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I have two distributions for the travel times between 30 cities on two days (Monday and Friday) for multiple starting times (3am to 9pm). I now want to test if the distribution between these two days is different. In other words, does Monday have different travel peak hours than Friday. The following figures visualize the distribution for the two days.

Friday:

Monday

and Monday: Friday

Which statistical test can I use for this? Is a Kolmogorov-Smirnov test or even a two-way Anova suitable?

Pedrinho
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    The question was partly answered here: https://stats.stackexchange.com/questions/1047/is-kolmogorov-smirnov-test-valid-with-discrete-distributions – ABK May 05 '20 at 13:29
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    Your measurements are related, so I would be skeptical of any test making an independence assumption like ANOVA and KS make. – Dave May 05 '20 at 13:32
  • In what useful sense can travel times be considered to have "discrete" distributions? – whuber May 05 '20 at 15:27
  • @whuber Not the travel times themselves but the time of the day is discrete. I have difficulties in finding the right headline for this problem. – Pedrinho May 05 '20 at 15:47

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