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I wish to average detections coming in over time.

I use the interquartile range to identify outliers and to discard them. I look at the last 30 values.

What do I do if each new value is an outlier, and hence is discarded? How do I detect that the average has significantly shifted?

I asked a fuller version of this question on stats.stackexchange.com.

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I'd suggest using a t-test, or similar suitable test depending on your particular distribution. These tests can be used as indicators of whether 2 distributions have the "same" mean. Treating a pair of your measurement sets from different times (say 30 values apart so there's no overlap) as though they come from different distributions will give you a measure of whether the means are significantly different, hence the average has "changed". If your data is fairly Normal, this should work. If not, you might try reviewing the t-test wikipedia page. There are some suggestions there of non-parametric techniques to apply in other cases. Those should get you started.

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