# Quantile-Quantile Plot in R (4 Examples) | qqplot, qqnorm & qqline Functions | ggplot2 Package

This tutorial explains how to **draw QQplots** in R programming.

Table of contents:

- Example 1: Basic QQplot & Interpretation
- Example 2: QQplot of Logistically Distributed Values
- Example 3: Compare Two Data Sets with QQplot
- Example 4: Create QQplot with ggplot2 Package
- Video, Further Resources & Summary

Let’s dive right into the R code:

## Example 1: Basic QQplot & Interpretation

In this example I’ll show you the basic application of QQplots (or Quantile-Quantile plots) in R. In the example, we’ll use the following normally distributed numeric vector:

set.seed(5432) # Set seed for reproducibility x <- rnorm(10000) # Create random normally distributed values |

set.seed(5432) # Set seed for reproducibility x <- rnorm(10000) # Create random normally distributed values

Our vector contains 10000 random values, which follows a normal distribution.

Now, we can use the qqnorm function to create a QQplot of this vector…

qqnorm(x) # QQplot of normally distributed values |

qqnorm(x) # QQplot of normally distributed values

…and the qqline function to add a theoretical line according to the normal distribution:

qqline(x, col = "red") # Add qqline to plot |

qqline(x, col = "red") # Add qqline to plot

**Figure 1: QQplot of Normally Distributed Random Numbers.**

Figure 1 shows the output of the previous R code: A QQplot of our normally distributed random data compared to the theoretical normal distribution and a QQline.

**We can interpret the graphic as follows:**

The quantiles of our sampled random data and the theoretical quantiles follow the QQline almost perfectly. For that reason, the QQplot indicates that our random values are normally distributed.

## Example 2: QQplot of Logistically Distributed Values

Let’s apply the same R code as in Example 1 to a different probability distribution in R:

y <- rlogis(10000) # Random values according to logistic distribution |

y <- rlogis(10000) # Random values according to logistic distribution

Our new random data follows a logistic distribution. Now, let’s draw a QQplot and a QQline to see the difference compared to Examples 1:

qqnorm(y) # QQplot of logistic distribution qqline(y, col = "red") |

qqnorm(y) # QQplot of logistic distribution qqline(y, col = "red")

**Figure 2: QQplot of Logisitc Distribution vs. Normal Distribution.**

Figure 2 shows the result. In contrast to Figure 1, the QQplot is not following the straight QQline, indicating that our random values do not follow a normal distribution.

## Example 3: Compare Two Data Sets with QQplot

So far, we have only compared one input data set vs. a theoretical normal distribution. However, it is also possible to compare two input data sets with each other.

Consider the following random values with a student t distribution:

z <- rt(10000, 3) # Random values according to student t distribution |

z <- rt(10000, 3) # Random values according to student t distribution

We can use the qqplot function to compare this distribution with the logistically distributed vector that we have created in Example 2:

qqplot(y, z) # QQplot of logistic & student t distribution |

qqplot(y, z) # QQplot of logistic & student t distribution

**Figure 3: QQplot with Two Input Data Sets.**

As you can see based on Figure 3, our two input data sets do now follow the same distribution, since the QQplot is not following a straight line.

## Example 4: Create QQplot with ggplot2 Package

Until now, we have used the base installation of R to produce our QQplots. However, there are many packages, which provide prettier representations of QQplots.

Probably the most common package for graphics in R is the ggplot2 package.

Let’s install and load the package:

install.packages("ggplot2") # Install & load ggplot2 library("ggplot2") |

install.packages("ggplot2") # Install & load ggplot2 library("ggplot2")

The ggplot2 package takes data frames as input, so let’s convert our numeric vector of Example 1 to a data frame:

data <- data.frame(x) # Create data frame containing x |

data <- data.frame(x) # Create data frame containing x

Now, we can use the stat_qq and stat_qq_line functions of the ggplot2 package to create a QQplot:

ggplot(data, aes(sample = x)) + # Create QQplot with ggplot2 package stat_qq() + stat_qq_line(col = "red") |

ggplot(data, aes(sample = x)) + # Create QQplot with ggplot2 package stat_qq() + stat_qq_line(col = "red")

**Figure 4: QQplot Created by ggplot2 Package.**

Figure 4 shows the same QQplot as Figure 1, but this time in the typical ggplot2 design.

## Video, Further Resources & Summary

Do you need more information on the R programming syntax of the present tutorial? Then you may want to have a look at the following video of my YouTube channel. In the video, I explain the R syntax of this article.

*The YouTube video will be added soon.*

Besides the video, you might read the other tutorials of this homepage. Some articles can be found below:

This article illustrated how to **make a Quantile-Quantile plot** in the R programming language. Please let me know in the comments section, in case you have additional questions.

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## 4 Comments. Leave new

PodrÃa ser interesante presentar la distribuciÃ³n logÃstica para mostrar cÃ³mo se pueden ver las colas cortas y largas en ggplot.

See my response on your English comment ðŸ™‚

It could be insightful presenting the logistic distribution in order to show how you cansee the short and long tails in qqplot.

Hey Alfredo,

Thank you for the comment!

Example 2 shows the logistic distribution, or did you mean something else?

Regards,

Joachim