# CSTest

This metric computes the similarity of a real column vs. a synthetic column in terms of the column shapes. You can think of the shape as what you observe when you plot a bar graph of the column.

## Data Compatibility

* **Categorical**: This metric is meant for discrete, categorical data
* **Boolean**: This metric works on boolean data

{% hint style="warning" %}
This metric does not accept missing values
{% endhint %}

## Score

**(best) 1.0**: The p-value is high, indicating that the synthetic data is not very different from the real data

**(worst) 0.0**: The p-value is low, indicating that the synthetic data is significantly different than the real data

## How does it work?

This test normalizes the real and synthetic data in order to compute the category frequencies. Then, it applies the Chi-squared test \[1] to test the null hypothesis that the synthetic data comes from the same distribution as the real data.

The test returns the p-value \[2], where a smaller p-value indicates that the synthetic data is significantly different from the real data, rejecting the null hypothesis and leading to a worse overall score.

## Usage

Access this metric from the `single_column` module and use the `compute` method.

```python
from sdmetrics.single_column import CSTest

CSTest.compute(
    real_data=real_column,
    synthetic_data=synthetic_column
)
```

**Parameters**

* (required) `real_data`: A pandas.Series containing a single column
* (required) `synthetic_data`: A similar pandas.Series object with the synthetic version of the column

## FAQs

{% hint style="info" %}
**This metric is in Beta.** Be careful when using the metric and interpreting its score.

* This test is invalid when the category frequencies are too small \[3]. Because this test normalizes all frequencies, they are all <1, affecting the overall results.
* The p-value may be hacked by supplying data of different sizes
* The p-value interpretation may not be useful. Most users are interested in quantifying the differences between real and synthetic data, not testing the null hypothesis. In fact, if the synthetic data model is a simplification of the real data, the null hypothesis will nearly always be always be false with enough data.

Consider switching to the [TVComplement](/sdmetrics/data-metrics/quality/tvcomplement.md) metric to quantify the differences between discrete real and synthetic columns.
{% endhint %}

## References

\[1] <https://en.wikipedia.org/wiki/Chi-squared_test>

\[2] <https://en.wikipedia.org/wiki/P-value>

\[3] <https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.chisquare.html>


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