Feature request: ttest_ind

[ahuang11]

Adding two tailed test?
https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.ttest_ind.html

[aaronspring]

would this be different from https://esmtools.readthedocs.io/en/latest/api/esmtools.testing.ttest_ind_from_stats.html?

I think there are many tests to be added for xskillscore in theory, but is the T-test applicable to forecasting and hence xskillscore?

[ahuang11]

I think my use case is relevant to forecasting (seeing whether the forecast anomaly values are statistically significantly different from some reference values), but I wasn't aware that xskillscore is only limited to forecasting; I thought it was simply a collection of scores for use with xarray/dask. In fact, I think that ttest_ind_from_stats in esmtools would be more better suited for xskillscore than esmtools because ttest_ind isn't just limited to ESM analysis (thus in scipy). Also ttest_ind is similar to pearson_r_p_val in my opinion, but instead of doing statistical significance testing on correlation, it'd be doing it on differences.

[bradyrx]

I think my use case is relevant to forecasting (seeing whether the forecast anomaly values are statistically significantly different from some reference values), but I wasn't aware that xskillscore is only limited to forecasting; I thought it was simply a collection of scores for use with xarray/dask. In fact, I think that ttest_ind_from_stats in esmtools would be more better suited for xskillscore than esmtools because ttest_ind isn't just limited to ESM analysis (thus in scipy).

We are entering the confusing web of scope creep :) My view is:

1. esmtools is really just my personal package of nice methods I find myself using frequently. That happens to be focused on Earth System analysis, so I called it that. It's a junk drawer for functions though.
2. xskillscore tagline is " Metrics for verifying forecasts ", so it should focus on statistical metrics for forecast verification. It can't really enter the territory of true skill scores, since you need three inputs: (a) the dynamical forecast, (b) the verification data, (c) the reference forecast (e.g. persistence or climatology). To get BSS for instance you need to run xs.brier_score(a, b) and xs.brier_score(c,b) and then derive from there. It could be done, but seems like scope creep.
3. climpred is a high-level package for forecast verification. It handles reference forecasts, bias correction, etc. That's where things like BSS should live, which will pull in low-level metrics from xskillscore.

[bradyrx]

But yes my question would be if you're looking for statistical significance that isn't bootstrapping, why not pearson_r_p_value? It uses the t-test there to get your pvalue. However, I think you can derive the critical correlation coefficient (i.e. the minimum corr needed for significance) by a simple manipulation of the t index. So I would be for adding it here. In the end, you'd get a gridded t-test value for a comparison of two gridded results. I don't care if there's redundancy here and esmtools because obviously xskillscore is used much more widely than my personal package.

[ahuang11]

Since I am not calculating any correlations, I don't think pearson_r_p_value is relevant, but I could be wrong.

For example, for pearson_r/_p_value, I commonly use it for anomaly correlations, e.g.
(forecast - climatology) correlated against (analysis - climatology)

In this case, I don't have climatology, I simply have
(forecast - reference)
and I think t_test would be more suitable here?

I could be wrong though~

[ahuang11]

2. xskillscore tagline is " Metrics for verifying forecasts ", so it should focus on statistical metrics for forecast verification. It can't really enter the territory of true skill scores, since you need three inputs: (a) the dynamical forecast, (b) the verification data, (c) the reference forecast (e.g. persistence or climatology). To get BSS for instance you need to run xs.brier_score(a, b) and xs.brier_score(c,b) and then derive from there. It could be done, but seems like scope creep.

At the same time the package name is xskillscore so should I trust the package name or tagline more hah; maybe xskillscore can be renamed to xscore or xverif similar to how xarray was renamed from xray.

Anyways, I don't think t-test ind is a skill score, so I think it could be added here similar to pearsonr p-value

[raybellwaves]

To add to the convo i'm seeing tests appear in the ML space e.g. https://spark.apache.org/docs/latest/api/python/pyspark.ml.html#module-pyspark.ml.stat

I'm fine with adding these tests as i'm personally interested in extending this package for use in ML workloads.

I see this repo as a host of ufuncs which can easily be applied to xarray objects (and pd.DataFrame.to_xarray()). Where the host of ufuncs is within the realm of how different/similar are two distributions (this started with deterministic metrics: correlation (and p-value), RMSE, etc. then we added probabilistic and recently contingency). I'm fine with adding stat tests which I imagine can be slotted here https://github.com/raybellwaves/xskillscore/blob/master/xskillscore/tests/test_metric_results_accurate.py#L28

[bradyrx]

We just recently officially modified the climpred tagline to broaden our scope to: "Verification of weather and climate forecasts." We could also broaden this tagline to be general. Something like: "Vectorized statistical assessments for forecasts and machine learning workloads."

The point @raybellwaves is to use these as minimization functions for training an ML model for instance? And then of course the testing like ttest_ind and https://github.com/raybellwaves/xskillscore/pull/176 can evaluate different model performances.

[raybellwaves]

Moving tagline discussion to https://github.com/raybellwaves/xskillscore/issues/180

testing like ttest_ind and #176 can evaluate different model performances

Yes I like the test module @aaronspring created in https://github.com/raybellwaves/xskillscore/pull/176

[ahuang11]

So to clarify, is it okay to add add ttest_ind to xskillscore?

I view xskillscore as my one stop for all xarray scoring~

[bradyrx]

@ahuang11, yes, I would add it to the new test.py module that @aaronspring is developing in #176. Another thing I have code for that is useful is a fisher z transformation to test statistical significance between two different grids of correlations.

[ahuang11]

I've been testing xr.apply_ufunc scipy.ttest_ind and I feel like the runtime is kind of slow, especially if applying it for each lat/lon. Maybe could try rewriting in numpy.