The phrase "a far higher degree" is correct and usable in written English.
It can be used to emphasize a significant increase or level of something compared to another.
Example: "The new software offers a far higher degree of efficiency than its predecessor."
Alternatives: "a significantly greater extent" or "a much higher level".
As noted here a fortnight ago, the dungareed yellow critters have a far higher degree of brand awareness than Puss-in-Boots and Madagascar's Penguins, which is why talk of $1bn for this spin-off ain't idle.
This story, while ill-received by us, must shock and anger those without to a far higher degree.
After all, for more than a century, movies were presented almost exclusively on photographic film, a medium offering a far higher degree of visual information than any home video format.
Descendants who were almost entirely white, with a smidgen of Cherokee heritage, were accepted into the tribe, but descendants who were black and Cherokee had to demonstrate a far higher degree of Cherokee stock.
In any case, a new American air campaign along the border would entail a far higher degree of coordination with Syrian insurgents than the United States has yet undertaken, including, American officials said, working out a system for using targeted airstrikes.
This applies, however, to a far higher degree to (forage) cropping than to true pastoral systems.
Finally, we investigate a profession involving far higher degree of public exposure and contact with customers than secretarial and accounting positions: real estate sales.
This far higher degree of carbonization was contributed from the dual role of the local carbonization of PS particles in the composite and the good dispersity of the composite powder, resulting in a much better contrast to the patterns.
The plot of Figure 4, shows that all DetMod modules have by far higher degree of protein complex overlap than MCL modules and few are the cases were these degrees are equal.
While natural collagen has shown promise for regenerative medicine, collagen mimetic peptides (CMPs) have emerged that allow far higher degrees of customization and ease of preparation.
While fighting sports, ball sports and (to a lesser degree) athletics have a far higher percentage of competitors from poor, black and mixed-race backgrounds.
