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[backport 2.3.x] API (string dtype): implement hierarchy (NA > NaN, pyarrow > python) for consistent comparisons between different string dtypes (#61138) (#61649)
In previous versions, comparing Series of different string dtypes (e.g. ``pd.StringDtype("pyarrow", na_value=pd.NA)`` against ``pd.StringDtype("python", na_value=np.nan)``) would result in inconsistent resulting dtype or incorrectly raise. pandas will now use the hierarchy
in determining the result dtype when there are different string dtypes compared. Some examples:
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- When ``pd.StringDtype("pyarrow", na_value=pd.NA)`` is compared against any other string dtype, the result will always be ``boolean[pyarrow]``.
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- When ``pd.StringDtype("python", na_value=pd.NA)`` is compared against ``pd.StringDtype("pyarrow", na_value=np.nan)``, the result will be ``boolean``, the NumPy-backed nullable extension array.
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- When ``pd.StringDtype("python", na_value=pd.NA)`` is compared against ``pd.StringDtype("python", na_value=np.nan)``, the result will be ``boolean``, the NumPy-backed nullable extension array.
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In previous versions, comparing :class:`Series` of different string dtypes (e.g. ``pd.StringDtype("pyarrow", na_value=pd.NA)`` against ``pd.StringDtype("python", na_value=np.nan)``) would result in inconsistent resulting dtype or incorrectly raise. pandas will now use the hierarchy
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