In noisy offices, actual silence reduces cognitive errors by one third

From Influence of active-noise-cacelling headphones on cognitive performance and employee satisfaction in open space offices by Muller et al.  From the Abstract:

High speech intelligibility in open space offices leads to problems. As a result of the irrelevant sound effect it influences cognitive performance negatively. Room acoustic measures do often not lead to improvements if an open space office design is to be maintained. For this reason a study was conducted to examine if active noise cancelling headphones influence cognitive performance and subjective feeling in an open space office. This was done with a cognitive task (serial recall) and a survey after every term. No significant difference between the condition with active noise cancelling headphones switched on and switched off as well as without headphones could be determined. However, active noise cancelling had an influence on subjective ratings. The background noise with active noise cancelling was rated as significantly less annoying, ability to concentrate significantly higher and the speaker distance was rated significantly larger in comparison with active noise cancelling switched off or without headphones. 

Wearing noise cancelling headphones in an open-plan office helps a little bit — reducing cognitive errors by 14% — but actual silence reduces those errors by one third.