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I am a little bit confused by the distinction. What are the formal definition of paired and unpaired? More specifically, if I have 2 time series measuring the same quantity (e.g. vacancy rate) with slightly different underlying data, are the data paired or unpaired?

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Paring comes from the experimental design; for example (1) when the same quantity is measured with two different devices (2) When a certain feature of two subjects is measured together with the same device (this is common in genetics and cytometry). Having the same sample size does not necessarily imply pairing. – user10525 Jun 15 '12 at 12:53

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Paired refers to the method of comparison. If you are comparing two data sets the comparison is paired if you take differences but matching data points from the two data sets. So this would be done if the two sample sizes are equal. So with the time series you are pairing if you match the two series at each time series. It is the difference between comparing the mean paired difference versus the difference of the two sample means. When data are not paired you can test for difference between means with unequal sample sizes.

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I know that it is related to the method of comparison. But in my example which method is more reasonable, paired or unpaired? I cannot somehow decide. IMHO, if I was interested in the effect of the data change on single time series points, I would choose a paired test. Otherwise, if I am only interested in the difference between the means of the 2 time series, i.e. are they equal or not, than I would choose an unpaired test (?) – teucer Jun 15 '12 at 12:11

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