[keithwhor]

As a summary;

- Participants preferred whatever they saw first

- Otherwise, accelerating or rapidly accelerating progress bars were generally preferred

If you're designing progress bars with an unknown time to completion, my recommendation is to use an accelerating function for the first 95% over the predicted median time to completion. Then linear timing function for the next 4% and set the time to 3x the median time to completion. Automatically fill the bar when progress completes, no matter what.

e.g. if an action takes a median time of 4s to complete;

   f(0 <= t < 4) = 0.95 * ((t / 4) ^ 2)
   f(4 <= t <= 16) = 0.95 + (0.04 * ((t - 4) / 12))
   f(t > 16) = 0.99

You can adjust this however you see fit but I find it gives a pleasant experience.