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First and foremost, I would like to declare that I have pretty basic knowledge in Statistics.

I have been googling etc which wasn't of much help.

Problem: I have data from 3 years - 2013, 2014, and 2015. Let's say the number of people who encountered an injury each year was:

  • 2013: 500 out of 50k (sample size survey in that year)
  • 2014: 600 out of 30k
  • 2015: 450 out of 39k

What test should I use to see if the increase/decrease is statistically significant?

Thank you.

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  • $\begingroup$ I suspect with such large sample size all tests will give you significant $\endgroup$
    – SmallChess
    Commented Sep 18, 2017 at 8:52
  • $\begingroup$ I suspect the opposite - the sample size is only 3 (3 years), and there is a decrease in percentage from year 2 to year 3. $\endgroup$
    – Zahava Kor
    Commented Sep 18, 2017 at 20:40
  • $\begingroup$ Differing views. Would there be any way at all to see if there's significant increase/decrease? $\endgroup$
    – Sai
    Commented Sep 20, 2017 at 6:41

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Although not the most rigorous statistical procedure, I would suggest using a linear regression. You can fit a linear model of the form

percentage of injuries = $a$ * year + $b$

And check whether $a$ is significantly positive (or negative), in which case you can say your time series is significantly increasing (or decreasing). The linear regression itself and the significance testing of the coefficients are common statistical operations, and there are implementations available in most stats software packages (e.g. R, Matlab, etc). I would also recommend you to do some web-searching to get a bit more familiar with linear regressions and this sort of tests if you don't know about them.

PS: I have to agree with Zahava Kor in the comment above -- with only three years it will be pretty hard to get a strong significance. I suspect $a$ will come out slightly positive, but perhaps not above significance threshold.

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  • $\begingroup$ Thank you. I did as recommended and as earlier suspected, 3 samples would be hard to get a strong significance. $\endgroup$
    – Sai
    Commented Sep 21, 2017 at 7:43

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