The phrase "a much smaller degree" is correct and usable in written English.
It can be used to compare the extent or magnitude of something in relation to another, indicating that it is significantly less.
Example: "The new policy has an impact on employee productivity, but only to a much smaller degree than anticipated."
Alternatives: "a significantly lesser extent" or "a considerably reduced level".
Authorities with a much smaller degree of independence from government are not uncommon across Europe.
However, our results also revealed — with one key exception — that support for redistribution increased to a much smaller degree.
Her polling tells her Mr Nader still hurts Mr Kerry more than Mr Bush, although by a much smaller degree than a few months ago.
"Authorities with a much smaller degree of independence from government are not uncommon across Europe," it added.
In contrast, the iBT straddled the boundary between the two to some extent and involved a much smaller degree of the information reduction that is required in summarizing.
Within the parameters of Earth's oceans, the electrical conductivity of seawater depends on temperature, salinity, and to a much smaller degree pressure (depth).
However, our results suggest that the variation of C(k) in biological networks, is caused by the abundance of large degree nodes connecting to those with much smaller degree, which we refer to as a heuristic "spoke" model.
Complex living cells produced in vivo (as products of evolution) raise the question whether all this complexity is really necessary for life, or whether cellular life can also be realised in human laboratories, involving much smaller degrees of complexity (p. 1293).
In contrast, cross-validation with 20 replications and bootstrapping with 200 samples showed much smaller degrees of variability between repeated analyses of the same small data set and, in both cases, the standard deviation of the C statistic was less than 0.01, which was small in relation to the absolute error.
The larger Tyrannosaurus rex could open its jaws at nearly the same angle, while a related plant-eating dinosaur had a much smaller gape of 43.5 degrees.
In contrast to the full-state-space approach, the numerical algorithm proposed in the previous section employs a much smaller number of the degrees of freedom.
