mean difference / composite tests

[arfriedman]

Hi all,

I was wondering: Are there any tests of mean difference (i.e. composite or superimposed epoch analysis) available in Pyleoclim? Specifically, I would like to compare the means of different intervals within a serially-correlated timeseries (e.g. Wilks, Statistical Methods in the Atmospheric Sciences, 4th ed., sec. 5.2.4).

Would it appropriate to calculate the confidence intervals of the means using phase-randomized surrogates similar to correlation (i.e. Ebisuzaki)? If so, does anyone know of any examples of this in the literature?

Thanks for any insights.

-Andrew

[CommonClimate]

hi @arfriedman , sorry I only just saw this. Yes, you can use the SurrogateSeries class to generate a null distribution for any test, including a difference of means. I think it's a generally healthy practice unless there is a more sensible alternative that better meets the assumptions of your problem (e.g. a two-sample T-test when the data are truly IID Gaussian). In your case, you would:

1. generate surrogates for series1 and series2 according to your method of choice (e.g. isospectral = phase-randomization = "Ebisuzaki")
2. compute pairwise differences of means, using itertools.product()
3. obtain the null distribution and compute what you need from it (e.g. a p-value)

Please let me know if you hit any snags.

[arfriedman]

Thank you @CommonClimate for this clear and thorough explanation!

[arfriedman]

I'm wondering if I could ask a follow-up:

In my case, I am comparing the means of subsets within a longer series, e.g., decadal means of a century-long record. For this type of comparison, would it make sense to also apply block bootstrapping within the surrogates to generate my null distribution of decadal means? I have previously seen block bootstrapping used to compare segments within autocorrelated time series, but I'm not sure if this technique adds anything to phase-shifted resampling. If not, would it be more straightforward to simply compare the same fixed periods from a large number of surrogates?