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Description
In document of xskillscore, result of halfwidth_ci_test is described as follow: difference in scores (score(f2) - score(f1))
However, I discovered that this is only partially right.
For example, when the metric is RMSE, this method returns the difference score(f2) - score(f1), but when the metric is ME, this function returns the difference score(f1) - score(f2).
Code Sample, a copy-pastable example if possible
length = 100
obs_1d = xarray.DataArray(
numpy.random.rand(length),
coords=[
numpy.arange(length),
],
dims=["time"],
name='var'
)
fct_1d = obs_1d.copy()
fct_1d.values = numpy.random.rand(length)
# create a worse forecast with high but different to perfect correlation and choose RMSE as the distance metric
fct_1d_worse = fct_1d.copy()
step = 3
fct_1d_worse[::step] = fct_1d[::step].values + 0.3
# half-with of the confidence interval at level alpha is larger than the RMSE differences,
# therefore not significant
metric = "rmse"
alpha = 0.05
significantly_different, diff, hwci = xskillscore.halfwidth_ci_test(
fct_1d, fct_1d_worse, obs_1d, metric, time_dim="time", dim=[], alpha=alpha
)
print("RMSE DIFF:",diff.values)
print("RMSE HWCI:",hwci.values)
print(
f"RMSEs significantly different at level {alpha} : {bool(significantly_different)}"
)
metric = "me"
alpha = 0.05
significantly_different, diff, hwci = xskillscore.halfwidth_ci_test(
fct_1d, fct_1d_worse, obs_1d, metric, time_dim="time", dim=[], alpha=alpha
)
print("ME DIFF:",diff.values)
print("ME HWCI:",hwci.values)
print(
f"MEs significantly different at level {alpha} : {bool(significantly_different)}"
)
print ( "RMSE 2,1: ",xskillscore.rmse(fct_1d_worse,obs_1d, dim=[]).values.mean(),xskillscore.rmse(fct_1d,obs_1d, dim=[]).values.mean() )
print ( "RMSE DIFF 2-1:", (xskillscore.rmse(fct_1d_worse,obs_1d, dim=[]).values-xskillscore.rmse(fct_1d,obs_1d, dim=[]).values).mean() )
print ( "ME 2,1: ",(fct_1d_worse-obs_1d).mean().values,(fct_1d-obs_1d).mean().values )
print ( "ME DIFF 2-1: ",((fct_1d_worse-obs_1d).values-(fct_1d-obs_1d).values).mean() )
print ("xskillscore version:",xskillscore.__version__)the result is listed as follow:
RMSE DIFF: 0.002145380792967111
RMSE HWCI: 0.03084942672029623
RMSEs significantly different at level 0.05 : False
ME DIFF: -0.10199999999999998
ME HWCI: 0.027772820244038265
MEs significantly different at level 0.05 : True
RMSE 2,1: 0.35575854107274524 0.3536131602797781
RMSE DIFF 2-1: 0.0021453807929670793
ME 2,1: 0.02998835594288012 -0.07201164405711986
ME DIFF 2-1: 0.102
xskillscore version: 0.0.24
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