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So here are the basic facts:

My population is a city. The sample is 500. I am calculating how many minutes it takes by foot to walk to their nearest shop.

The participants are split into two groups: car users n= 210 and public transport users n=290. I want to see if the means differ between the groups.

Which test should I use?

If a t-test, should it be paired or unpaired?

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  • $\begingroup$ You've tagged your question with t-test, so you have an idea about where to start. What have you tried so far? Please check the community guidelines on how to ask a good question to increase your chances of getting an answer. $\endgroup$ Apr 8, 2017 at 16:51
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    $\begingroup$ T-tests should be ok... - is your data normally distributed? $\endgroup$
    – Dragonfly
    Apr 8, 2017 at 16:53
  • $\begingroup$ This is where i get confused. Like my range is approx 1-30. But i dont understand how I tell if my data is normally distributed? Also, would i be using a paired or unpaired t-test? $\endgroup$ Apr 8, 2017 at 16:56
  • $\begingroup$ Tests shoud definitely be unpaired. Can you show us histograms? Walking time to closest shop doesnt sound a like a normal distribution (since it will be capped at zero ...), so maybe some nonparametric (rank) test, or bootstrapping. $\endgroup$ Apr 8, 2017 at 17:45

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Test should definitely be unpaired, car users and public transport users are presumably defined as disjoint groups. Walking distance to nearest shop (min) will not be normally distributed, and there is no other natural alternative distribution model. I would not be surprised with some long-tailed distribution! and distributions in the two groups could well have different shape.

So, I would go for some permutation test here. If you can post (a link to) data we can have a look.

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  • $\begingroup$ +1 for mentioning the permutation test. @isuckatmaths the gist of the permuation test is that you assume that the two sets of data come from the same distribution (null hypothesis), and if that is the case, the it doesn't matter if you scramble the labels. So scramble the labels, calculate something (like the difference in mean), and see how likely the real observed something is. If the scrambled somethings are pretty much all between -1 and 1 but your observed something is 12, the labels probably matter. $\endgroup$
    – Dave
    Sep 13, 2019 at 15:02

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