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I have a set of time series data with one observation per week for each county in a certain state. I want to see if there is a statistical difference between the observations at the point in time indicated by the black line and the red line. The blue line is the mean of each time point, the orange line is zero, and the blue shaded area is two standard deviations. Unfortunately, there is quite high variance. What is an appropriate test to determine if the set of data collected at the red time is different from that at the black time? Since my observations are from the exact same counties, would a paired t-test be appropriate? I have already run an F-test, and the variances are significantly different at the two time points, and the errors are two-tailed. Thank you!

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  • $\begingroup$ Why are you comparing those two time points? Because the data make it look like there might be an interesting difference, or because those time points were of interest prior to obtaining the data? It makes a BIG difference because you can never test a hypothesis with the data that suggested the hypothesis in the first place. $\endgroup$ Jul 18, 2020 at 22:56
  • $\begingroup$ I decided these two time points before observing the data. $\endgroup$
    – taurus
    Jul 18, 2020 at 23:05

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