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I would like to compare the total number of public M&A transactions observed in two separate years (e.g. 2021 vs 2022). Given the data set for each year is complete (i.e. a population), can I simply compare the counts and determine an increase or decrease in activity? Or should I view each count merely as samples of a population of all M&A activity (all-time) and use hypothesis testing to demonstrate the two samples are likely to come from different populations before concluding a significant difference?

Thanks

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There are two issues here:

One is what you are interested in. If you are only interested in those two years, then you don't need a hypothesis test. Hypothesis tests are inferential statistics that go from a sample to a population. You have the population.

OTOH, if you are using those two years as a sample, then you might want a hypothesis test, but, depending on exactly what it is and what data you have, you probably won't be able to do one, because your N = 2. (Again, that would depend on what you are testing).

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  • $\begingroup$ Thanks for your thoughtful response, Peter, it’s much appreciated. If I could break down the annual count in each year to weekly or monthly totals within each year (to boost N), do you think I could use a Poisson rate test to demonstrate the rate in one of the years was significantly different from the other? Thanks again, Kerry. $\endgroup$
    – Kerry
    Aug 6, 2023 at 19:09
  • $\begingroup$ Why would you do that? People get hung up on "significance" but, if you have the population then, in effect, p = 0.000 $\endgroup$
    – Peter Flom
    Aug 6, 2023 at 23:32
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    $\begingroup$ Ah - I see. That clears everything up for me and answers my original question. Thanks, Peter. $\endgroup$
    – Kerry
    Aug 7, 2023 at 9:33

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