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I'm looking at some accident statistics and have a question about how it's reasonable to interpret the data. The numbers are fatalities in traffic accidents, and I want to discuss a newspaper article where the increase from 2012 to 2013 is described as "dramatic". I'd like to know if the increase, which is from 145 to 187, is really anything out of the ordinary.

Let's say I have access to data for all years back to 1960 - is it possible to find mathematically if this "jump" is anything but normal variation? Just by looking at the data, I can see several other increases from one year to another that are as high, though the general trend seems to be falling. What's the "fair" way to assess this data?

I'll admit, I am a noob at statistics and am basically after a nudge in the right direction on how to figure this out.

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A simple and practical way of doing it could be to remove the trend from the data (you can do this fairly easily in Excel) and then calculate the standard deviation of the stationary time series (i.e with the trend removed). You should do this without the most recent data point in it (i.e. where the jump occurred). You then calculate how big the increase is from the stationary time series point. You can then calculate how many standard deviations the increase represents. If it is three or more standard deviations then you could argue that this increase in accidents is significant.

Having said that, if you have noticed similar increases in the past then it is likely that there is some dynamic at play that is causing these increases (for example, there could've been bad weather in all of the years where there was an increase, or some similar dynamic). It won;t be possible for you to tell this without having access to other data that may be correlated or causally linked to the accident data.

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