> For the complete documentation index, see [llms.txt](https://docs.seldon.ai/alibi-detect/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.seldon.ai/alibi-detect/api-reference/utils/statstest.md).

# alibi\_detect.utils.statstest

## Functions

### `fdr`

```python
fdr(p_val: numpy.ndarray, q_val: float) -> Tuple[int, Union[float, numpy.ndarray]]
```

Checks the significance of univariate tests on each variable between 2 samples of

multivariate data via the False Discovery Rate (FDR) correction of the p-values.

| Name    | Type            | Default | Description                        |
| ------- | --------------- | ------- | ---------------------------------- |
| `p_val` | `numpy.ndarray` |         | p-values for each univariate test. |
| `q_val` | `float`         |         | Acceptable q-value threshold.      |

**Returns**

* Type: `Tuple[int, Union[float, numpy.ndarray]]`

### `permutation_test`

```python
permutation_test(x: numpy.ndarray, y: numpy.ndarray, metric: Callable, n_permutations: int = 100, kwargs) -> Tuple[float, float, numpy.ndarray]
```

Apply a permutation test to samples x and y.

| Name             | Type            | Default | Description                                                                        |
| ---------------- | --------------- | ------- | ---------------------------------------------------------------------------------- |
| `x`              | `numpy.ndarray` |         | Batch of instances of shape \[Nx, features].                                       |
| `y`              | `numpy.ndarray` |         | Batch of instances of shape \[Ny, features].                                       |
| `metric`         | `Callable`      |         | Distance metric used for the test. Defaults to Maximum Mean Discrepancy.           |
| `n_permutations` | `int`           | `100`   | Number of permutations used in the test.                                           |
| `kwargs`         |                 |         | Kwargs for the metric. For the default this includes for instance the kernel used. |

**Returns**

* Type: `Tuple[float, float, numpy.ndarray]`