Test for change over time in a time series I have a time series of anomalies in some data, with 69 observations in total. I want to statistically test if the number of anomalies in the time series have increased over time? Can I use a t-test for the purpose, possibly by dividing my data into 2 or 3 groups, and then comparing these groups? In case, I'm completely off, please suggest a better test/approach. Statistics, unfortunately, isn't my strong suit.
 A: "Increasing over time" kind of implies a smooth increase. Splitting the time series would actually be testing for the difference in the number of anomalies in the two periods. That's valid, but if you're looking for a smooth increase, you might be better off just doing a simple linear fit, and then calculating the confidence intervals on the trend. If there's a possible constant trend (horizontal line across your data that fits within the confidence intervals), then it's likely that there's no statistically significant change. 
From glancing at your graph, It's difficult to tell if that's the case, but if you want some quick R code, try this (replace AirPassengers with your data, assumes your data is in the ts format):
AP.fit <- lm(AirPassengers ~ time(AirPassengers))
AP.ci <- predict(fit, interval="confidence")
plot(AirPassengers)
abline(AP.fit, col='red')
lines(x=as.vector(time(AirPassengers)), y=as.vector(AP.ci[,3]), col='red', lty=2)
lines(x=as.vector(time(AirPassengers)), y=as.vector(AP.ci[,2]), col='red', lty=2)

Which gives you something like:

