BUG: DataFrame.select_dtypes(include=number) still included BooleanDtype

doc/source/whatsnew/v1.4.4.rst

@@ -17,6 +17,7 @@ Fixed regressions
 - Fixed regression in taking NULL :class:`objects` from a :class:`DataFrame` causing a segmentation violation. These NULL values are created by :meth:`numpy.empty_like` (:issue:`46848`)
 - Fixed regression in :func:`concat` materializing :class:`Index` during sorting even if :class:`Index` was already sorted (:issue:`47501`)
 - Fixed regression in :func:`cut` using a ``datetime64`` IntervalIndex as bins (:issue:`46218`)
+- Fixed regression in :meth:`DataFrame.select_dtypes` where ``include="number"`` included :class:`BooleanDtype` (:issue:`46870`)
 - Fixed regression in :meth:`DataFrame.loc` not updating the cache correctly after values were set (:issue:`47867`)
 - Fixed regression in :meth:`DataFrame.loc` not aligning index in some cases when setting a :class:`DataFrame` (:issue:`47578`)
 - Fixed regression in :meth:`DataFrame.loc` setting a length-1 array like value to a single value in the DataFrame (:issue:`46268`)

pandas/core/frame.py

@@ -4687,8 +4687,11 @@ def check_int_infer_dtype(dtypes):
             raise ValueError(f"include and exclude overlap on {(include & exclude)}")
 
         def dtype_predicate(dtype: DtypeObj, dtypes_set) -> bool:
+            # GH 46870: BooleanDtype._is_numeric == True but should be excluded
             return issubclass(dtype.type, tuple(dtypes_set)) or (
-                np.number in dtypes_set and getattr(dtype, "_is_numeric", False)
+                np.number in dtypes_set
+                and getattr(dtype, "_is_numeric", False)
+                and not is_bool_dtype(dtype)
             )
 
         def predicate(arr: ArrayLike) -> bool:

pandas/tests/frame/methods/test_select_dtypes.py

@@ -441,3 +441,18 @@ def test_select_dtypes_float_dtype(self, expected, float_dtypes):
         df = df.astype(dtype_dict)
         result = df.select_dtypes(include=float_dtypes)
         tm.assert_frame_equal(result, expected)
+
+    def test_np_bool_ea_boolean_include_number(self):
+        # GH 46870
+        df = DataFrame(
+            {
+                "a": [1, 2, 3],
+                "b": pd.Series([True, False, True], dtype="boolean"),
+                "c": np.array([True, False, True]),
+                "d": pd.Categorical([True, False, True]),
+                "e": pd.arrays.SparseArray([True, False, True]),
+            }
+        )
+        result = df.select_dtypes(include="number")
+        expected = DataFrame({"a": [1, 2, 3]})
+        tm.assert_frame_equal(result, expected)