---
title: "Correlation Matrix"
slug: "correlation-matrix"
updated: 2024-01-23T14:03:05Z
published: 2024-01-23T14:03:05Z
canonical: "userguide.dataclassroom.com/correlation-matrix"
---

> ## Documentation Index
> Fetch the complete documentation index at: https://userguide.dataclassroom.com/llms.txt
> Use this file to discover all available pages before exploring further.

# Correlation Matrix

A **correlation matrix** is a way to show how closely related a number of numeric variables are with each other.

The following example uses the **mtcars** dataset which has various performance and physical parameters for a selection of car makes and models. It uses **Spearman's Rho** correlation to produce a number between 0 and +1 or -1 (negative numbers indicate a negative correlation) for **each pair of variables**. You can then see, as you would expect:

- A strong positive correlation between **disp** (engine size) and **hp** (horsepower) - the bigger the engine, the more powerful it is
- A strong negative correlation between **wt** (Weight) and **mpg** (miles per gallon) - heavier cars use more gas, so MPG gets lower with a higher value for weight.

![](https://cdn.document360.io/62f8f41e-e041-42c4-b9bc-8ae1eb45d064/Images/Documentation/unipol.png)

To view the example, open [the dataset in DataClassroom](https://dataclassroom.com/en/dataseteditor/65630945-24f2-456e-9add-e839c1c671bc) and go to the left-hand menu **Advanced->Correlation Matrix** option.

![](https://cdn.document360.io/62f8f41e-e041-42c4-b9bc-8ae1eb45d064/Images/Documentation/image-1703953757729.png)

### Selecting a correlation test

You can choose between the following correlation coefficients:

- **Spearman (rho)** (default) - this evaluates whether the relationship between the variables is **monotonic** (if one goes up, does the other) *even if not a linear relationship*.
- **Pearson (r)** - evaluates how **close to linear** the relationship is between the variables.

Spearman is especially relevant where you have survey data including opinions expressed on a numerical scale (e.g. "how happy do you feel on a scale of 1-10?") where the scale is effectively arbitrary and can vary from subject to subject, and you are interested in the correlation with other variables which also have arbitrary scales.

### Selecting columns of data

You can select which (numeric) columns are to be included in the matrix, using the **column selector** on the left. You can hide the column selector when you are done with it.

![](https://cdn.document360.io/62f8f41e-e041-42c4-b9bc-8ae1eb45d064/Images/Documentation/image-1703954165828.png)

### Exporting image and data

The **camera** and **copy** tools let you copy the matrix as an **image**, or copy the **numerical contents as a table** suitable for pasting into a spreadsheet: ![](https://cdn.document360.io/62f8f41e-e041-42c4-b9bc-8ae1eb45d064/Images/Documentation/image-1705917870321.png) The image resolution obtained from the camera is related to the actual size of the image on your screen. To get a **high-resolution image for a poster**:

- Make your browser window as large as possible
- Hide the column selector on the left so as much of the screen as possible is available for the width of the matrix
- Make sure the **Autosize** option under **Customize Appearance** is checked to ensure the full width is being used

### Customizing the appearance

![](https://cdn.document360.io/62f8f41e-e041-42c4-b9bc-8ae1eb45d064/Images/Documentation/image-1705918860286.png)

You can also customize the appearance in several ways. You can use the **Customize Appearance** button and:

- Change the color used (in the example below, green has been selected instead of blue).
- Fill the entire matrix, instead of just the bottom-left quadrant.
- Color negative values differently.
- Hide or show the color scale indicator.
- Adjust the matrix heading sizes if you have especially long or short variable names.

![](https://cdn.document360.io/62f8f41e-e041-42c4-b9bc-8ae1eb45d064/Images/Documentation/full.png)

### Adding P-values

Under **Customize Appearance** there is also the option to add P-values for each comparison.

![](https://cdn.document360.io/62f8f41e-e041-42c4-b9bc-8ae1eb45d064/Images/Documentation/image-1706018142617.png)

![](https://cdn.document360.io/62f8f41e-e041-42c4-b9bc-8ae1eb45d064/Images/Documentation/image-1706018395528.png)

By default, the P-values shown have been corrected for the [**multiple comparisons problem**](https://en.wikipedia.org/wiki/Multiple_comparisons_problem) using a [**Bonferroni correction**](https://en.wikipedia.org/wiki/Bonferroni_correction).

To explain:

**When doing N simultaneous correlations in a matrix there is a higher chance of seeing a significant result in one of the tests, just due to randomness.**

For example, if you have a matrix with 5 variables, then you are doing 10 different correlations, as there are 10 ways (4 + 3 + 2 + 1) to combine the 5 variables. This means that instead of a P-value of 0.05 having a 5% chance of appearing by random chance alone, that chance is now much higher.

The Bonferroni correction is very simple - it just multiplies each P-value by the number of correlations (10 in this case).