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> Reference material for COVAR_POP

# COVAR_POP

Computes the population covariance between two numeric expressions. If either one of expressions is `NULL` - that input row is ignored.
Use this when analyzing an entire population rather than a sample. For covariance of sample see [COVAR\_SAMP](/reference-sql/functions-reference/aggregation/covar-samp).

## Covariance vs Correlation

**Covariance** and **correlation** both describe how two variables change together, but they do so in different ways:

* **Covariance** measures the **direction** of the relationship between two variables:
  * Positive covariance: variables tend to increase together.
  * Negative covariance: one increases as the other decreases.
  * Its value is **unbounded** and depends on the units of the variables, making it hard to interpret on its own.

* **Correlation**, specifically **Pearson correlation**, standardizes the relationship:
  * It is the **normalized version of covariance**, giving a unitless measure between **-1 and 1**.
  * This makes it easier to compare the strength of relationships between different pairs of variables.

For information on correlation see [CORR](/reference-sql/functions-reference/aggregation/corr)

## Syntax

```sql theme={"theme":{"light":"css-variables","dark":"css-variables"}}
COVAR_POP(<expr1>, <expr2>) [FILTER ([WHERE] <condition>)]
```

## Parameters

| Parameter     | Description                                                       | Supported input types |
| :------------ | :---------------------------------------------------------------- | :-------------------- |
| `<expr1>`     | First numeric expression to use for covariance computation.       | `DOUBLE PRECISION`    |
| `<expr2>`     | Second numeric expression to use for covariance computation.      | `DOUBLE PRECISION`    |
| `<condition>` | An optional boolean expression to filter rows used in aggregation | `BOOL`                |

## Return Type

`COVAR_POP` returns a result of type `DOUBLE PRECISION`.

## Examples

The `playstats` table contains the following data:

<div className="query-window">
  ```
  SELECT currentlevel, currentscore, currentspeed FROM playstats ORDER BY currentlevel DESC, currentscore DESC LIMIT 5;
  ```

  | currentlevel <span>int null</span> | currentscore <span>long null</span> | currentspeed <span>float null</span> |
  | :--------------------------------- | :---------------------------------- | :----------------------------------- |
  | 7                                  | 501667                              | 345                                  |
  | 7                                  | 501642                              | 30                                   |
  | 7                                  | 501618                              | 62                                   |
  | 7                                  | 501581                              | 64                                   |
  | 7                                  | 501544                              | 171                                  |

  <p><span>Rows: 5</span><span>Execution time: 4.19ms</span></p>
</div>

`currentscore` and `currentlevel` in the `playstats` table are highly correlated, producing a large covariance value:

<div className="query-window">
  ```
  SELECT ROUND(COVAR_POP(currentscore::double precision, currentlevel::double precision), 2) AS covariance
  FROM playstats;
  ```

  | covariance <span>double null</span> |
  | :---------------------------------- |
  | 73152.22                            |

  <p><span>Rows: 1</span><span>Execution time: 7.65ms</span></p>
</div>

`currentlevel` and `currentspeed` are not correlated, so their covariance is close to zero:

<div className="query-window">
  ```
  SELECT ROUND(COVAR_POP(currentlevel::double precision, currentspeed::double precision), 4) AS covariance
  FROM playstats;
  ```

  | covariance <span>double null</span> |
  | :---------------------------------- |
  | -0.8091                             |

  <p><span>Rows: 1</span><span>Execution time: 6.90ms</span></p>
</div>