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My very first IT manager back in the 90s once stated that the absolute worst repetitive response time an application can have is three seconds. His argument was that this is long enough to be a significant annoyance, and too short to get a (cognitive) break. So if you want to design a system for maximum frustration, make every action have an average response time of three seconds (and allow for some variation too, just to make it unpredictable as well).

This was my managers anecdotal input, but I have always thought of it as valid. And it seems to make sense given Jakob Nielsen's thoughts on the matter.

Is there any research to back up (or invalidate) the claim?

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Some papers are mentioned in the article - Miller 1968; Card et al. 1991

There is also this one revisiting the concept, it suggests that delays below 100ms are still perceivable and impact the experience.

[...] performance in zero-order and more demanding second-order tasks already gets impaired by latencies between 16-60 ms. Therefore, the lower boundary of 100 ms as mentioned in several design guidelines appears outdated.

It also has a nice table comparing all previous studies.

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