"show substantial improvement" is correct and usable in written English.
You can use this phrase when discussing something that has the potential to improve. For example, you might say, "If John can show substantial improvement on his math test scores, he will be better prepared for college."
The city has also raised principals' salaries and is offering bonuses to experienced principals who agree to work in low-performing schools, as well as those whose schools show substantial improvement in standardized test scores.
The simulation results show substantial improvement in throughput and delay for real-time traffic.
Our simulation results show substantial improvement in the network sum rate capacity.
Post-packaging data show substantial improvement in the stiction behavior of coated devices versus uncoated devices.
However, for a particular system used in this work, it does not show substantial improvement of production efficiency.
It does not show substantial improvement of gas productivity for the particular system used in this study.
Despite the efforts of its new chairman, Luc Vandevelde, the retailer has yet to show substantial improvements.
Experimental results show substantial improvements in performance as a result of these improvements.
Experimental results on a 7 T human eight-channel parallel transmit system show substantial improvements on excitation patterns with the use of eddy current correction.
For Fitch — and really for all of us watching the company — Nokia needs to show "substantial improvements" over the next few quarters in cash flow and profit margins if it hopes to improve its credit standing and avoid slipping even more.
In addition, these models fail to show substantial improvements in risk factor control and health outcomes for chronic patients [ 10- 12].
