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The phrase 'higher level of difficulty' is correct and usable in written English.
You can use it to describe an increase in the difficulty of a task, activity, or challenge. For example, "The students were given a higher level of difficulty on the final exam than on previous standardized tests."
Exact(20)
At a higher level of difficulty, you are often required to show even more restraint, completing your mission without leaving any trace of your presence.
And there is a class of survey that represents an even higher level of difficulty – cohort studies.
The report's author, Keith Topping, who is professor of educational and social research at Dundee University, said that the findings revealed primary school children were reading "at a much higher level of difficulty and with a greater level of comprehension than those recommended to them".
More laparoscopic training and experience during residency may partly melt away this subjective higher level of difficulty.
The subjective higher level of difficulty of LH versus AH may have a substantial role in the slow implementation of laparoscopic hysterectomy in The Netherlands.
If academic results improve, despite a higher level of difficulty of the assessment activities, the learning experience will be better and the target competences will be achieved.
Similar(40)
The study was designed to progress patients through higher levels of difficulty.
Object manipulation and/or intertrial variability mark higher levels of difficulty.
Fact training was only present at the higher levels of difficulty, and the software took too long to reach these levels.
At higher levels of difficulty of the software we therefore included small addition and subtraction facts which children had to solve prior to making a numerical comparison.
Older males rated higher levels of difficulty in performing functions and tasks in all health domains as compared to older females.
More suggestions(18)
higher level of pain
higher level of disability
higher level of concern
higher level of effort
higher level of ability
higher level of skill
higher level of disadvantage
higher rate of difficulty
higher level of complication
higher degree of difficulty
higher level of constraint
higher level of reluctance
higher level of burden
highest of difficulty
higher level of uncertainty
increasing level of difficulty
higher level of stress
higher level of complexity
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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