Pandas version checks
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[X] I have checked that this issue has not already been reported.
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[X] I have confirmed this bug exists on the latest version of pandas.
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[ ] I have confirmed this bug exists on the main branch of pandas.
Reproducible Example
>>> df = pd.DataFrame({"A": pd.Series([1,2,3], dtype=pd.ArrowDtype(pa.int8())), "B": pd.Series([1,2,3], dtype=pd.ArrowDtype(pa.int16()))})
>>> df.describe(include=pd.ArrowDtype(pa.int8()))
A B
count 3.0 3.0
mean 2.0 2.0
std 1.0 1.0
min 1.0 1.0
25% 1.5 1.5
50% 2.0 2.0
75% 2.5 2.5
max 3.0 3.0
>>>
Issue Description
Only describe for column "A" should have been calculated, because it's the only int8 column in the dataframe.
Expected Behavior
Expected behavior is behavior with numpy types:
>>> df = pd.DataFrame({"A": pd.Series([1,2,3], dtype=np.dtype("int8")), "B": pd.Series([1,2,3], dtype=np.dtype("int16"))})
>>> df.describe(include=np.dtype("int8"))
A
count 3.0
mean 2.0
std 1.0
min 1.0
25% 1.5
50% 2.0
75% 2.5
max 3.0
>>>
This only calculates describe for column "A".
Installed Versions
>>> pd.show_versions()
INSTALLED VERSIONS
------------------
commit : 478d340667831908b5b4bf09a2787a11a14560c9
python : 3.8.10.final.0
python-bits : 64
OS : Windows
OS-release : 10
Version : 10.0.22621
machine : AMD64
processor : Intel64 Family 6 Model 85 Stepping 7, GenuineIntel
byteorder : little
LC_ALL : None
LANG : None
LOCALE : English_United States.1252
pandas : 2.0.0
numpy : 1.24.2
pytz : 2023.3
dateutil : 2.8.2
setuptools : 67.5.1
pip : 23.0.1
Cython : None
pytest : 7.0.1
hypothesis : None
sphinx : 4.2.0
blosc : None
feather : None
xlsxwriter : None
lxml.etree : None
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : 3.1.2
IPython : 8.12.0
pandas_datareader: None
bs4 : 4.12.0
bottleneck : None
brotli : None
fastparquet : None
fsspec : None
gcsfs : None
matplotlib : None
numba : None
numexpr : None
odfpy : None
openpyxl : None
pandas_gbq : None
pyarrow : 11.0.0
pyreadstat : None
pyxlsb : None
s3fs : None
scipy : None
snappy : None
sqlalchemy : None
tables : None
tabulate : 0.8.9
xarray : None
xlrd : None
zstandard : None
tzdata : 2023.3
qtpy : None
pyqt5 : None
>>>