# What are some common measures of variation in an interval?

Context: I'm working on an app that "listens" to breathing/snoring and "diagnoses" apnea by taking note of pauses between breaths. For the most part this works well, but it's (rather amazingly) difficult, in the app, to distinguish snoring/breathing from talking/music (as with a TV playing in the room). I've pretty well exhausted signal processing techniques to distinguish this, so I'm trying some basic statistical measures.

I find that simply taking the normalized standard deviation of the breath/snore interval is fairly effective (values below roughly 0.35 are "good"), but I'm wondering if there might be another measure of variation, other than standard deviation, that would produce better results (a crisper dividing line). Basically, I want to distinguish "snore, snore, snore, pause, snore" from a random string of intervals with the same mean (such as you would get with voice), keeping in mind that snoring/breathing is not exactly clockwork regular.

So what other (reasonably simple) measures of variation in a train of numbers are there?

Update: It occurs to me that a measure of skewness might be useful here. Music/voice would presumably tend to have less skew than breathing/snoring. How does one measure skewness (particularly with some sort of moving average)?

Update 2: I've placed some sample interval lists out in Dropbox:

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Not all those samples are similar: the second snoring sample is sorted. Please, then, tell us more about what these numbers mean and how they were collected. Are the numbers lengths of pauses? If so, how does one recover the "snore, snore, snore, pause, snore" sequence in the question? In the first three samples, are these intervals observed in the order encountered or not? (The temporal sequence may include a lot of information that sorting obviously destroys.) –  whuber Jul 6 '12 at 16:57
With the exception of my "oops", the samples are in time order. The numbers represent the time between events, in 8000ths of a second. –  Daniel R Hicks Jul 6 '12 at 17:15
(I corrected my "oops" -- they should all be in time order now.) –  Daniel R Hicks Jul 6 '12 at 17:20
Thanks. What are the "events"? Are these just intervals corresponding to apparent pauses in the sounds? BTW, it looks like the measurement was done only with 1/8 second precision: almost all values are multiples of 1024. –  whuber Jul 6 '12 at 18:34
Right, measurements are done with about 1/8 second precision -- analyzed in blocks of 1024 samples. The "event" is a "snore" detected by the sound analysis. The "interval" values in the file represent the time from the end of one "snore" to the start of the next. (It would perhaps be more valid to go start-to-start or stop-to-stop, vs stop-to-start, but these are the numbers most readily at hand.) –  Daniel R Hicks Jul 6 '12 at 18:47
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## 1 Answer

Try spectral entropy; the paper by Vierto-Oja et al ("Description of the Entropy(tm) algorithm as applied in the Datex-Ohmeda S/5(tm) Entropy Module", H. Viertio-Oja, et al, Acta Anaesthesiol Scandinavica, 2004, 48:154-161.) gives a good definition. Basically, a more rhythmic signal will display lower spectral entropy: a pure sine wave will have 0 entropy while white noise has a value of 1. Snoring should be more rhythmic than speech and this variable may discriminate.

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Not sure yet if this is what I was looking for, but I've got to admit that the authors know how to express this stuff much more clearly than most such articles. I can almost make sense of it! (Or maybe I'm just trying to justify the \$35 I spent on the article.) –  Daniel R Hicks Sep 18 '12 at 19:02
(The article is "Description of the Entropy(tm) algorithm as applied in the Datex-Ohmeda S/5(tm) Entropy Module", H. Viertio-Oja, et al, Acta Anaesthesiol Scandinavica, 2004, 48:154-161.) –  Daniel R Hicks Sep 18 '12 at 19:05
Always a good idea to email the author before paying for an article. Most people are delighted that somebody wants to read their paper and are happy to send on! –  BGreene Sep 18 '12 at 21:08
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