diff --git a/src/delayedarray/DelayedArray.py b/src/delayedarray/DelayedArray.py
index d52a583..9a90d60 100644
--- a/src/delayedarray/DelayedArray.py
+++ b/src/delayedarray/DelayedArray.py
@@ -749,7 +749,7 @@ def __and__(self, other) -> "DelayedArray":
         Returns:
             A ``DelayedArray`` containing the delayed AND operation.
         """
-        return _wrap_isometric_with_args(self, other, operation="logical_or", right=True)
+        return _wrap_isometric_with_args(self, other, operation="logical_and", right=True)
 
     def __rand__(self, other) -> "DelayedArray":
         """Element-wise AND with the right-hand-side of a ``DelayedArray``.
@@ -907,7 +907,7 @@ def var(self, axis: Optional[Union[int, Tuple[int, ...]]] = None, dtype: Optiona
                 masked=is_masked(self),
             )
 
-    def any(self, axis: Optional[Union[int, Tuple[int, ...]]] = None, dtype: Optional[numpy.dtype] = None, buffer_size: int = 1e8) -> numpy.ndarray:
+    def any(self, axis: Optional[Union[int, Tuple[int, ...]]] = None, dtype: Optional[numpy.dtype] = numpy.bool_, buffer_size: int = 1e8) -> numpy.ndarray:
         """Test whether any array element along a given axis evaluates to True.
 
         Compute this test across the ``DelayedArray``, possibly over a
@@ -916,14 +916,14 @@ def any(self, axis: Optional[Union[int, Tuple[int, ...]]] = None, dtype: Optiona
 
         Args:
             axis: 
-                A single integer specifying the axis over which to calculate
-                the mean. Alternatively, a tuple (multiple axes) or None (no
-                axes), see :py:func:`~numpy.mean` for details.
+                A single integer specifying the axis over which to test
+                for any. Alternatively, a tuple (multiple axes) or None (no
+                axes), see :py:func:`~numpy.any` for details.
 
             dtype:
                 NumPy type for the output array. If None, this is automatically
                 chosen based on the type of the ``DelayedArray``, see
-                :py:func:`~numpy.mean` for details.
+                :py:func:`~numpy.any` for details.
 
             buffer_size:
                 Buffer size in bytes to use for block processing. Larger values
@@ -934,7 +934,7 @@ def any(self, axis: Optional[Union[int, Tuple[int, ...]]] = None, dtype: Optiona
             be a NumPy scalar instead.
         """
         if hasattr(self._seed, "any"):
-            return self._seed.any(axis=axis, dtype=dtype)
+            return self._seed.any(axis=axis)
         else:
             return array_any(
                 self, 
@@ -944,23 +944,23 @@ def any(self, axis: Optional[Union[int, Tuple[int, ...]]] = None, dtype: Optiona
                 masked=is_masked(self),
             )
 
-    def all(self, axis: Optional[Union[int, Tuple[int, ...]]] = None, dtype: Optional[numpy.dtype] = None, buffer_size: int = 1e8) -> numpy.ndarray:
+    def all(self, axis: Optional[Union[int, Tuple[int, ...]]] = None, dtype: Optional[numpy.dtype] = numpy.bool_, buffer_size: int = 1e8) -> numpy.ndarray:
         """Test whether all array elements along a given axis evaluate to True.
 
         Compute this test across the ``DelayedArray``, possibly over a
-        given axis or set of axes. If the seed has a ``any()`` method, that
+        given axis or set of axes. If the seed has a ``all()`` method, that
         method is called directly with the supplied arguments.
 
         Args:
             axis: 
-                A single integer specifying the axis over which to calculate
-                the mean. Alternatively, a tuple (multiple axes) or None (no
-                axes), see :py:func:`~numpy.mean` for details.
+                A single integer specifying the axis over which to test 
+                for all. Alternatively, a tuple (multiple axes) or None (no
+                axes), see :py:func:`~numpy.all` for details.
 
             dtype:
                 NumPy type for the output array. If None, this is automatically
                 chosen based on the type of the ``DelayedArray``, see
-                :py:func:`~numpy.mean` for details.
+                :py:func:`~numpy.all` for details.
 
             buffer_size:
                 Buffer size in bytes to use for block processing. Larger values
@@ -971,7 +971,7 @@ def all(self, axis: Optional[Union[int, Tuple[int, ...]]] = None, dtype: Optiona
             be a NumPy scalar instead.
         """
         if hasattr(self._seed, "all"):
-            return self._seed.all(axis=axis, dtype=dtype)
+            return self._seed.all(axis=axis)
         else:
             return array_all(
                 self, 
diff --git a/src/delayedarray/SparseNdarray.py b/src/delayedarray/SparseNdarray.py
index 7ca2a59..eca08eb 100644
--- a/src/delayedarray/SparseNdarray.py
+++ b/src/delayedarray/SparseNdarray.py
@@ -14,7 +14,7 @@
     _concatenate_unmasked_ndarrays,
     _concatenate_maybe_masked_ndarrays
 )
-from ._statistics import array_mean, array_var, array_sum, _create_offset_multipliers
+from ._statistics import array_mean, array_var, array_sum, _create_offset_multipliers, array_all, array_any
 
 __author__ = "ltla"
 __copyright__ = "ltla"
@@ -665,6 +665,71 @@ def __abs__(self):
             A ``SparseNdarray`` containing the delayed absolute value operation.
         """
         return _transform_sparse_array_from_SparseNdarray(self, lambda l, i, v : (i, abs(v)), self._dtype)
+    
+    def __or__(self, other) -> Union["SparseNdarray", numpy.ndarray]:
+        """Element-wise OR with something.
+
+        Args:
+            other:
+                A numeric scalar;
+                or a NumPy array with dimensions as described in
+                :py:class:`~delayedarray.UnaryIsometricOpWithArgs.UnaryIsometricOpWithArgs`;
+                or a ``DelayedArray`` of the same dimensions as :py:attr:`~shape`.
+
+        Returns:
+            Array containing the result of the check.
+            This may or may not be sparse depending on ``other``.
+        """
+        return _operate_with_args_on_SparseNdarray(self, other, operation="logical_or", right=True)
+
+    def __ror__(self, other) -> Union["SparseNdarray", numpy.ndarray]:
+        """Element-wise OR with the right-hand-side of a ``DelayedArray``.
+
+        Args:
+            other:
+                A numeric scalar;
+                or a NumPy array with dimensions as described in
+                :py:class:`~delayedarray.UnaryIsometricOpWithArgs.UnaryIsometricOpWithArgs`;
+                or a ``DelayedArray`` of the same dimensions as :py:attr:`~shape`.
+
+        Returns:
+            Array containing the result of the check.
+            This may or may not be sparse depending on ``other``.
+        """
+        return _operate_with_args_on_SparseNdarray(self, other, operation="logical_or", right=False)
+
+    def __and__(self, other) -> Union["SparseNdarray", numpy.ndarray]:
+        """Element-wise AND with something.
+
+        Args:
+            other:
+                A numeric scalar;
+                or a NumPy array with dimensions as described in
+                :py:class:`~delayedarray.UnaryIsometricOpWithArgs.UnaryIsometricOpWithArgs`;
+                or a ``DelayedArray`` of the same dimensions as :py:attr:`~shape`.
+
+        Returns:
+            Array containing the result of the check.
+            This may or may not be sparse depending on ``other``.
+        """
+        return _operate_with_args_on_SparseNdarray(self, other, operation="logical_and", right=True)
+
+    def __rand__(self, other) -> Union["SparseNdarray", numpy.ndarray]:
+        """Element-wise AND with the right-hand-side of a ``DelayedArray``.
+
+        Args:
+            other:
+                A numeric scalar;
+                or a NumPy array with dimensions as described in
+                :py:class:`~delayedarray.UnaryIsometricOpWithArgs.UnaryIsometricOpWithArgs`;
+                or a ``DelayedArray`` of the same dimensions as :py:attr:`~shape`.
+
+        Returns:
+            Array containing the result of the check.
+            This may or may not be sparse depending on ``other``.
+        """
+        return _operate_with_args_on_SparseNdarray(self, other, operation="logical_and", right=False)
+
 
     # Subsetting.
     def __getitem__(self, subset: Tuple[Union[slice, Sequence], ...]) -> Union["SparseNdarray", numpy.ndarray]:
@@ -760,6 +825,21 @@ def __array_function__(self, func, types, args, kwargs) -> "SparseNdarray":
         if func == numpy.round:
             return _transform_sparse_array_from_SparseNdarray(self, lambda l, i, v : (i, func(v, **kwargs)), self._dtype)
 
+        if func == numpy.mean:
+            return self.mean(**kwargs)
+
+        if func == numpy.sum:
+            return self.sum(**kwargs)
+
+        if func == numpy.var:
+            return self.var(**kwargs)
+
+        if func == numpy.any:
+            return self.any(**kwargs)
+
+        if func == numpy.all:
+            return self.all(**kwargs)
+
         raise NotImplementedError(f"'{func.__name__}' is not implemented!")
 
 
@@ -872,6 +952,64 @@ def var(self, axis: Optional[Union[int, Tuple[int, ...]]] = None, dtype: Optiona
             masked=self._is_masked,
         )
 
+    def any(self, axis: Optional[Union[int, Tuple[int, ...]]] = None, dtype: Optional[numpy.dtype] = numpy.bool_) -> numpy.ndarray:
+        """Test whether any array element along a given axis evaluates to True.
+
+        Compute this test across the ``SparseNdarray``, possibly over a
+        given axis or set of axes. If the seed has a ``any()`` method, that
+        method is called directly with the supplied arguments.
+
+        Args:
+            axis: 
+                A single integer specifying the axis over which to test
+                for any. Alternatively, a tuple (multiple axes) or None
+                (no axes), see :py:func:`~numpy.any` for details.
+
+            dtype:
+                NumPy type for the output array. If None, this is automatically
+                chosen based on the type of the ``SparseNdarray``, see
+                :py:func:`~numpy.any` for details.
+
+        Returns:
+            A NumPy array containing the variances. If ``axis = None``,
+            this will be a NumPy scalar instead.
+        """
+        return array_any(
+            self, 
+            axis=axis, 
+            dtype=dtype, 
+            reduce_over_x=_reduce_SparseNdarray,
+            masked=self._is_masked,
+        )
+
+    def all(self, axis: Optional[Union[int, Tuple[int, ...]]] = None, dtype: Optional[numpy.dtype] = numpy.bool_) -> numpy.ndarray:
+        """Test whether all array elements along a given axis evaluate to True.
+
+        Compute this test across the ``SparseNdarray``, possibly over a
+        given axis or set of axes. If the seed has a ``all()`` method, that
+        method is called directly with the supplied arguments.
+        Args:
+            axis: 
+                A single integer specifying the axis over which to test
+                for any. Alternatively, a tuple (multiple axes) or None
+                (no axes), see :py:func:`~numpy.any` for details.
+
+            dtype:
+                NumPy type for the output array. If None, this is automatically
+                chosen based on the type of the ``SparseNdarray``, see
+                :py:func:`~numpy.any` for details.
+
+        Returns:
+            A NumPy array containing the variances. If ``axis = None``,
+            this will be a NumPy scalar instead.
+        """
+        return array_all(
+            self, 
+            axis=axis, 
+            dtype=dtype, 
+            reduce_over_x=_reduce_SparseNdarray,
+            masked=self._is_masked,
+        )
 
     # Other stuff
     def __copy__(self) -> "SparseNdarray":
diff --git a/src/delayedarray/_statistics.py b/src/delayedarray/_statistics.py
index b0ce40a..fa3ffda 100644
--- a/src/delayedarray/_statistics.py
+++ b/src/delayedarray/_statistics.py
@@ -52,14 +52,17 @@ def _choose_output_type(dtype: numpy.dtype, preserve_integer: bool) -> numpy.dty
     return dtype
 
 
-def _allocate_output_array(shape: Tuple[int, ...], axes: List[int], dtype: numpy.dtype) -> numpy.ndarray:
+def _allocate_output_array(shape: Tuple[int, ...], axes: List[int], dtype: numpy.dtype, default_func: Callable = numpy.zeros) -> numpy.ndarray:
+    if default_func is None:
+        default_func = numpy.zeros
+
     if len(axes) == 0:
         # Returning a length-1 array to allow for continued use of offsets.
-        return numpy.zeros(1, dtype=dtype)
+        return default_func(1, dtype=dtype)
     else:
         # Use Fortran order so that the offsets make sense. 
         shape = [shape[i] for i in axes]
-        return numpy.zeros((*shape,), dtype=dtype, order="F")
+        return default_func((*shape,), dtype=dtype, order="F")
 
 
 def _create_offset_multipliers(shape: Tuple[int, ...], axes: List[int]) -> List[int]:
@@ -195,15 +198,18 @@ def array_any(x, axis: Optional[Union[int, Tuple[int, ...]]], dtype: Optional[nu
         mask_buffer = masked.ravel(order="F")
         def op(offset, value):
             if value is not numpy.ma.masked:
-                buffer[offset] = numpy.any([buffer[offset], value])
+                if value and not buffer[offset]:
+                    buffer[offset] = True
             else:
                 mask_buffer[offset] += 1
         reduce_over_x(x, axes, op)
         size = _expected_sample_size(x.shape, axes) 
-        output = numpy.ma.MaskedArray(output, mask=(masked == size))
+        denom = size - masked
+        output = numpy.ma.MaskedArray(output, mask=(denom == 0))
     else:
         def op(offset, value):
-            buffer[offset] = numpy.any([buffer[offset], value])
+            if value and not buffer[offset]:
+                buffer[offset] = True
         reduce_over_x(x, axes, op)
 
     if len(axes) == 0:
@@ -216,24 +222,26 @@ def array_all(x, axis: Optional[Union[int, Tuple[int, ...]]], dtype: Optional[nu
     axes = _find_useful_axes(len(x.shape), axis)
     if dtype is None:
         dtype = _choose_output_type(x.dtype, preserve_integer = True)
-    output = _allocate_output_array(x.shape, axes, dtype)
+    output = _allocate_output_array(x.shape, axes, dtype, default_func=numpy.ones)
     buffer = output.ravel(order="F")
-    buffer += 1 # since all has to be true, we start with a value other than 0's
 
     if masked:
         masked = numpy.zeros(output.shape, dtype=numpy.uint, order="F")
         mask_buffer = masked.ravel(order="F")
         def op(offset, value):
             if value is not numpy.ma.masked:
-                buffer[offset] = numpy.all([buffer[offset], value])
+                if not value and buffer[offset]:
+                    buffer[offset] = False
             else:
                 mask_buffer[offset] += 1
         reduce_over_x(x, axes, op)
         size = _expected_sample_size(x.shape, axes) 
-        output = numpy.ma.MaskedArray(output, mask=(masked == size))
+        denom = size - masked
+        output = numpy.ma.MaskedArray(output, mask=(denom == 0))
     else:
         def op(offset, value):
-            buffer[offset] = numpy.all([buffer[offset], value])
+            if not value and buffer[offset]:
+                buffer[offset] = False
         reduce_over_x(x, axes, op)
 
     if len(axes) == 0:
diff --git a/tests/test_DelayedArray.py b/tests/test_DelayedArray.py
index 6d9c066..add39ea 100644
--- a/tests/test_DelayedArray.py
+++ b/tests/test_DelayedArray.py
@@ -247,3 +247,118 @@ def test_SparseNdarray_var_sparse(mask_rate, buffer_size):
     with pytest.warns(RuntimeWarning):
         y = delayedarray.wrap(delayedarray.SparseNdarray((0,), None, dtype=numpy.int32, index_dtype=numpy.int32)) * 50
         assert numpy.isnan(y.var())
+
+@pytest.mark.parametrize("mask_rate", [0, 0.5])
+@pytest.mark.parametrize("buffer_size", [100, 500, 2000])
+def test_SparseNdarray_any_dense(mask_rate, buffer_size):
+    raw = simulate_ndarray((30, 40, 15), mask_rate = mask_rate)
+    assert_identical_ndarrays(raw.any(), delayedarray.wrap(raw).any())
+    assert_identical_ndarrays(raw.any(axis=0), delayedarray.wrap(raw).any(axis=0))
+
+    y = delayedarray.wrap(raw) - 12
+    ref = raw - 12
+    assert numpy.isclose(ref.any(), y.any(buffer_size=buffer_size))
+    assert_close_ndarrays(ref.any(axis=1), y.any(axis=1, buffer_size=buffer_size))
+    assert_close_ndarrays(ref.any(axis=-1), y.any(axis=-1, buffer_size=buffer_size))
+    assert_close_ndarrays(ref.any(axis=(0, 2)), y.any(axis=(0, 2), buffer_size=buffer_size))
+
+    # Trying with a single dimension.
+    test_shape = (100,)
+    raw = simulate_ndarray((100,), mask_rate=mask_rate)
+    y = delayedarray.wrap(raw) + 29
+    ref = raw + 29
+    assert numpy.isclose(ref.any(), y.any(buffer_size=buffer_size))
+
+    # Full masking is respected.
+    y = delayedarray.wrap(numpy.ma.MaskedArray([1], mask=True)) + 20
+    assert y.any() is numpy.ma.masked
+
+    # Zero-length array is respected.
+    y = delayedarray.wrap(numpy.ndarray((10, 0))) * 50
+    assert y.any() == False
+
+
+@pytest.mark.parametrize("mask_rate", [0, 0.5])
+@pytest.mark.parametrize("buffer_size", [100, 500, 2000])
+def test_SparseNdarray_any_sparse(mask_rate, buffer_size):
+    raw = simulate_SparseNdarray((20, 30, 25), mask_rate = mask_rate)
+    ref = raw * 19
+    y = delayedarray.wrap(raw) * 19
+
+    assert numpy.isclose(ref.any(), y.any(buffer_size=buffer_size))
+    assert_close_ndarrays(ref.any(axis=1), y.any(axis=1, buffer_size=buffer_size))
+    assert_close_ndarrays(ref.any(axis=-1), y.any(axis=-1, buffer_size=buffer_size))
+    assert_close_ndarrays(ref.any(axis=(0, 2)), y.any(axis=(0, 2), buffer_size=buffer_size))
+
+    # Trying with a single dimension.
+    test_shape = (100,)
+    raw = simulate_SparseNdarray((100,), mask_rate=mask_rate)
+    y = delayedarray.wrap(raw) * 12
+    ref = raw * 12
+    assert numpy.isclose(ref.any(), y.any(buffer_size=buffer_size))
+
+    # Full masking is respected.
+    ref = delayedarray.SparseNdarray((1,), (numpy.zeros(1, dtype=numpy.int_), numpy.ma.MaskedArray([1], mask=True)))
+    y = delayedarray.wrap(ref) / 5
+    assert y.any() is numpy.ma.masked
+
+    # Zero-length array is respected.
+    y = delayedarray.wrap(delayedarray.SparseNdarray((0,), None, dtype=numpy.int32, index_dtype=numpy.int32)) * 50
+    assert y.any() == False
+
+@pytest.mark.parametrize("mask_rate", [0, 0.5])
+@pytest.mark.parametrize("buffer_size", [100, 500, 2000])
+def test_SparseNdarray_all_dense(mask_rate, buffer_size):
+    raw = simulate_ndarray((30, 40, 15), mask_rate = mask_rate)
+    assert_identical_ndarrays(raw.all(), delayedarray.wrap(raw).all())
+    assert_identical_ndarrays(raw.all(axis=0), delayedarray.wrap(raw).all(axis=0))
+
+    y = delayedarray.wrap(raw) - 12
+    ref = raw - 12
+    assert numpy.isclose(ref.all(), y.all(buffer_size=buffer_size))
+    assert_close_ndarrays(ref.all(axis=1), y.all(axis=1, buffer_size=buffer_size))
+    assert_close_ndarrays(ref.all(axis=-1), y.all(axis=-1, buffer_size=buffer_size))
+    assert_close_ndarrays(ref.all(axis=(0, 2)), y.all(axis=(0, 2), buffer_size=buffer_size))
+
+    # Trying with a single dimension.
+    test_shape = (100,)
+    raw = simulate_ndarray((100,), mask_rate=mask_rate)
+    y = delayedarray.wrap(raw) + 29
+    ref = raw + 29
+    assert numpy.isclose(ref.all(), y.all(buffer_size=buffer_size))
+
+    # Full masking is respected.
+    y = delayedarray.wrap(numpy.ma.MaskedArray([1], mask=True)) + 20
+    assert y.all() is numpy.ma.masked
+
+    # Zero-length array is respected.
+    y = delayedarray.wrap(numpy.ndarray((10, 0))) * 50
+    assert y.all()
+
+@pytest.mark.parametrize("mask_rate", [0, 0.5])
+@pytest.mark.parametrize("buffer_size", [100, 500, 2000])
+def test_SparseNdarray_all_sparse(mask_rate, buffer_size):
+    raw = simulate_SparseNdarray((20, 30, 25), mask_rate = mask_rate)
+    ref = raw * 19
+    y = delayedarray.wrap(raw) * 19
+
+    assert numpy.isclose(ref.all(), y.all(buffer_size=buffer_size))
+    assert_close_ndarrays(ref.all(axis=1), y.all(axis=1, buffer_size=buffer_size))
+    assert_close_ndarrays(ref.all(axis=-1), y.all(axis=-1, buffer_size=buffer_size))
+    assert_close_ndarrays(ref.all(axis=(0, 2)), y.all(axis=(0, 2), buffer_size=buffer_size))
+
+    # Trying with a single dimension.
+    test_shape = (100,)
+    raw = simulate_SparseNdarray((100,), mask_rate=mask_rate)
+    y = delayedarray.wrap(raw) * 12
+    ref = raw * 12
+    assert numpy.isclose(ref.any(), y.all(buffer_size=buffer_size))
+
+    # Full masking is respected.
+    ref = delayedarray.SparseNdarray((1,), (numpy.zeros(1, dtype=numpy.int_), numpy.ma.MaskedArray([1], mask=True)))
+    y = delayedarray.wrap(ref) / 5
+    assert y.all() is numpy.ma.masked
+
+    # Zero-length array is respected.
+    y = delayedarray.wrap(delayedarray.SparseNdarray((0,), None, dtype=numpy.int32, index_dtype=numpy.int32)) * 50
+    assert y.all()
\ No newline at end of file