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I have time-dependent data from experiments done by two different labs. Lab1 has measurements at 60 different time-points. Lab2 has measurements at 40 different time-points (within the same range as Lab1 but not exactly the same time-points). I fitted the splines for data from Lab1 and Lab2. The curves look very similar. I would like to test if the fits/data are significantly different. I would like to answer the question if the difference between the results from both labs is statistically significant. What type of test I should use?

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  • $\begingroup$ when you say you "fitted the splines" are these regression splines with fixed knots or something else (smoothing splines, say)? If something else, how was the amount of smoothing chosen? Do you want separate estimates of noise variance from the two regressions or a common estimate? If these are time series are you taking any account of serial dependence in the data? $\endgroup$ – Glen_b -Reinstate Monica Aug 21 '18 at 2:00
  • $\begingroup$ I used linear regression (with least square method), as my data are nicely described by linear function in log scale. The data have 1 to 5 measurements at each time point. I am not taking any account of serial dependence. But I would like to test is these two sets of data are statistically similar within the time range, not only at any specific time point. $\endgroup$ – Kasia Kowalska Aug 21 '18 at 14:03
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Well one really helpful answer has been already given here. However I am not sure that you have gaussian modeling in your time series. A known test you can use is the Granger Causality test, however it seems that you do not want to predict Lab2 from Lab1, so I just state it to be safe.

Otherwise, study these two posts: 1, 2. I would standardize the time series (by scale) and then use interpolation in order to split each series in the same time-points in order to use an ARIMA model. ARIMA models can describe each series separately as stated here.

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  • $\begingroup$ I don't have gaussian modelling in my time series. My time series looks like linear function (on log scale). I don't think the Granger Causality test will be good choice in my case as I don't want to predict data from one lab using information from second lab. $\endgroup$ – Kasia Kowalska Aug 21 '18 at 14:05
  • $\begingroup$ There is a problem with approaches proposed in link as in those examples the time points are the same in both groups. In my data time points of measurements from Lab1 and Lab2 do not overlap. Time range is in (0,500)days but the actual measurements could be taken, say at day 20 for Lab1 and day 22 for Lab2, etc. $\endgroup$ – Kasia Kowalska Aug 21 '18 at 14:10
  • $\begingroup$ In the link the ARIMA is decribed but Peter Ellis commented that ARIMA is poor choice in that situation. It has been suggested that one should construct F-test to test the hypothesis of a common set of parameters. Having my linear regression analysis how could I construct that test? I am not a statistician so I would appreciate some directions. $\endgroup$ – Kasia Kowalska Aug 21 '18 at 14:20
  • $\begingroup$ I am sorry for the late response. You cannot use the F-test for non-nested models and that's why many propose making ARIMA models first and then using the F-test to compare specific parameters. Peter Ellis has a reference here. As it seems this is a clever way to be sure about your distribution of the model. It is the best way to check how your time series related. Now having used linear model, consider using information criterions such as AIC or BIC. $\endgroup$ – M. Cris Aug 25 '18 at 23:07

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