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I have two data loggers which are recording a physiological signal. Device A is a system that has been in place for many years, and records data ~once/minute. Device B is a prototype device which collects data ~40 times as often. The devices don't necessarily record synchronised data. Also, Device B does not record data on a regular time base.

I was intending to compare the two recordings using a t-test, but a colleague pointed out that as the two devices are recording the same data they are not truly independent. However, as the data points were not collected simultaneously on both devices it's not possible to perform a paired t-test. Is there any other test that could be carried out to check the similarity of the two data sets?

EDIT: I'm not necessarily interested in the fact that it is a time series. Looking at the distribution of values recorded can be enough.

Edit2: The data is analysed in 2 different ways currently. A clinician will look at the trace itself, making conclusions simply by 'eyeballing' it. They will also look at a histogram of the values recorded.

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  • $\begingroup$ "Is there any other test that could be carried out to check the similarity of the two data sets?" Is your intent simply to show that they give the same distribution of outputs (which you could test eg by comparing the CDFs)? This seems a bit odd since I would expect you to be more interested in checking their measurements agree when they're measuring the same thing (which in your case, if I understand your setup, means that their measurements at a given time should be close to agreement?). $\endgroup$
    – Silverfish
    Jan 28, 2015 at 10:48
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    $\begingroup$ In medical statistics a common way to compare measurements from two different devices is a Bland-Altman plot $\endgroup$
    – Silverfish
    Jan 28, 2015 at 10:52
  • $\begingroup$ I know about Bland-Altman plots, but I don't think (could be wrong here) that it is applicable in this case as the data isn't collected at the same points in time. The data is analysed in 2 different ways currently. A clinician will look at the trace itself, making conclusions simply by 'eyeballing' it. They will also look at a histogram of the values recorded. $\endgroup$
    – Doragan
    Jan 28, 2015 at 11:58
  • $\begingroup$ That's correct about Bland-Altman and it now makes more sense why the distribution is all you care about from the histogram point of view (but you still need to do something different to check the traces agree, I'd suggest). Would I be correct to think you need to investigate whether the two devices produce similar output distributions for each patient? IE they should produce two similar histograms for Patient A, and two similar histograms for Patient B (possibly quite different to A), and so on? $\endgroup$
    – Silverfish
    Jan 28, 2015 at 12:05
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    $\begingroup$ Since not everybody reads the comments, you should probably try to edit some of these key points into your question - particularly the way the output gets used by the physician (as histogram and trace). For the histogram side of things, you're trying to test how well one whole bunch of empirical distributions match with their pairs, which is a harder task than just seeing if a single distribution matches its pair. $\endgroup$
    – Silverfish
    Jan 28, 2015 at 12:09

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A t-test is also not adequate because this is time series data. You need to start with time series methods, which could be ARIMA or spectral analysis methods.

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    $\begingroup$ Will this matter if I am not particularly bothered about the time series aspect, and just interested in the distribution of values logged by each device? $\endgroup$
    – Doragan
    Jan 27, 2015 at 16:16
  • $\begingroup$ Any autocorrelation will influence (heavily) the distribution of any test statistics you might compute, so is relevant, yes. $\endgroup$ Sep 30, 2015 at 8:34

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