantially.
Yet studies showed that when kids received a commercial toy, usually they'd play with it for only a short while.
The researchers showed that when they excite the molecule with a photon, one of its methyl groups quickly splits away.
