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I have data:

  1. How many people register on cinema web site
  2. How many of these registrations purchase tickets

Conversion from (1) to (2) is exponentially distributed.

However, I've noticed that conversion on Friday + weekends is slightly higher than on work days. Each day I have same number of registration. One registration costs the same amount of money regardless day of week.

Hypothesis:

Users registered on Friday + weekends are from another distribution in compare with users registered on workdays.

What For:

To spend more money on internet advertising during weekends and less during work days. Taking into account that registration costs the same regardless of a day of week.

Question

  1. Is it correct to test such hypothesis ?
  2. What test is more suitable for such situation?

My own thoughts were to compare this 2 distributions using Mann-Whitney U test.

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  1. Yes, you can test this hypothesis.
  2. It sounds like you care for whether one has more conversions, but then you also care about whether they are distributed differently. Each question has an appropriate test.

For future reference, if you are interested in whether there is a shift in location, I recommend using the Mann-Whitney U test.

If you are interested in whether the two distributions are different in either location and/or shape, I recommend using the K-S test.

NOTE: You may want to consider whether the weekday conversion and weekend conversion are independent. If you do not feel that they are, neither test is valid.

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  • $\begingroup$ thanks! If I care more about conversion (not that these distribtuions are independent), does it refer more to a shift in location? And if I want more powerful test then I do K-S test? $\endgroup$ – Rimo Jun 1 '18 at 20:02
  • $\begingroup$ 1. If you care more about whether weekends have higher conversion, M-W U will work just fine (you may have to modify it if there are ties in number of conversions between any of the days [although, I suspect this to be unlikely]). 2. You can't compare the power, as the two tests test different things. The M-W U tests for a shift in location (in your case, whether conversion is higher for weekends). The K-S tests for a difference in location/shape of the distributions (in your case, whether conversion is distributed differently for weekends vs. weekdays). $\endgroup$ – Octavio Urista Jun 1 '18 at 20:14

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