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I have a dataset which has temperature measurements for every minute in a certain time period.

I want to focus on 10 minute intervals and determine whether two adjacent 10 minute intervals differ significantly. Now this is fairly simple to do, but first I want to find out how big the difference should be for it to be significant.

I tried finding this out by looking at an average difference between 10 minute intervals. This works well enough but I'm wondering is it better to use an average or a min-max kind of difference?

Example:

10, 11, 10, 10, 11, 12, 12, 12, 13, 13 -> Average: 11.4, MinMaxDiff: 3

Let's say something goes wrong with the measurements in the next 10 minutes:

13, 13, 14, 28, 29, 28, 29, 30, 30, 31 -> Average: 24.5, MinMaxDiff: 18

Now in this example obviously both approaches would work, but is one approach generally better than the other?

Jamess11
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    Could you please read this thread and explain what your purpose is for identifying these 'outliers'? https://stats.stackexchange.com/questions/200534/is-it-ok-to-remove-outliers-from-data – mkt Sep 30 '22 at 07:12
  • @mkt The purpose is to detect faulty measurements from a device (let's say a fan stopped working on one device so measurements are 5 degrees higher than they were 10 minutes ago, which is basically impossible when it comes to temperature). I want to capture that moment when the device 'breaks down'. – Jamess11 Sep 30 '22 at 07:17
  • That's helpful context - could you edit it into the question? Comments are not read by many. – mkt Sep 30 '22 at 14:01
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    You should really follow the advice to edit contextual information into the post, with details ... what kind of equipment, what kind of device, ... but this sounds like what control charts were made for, Consider adding the tag [tag:quality-control]. If you have some temperature series from equipment known to be correctly functioning, but otherwise the same context, that could be useful for making reference distributions. – kjetil b halvorsen Oct 01 '22 at 23:34

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