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I have data on market share. I would like to compare a firm's mean market share before and after an event.

The data is quarterly and I have only been provided with 16 observations, 8 before the event and 8 after the event.

The data looks to be non-normal (most likely due to small number of observations).

The variances are not equal.

So in this case, am I able to use the Mann-Whitney test?

I worry that:

(1)There are not enough observations (2)The data is from a single firm so may not be truly independent

Are these okay to ignore or should I be looking for a different test?

Thank you for having a look.

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The sample size is small, but it is not so small as to rule out use of the Mann-Whitney test.  However, if you are concerned, it would be reasonable to do a boot-strap analysis (shuffling the data many times and calculating the statistic).  The resulting $P$-value from this analysis may be more informative.

Regarding the issue of lack of independence, unfortunately there is no alternative test that can correct for this issue if it is present.  (Unless it is a systematic form of dependence, like multiple data from different firms.)

Happy to share more on the boot-strap approach if that seems useful.

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  • $\begingroup$ Shuffling the data sounds more like permutation test than bootstrap ... $\endgroup$ – kjetil b halvorsen Apr 18 '18 at 17:21

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