"by a higher standard" is correct and can be used in written English.
You can use it when referring to a metric or level which surpasses another. For example: "We must strive to meet our goals by a higher standard than ever before."
Judges were to be judged by a higher standard.
I don't mean to say that drama should never concern itself with factual accuracy, only that a work of art must be judged by a higher standard.
Perhaps for some he exceeded the low expectations they previously had of him, whereas Cameron was being judged by a higher standard.
And by investigating the sins of the former regime, the new governments have publicly invited their own people to judge them by a higher standard of behaviour.
A Foreign Office spokesman told members of the House of Commons that the United States and Britain "are well aware that we will be judged by a higher standard than Al Qaeda or the Taliban" and that a British delegation that visited the Guantánamo Bay Navy Base on Friday had found "that these standards are being met".
Once you've been exposed to a new and exciting thing, you're influenced by a "higher" standard -- someone else's.
Foster: When somebody says they Swear By something, it's a higher standard.
And a child prodigy becomes just another musician — held, if anything, to a higher standard by skeptics of hype.
In our recent work with countries we have sought to achieve a higher standard, by validating all data sources.
You're less likely to be ghosted or homme fataled by a match brought to you by a matchmaker, because there is a higher standard for personality and accountability.
Mr. Gore accused him of negative campaigning and said, "If you're going to talk about a higher standard, live by it".
