Identifying and handling variability and outliers

[bpbond]

Currently we identify outliers by comparing Core X's mass-normalized flux rate to those of all other cores subject to the same treatment and temperature within ~10 days. We apply ridiculously permissive standards though, only excluding if it's outside of 5 (CO2) or 10 (CH4) mean absolute deviations from the mean.

Question 1: tighten these up? @bpbond to do - double-check how many are actually being excluded (I think zero) actually it's currently 172

Question 2: @apeyton suggests we could just look at Core X and exclude its data, on a given date, if the CV between its replications is too high. Think about this; I am concerned we might end up tossing out a lot of cores, but we can test this.

[apeyton]

I actually think that option 2 is better than 1 (and not because I suggested it) because it is a better identified of potentially erroneous measurements (for the issue of high variability between duplicate measurements - issue #19 ). There are ways to make sure that we do not toss out a lot of cores, such as: (1) Apply a "ridiculously permissive" threshold for throwing out cores (throw out that core if the CV > 50%, versus the standard 10% or 20%), or (2) Use an alternative evaluation of precision (root mean square of relative differences, percentile precision, etc).

Hyslop & White, 2009 (J of Air & Waste Mgmt Assoc) use three different precision estimates and noted that a percentile-based precision and a mean absolute relative difference had a better fit to the data (i.e. did not overestimate observed differences).

*Percentile Precision (%) = 0.5(P84(D) - P16(D))100** P84, P16 == 84th and 16th percentiles in a scaled relative difference distribution (68% of normally distributed data lies within 1 sd of the mean, so this precision would be estimated at 0.5 the range between these percentiles). We could remove the 0.5, to make this more "permissive" because...soils, ya know. D == scaled relative difference, or [(rep1-rep2) / sqrt(2)] / rep1 (personally, I would throw in an absolute value, [abs(rep1-rep2)/sqrt(2)] / rep1 to avoid negative values....

The mean abs precision equation is less complicated, but more difficult for me to compose in Git. See can see for yourself in publication attached.

[apeyton]

Hysop & White 2009 est. precision in duplicates.pdf

[bpbond]

Here's a histogram of the per-core CV values for CO2, i.e. CV for a given core on a given day. The mean is 67%!

[bpbond]

Thanks for the Hysop and White reference. Glad to know that they also like MAD, which we're using, even though they're in a totally different field.

Re the graph above and "the standard 10% or 20%": these numbers are a bit higher than I would've guessed but fluxes are always, in my experience more variable than measurements of a static quantity. There's variability in the biology, and in the abiotic transport processes, and more error in the measurement itself. Anyway, obviously if we try excluding based on core CV it'll have to be based on a relatively high threshold.

[bpbond]

Outstanding question here: do we want to tighten 'ridiculously permissive' MAD standards? (And if so, why.)

[bpbond]

I think we're good here. Closing.