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If I have a distribution like the one below, is there a way to say to what degree a value is part of the distribution?

e.g. if I am considering the value 4.122e-4, it clearly falls within the distribution, but I guess I am asking to what extent is it an average value - for instance, if I was considering 7.524e-4 I would say this is quite an extreme value (towards the edge of the distribution) in comparison to 4.122e-4 - is there a measure of how extreme (or "un-extreme" a value is)?

This may be a stupid question - perhaps it just requires a simple description i.e. 4.122e-4 is XXX away from the mean.

Background:

The parameter "ratio" is the ratio of repeats (%) (i.e. % of repeat-like bases) within a nucleotide sequence (cf. bioinformatics) to length of the sequence itself.

The question for the value 4.122e-4 is, is this ratio particularly high - i.e. does this particular sequence, this region of the genome, have a high per-base repeat percentage in comparison to other sequences in the genome, or is just average? So I think yes, it was generated by the same process.

I hope this makes sense (I guess I could just use repeat (%) without dividing by the sequence length, but my thoughts were that longer/shorter sequences might tend to be more repetitive, and I wanted to take this into account).

Thanks

rep density plot

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You can only tell how is your value relative to the distribution. One option could be using the percentile. Telling the percentage of values smaller (or bigger) than your value gives you an idea of where the value is respect to the distribution. If you assume that your data is normally distributed, you can also use a Z-score, which will tell you how many standard deviations from the mean is a given value.

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  • $\begingroup$ Thanks, I think the percentile value will be useful for describing what is seen. Is there a test available if the data is not normally distributed? I carried out the Shapiro-Wilk test and the data is not normally distributed $\endgroup$ – meld24 Aug 6 '15 at 10:24
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retrot has suggested a good idea, and this is the basic logic behind significance testing in general. You have a model and you look at how compatible a given data point is with that model, and then you either reject or don't reject the model on this basis.

In this case it might be useful to supplement this thinking with any prior information you might have about where the value is coming from. Is it a priori likely that it was generated by the same process that generated the points used to construct this density estimate? In that case it might be naive to reject the model just because the data point fell in the tail of the distribution. By the way, presumably you were confident in pooling together the observations that produced this estimate. What was it that gave you this confidence?

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  • $\begingroup$ Thanks, I've added more background detail to the question - I think the value was generated by the same process $\endgroup$ – meld24 Aug 2 '15 at 14:35

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