The phrase "a difference between the former" is correct and usable in written English.
It can be used when comparing two previously mentioned items or concepts, highlighting a distinction related to the first one mentioned.
Example: "There is a significant difference between the former and the latter in terms of their effectiveness."
Alternatives: "a distinction regarding the former" or "a contrast with the former".
I'm not entirely sure it's a difference between the leadership of former CEO Steve Ballmer and current CEO Satya Nadella, but the transformation does appear to coincide with the transition in leadership.
There was no evidence of a difference between the arms in the former but strong evidence of an increase in the latter (adjusted risk ratio 5.28 (2.5 to 10.77)).
The results show a substantial difference between the former models and the latter, in terms of the estimated total marginal impacts of the different variables and the pattern of the error terms.
As shown in Table 1, Dicken's empirical method calculated a peak flood discharge of 691.5 m3/s, while that of SCS was 179 m3/s, implying a significant difference between the former and the latter.
It was only after researchers combined all the data from various types of cancers that they were able to show a statistically significant difference between the former hormone users and those who had used placebos during the study.
It was only after researchers combined all the data from various types of cancers that they were able to show a statistically significant difference between the former hormone users and those who had used placebos.
Republicanism does not collapse into liberalism if there is a real and substantial difference between the former's view of liberty as independence from arbitrary or uncontrolled power, and the view of negative liberty as non-interference, generally embraced by the latter.
The waveforms in Fig. 10 show the difference between the former protection and the improved protection when a single phase-ground fault occurres in the collector 1 from 1.2 s to 1.5 s.
The only real difference between the former teammates on last season's World Series champion Florida Marlins was a bloop single and a base-running mistake.
As the equivalence ratio is reduced, the difference between the former and the latter shrinks until the dynamic stability condition (2) is violated, leading to blow-off.
