How are QQ Plots Created?

Creating one from scratch.

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How are QQ Plots Created?

A QQ plot lets you visually assess the similarity between two distributions:

By plotting the quantiles of the two distributions against each other, we can look at the deviations from the straight line to determine the differences between the two distributions.

But how is it created?

Let’s understand today!

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The following visual depicts this process:

Consider two distributions—D1 and D2.

Step 1) Arrange points on axes:

Arrange points of D1 on the y-axis and D2 on the x-axis.

Step 2) Draw percentile lines

Create some percentile lines for both distributions.

For instance, mark the points of 10th percentile, 20th percentile, 30th percentile, etc. Once marked, intersect the corresponding lines:

• Match the 10th percentile of D1 with 10th percentile of D2.

• Match the 20th percentile of D1 with 20th percentile of D2.

• and so on.

The intersection points gives us the points in a QQ plot:

Now, remove the percentile marker lines.

In a gist, the above plot depicts the location where the corresponding percentiles of the two distributions match.

Step 3) Add the reference line

Finally, add a reference line to determine the deviations between the two distributions. There are many ways to do this:

1. Draw a line connecting the 25th and 75th percentiles of both distributions.

2. Or, create a regression fit on the above scatter plot.

Typically, option #1 is preferred since a regression fit can be influenced by outliers.

Adding the reference lines gives this QQ plot:

The deviations from this reference line mean that the corresponding percentiles do not align, which is an indicator of dissimilarity:

And the more percentiles we plot, the more accurate the QQ plot we get.

There are many applications of the QQ plot.

Imagine we want to determine if a distribution resembles a normal distribution. We can use a QQ plot for this.

• D1: The observed distribution

• D2: Normal distribution.

The closer the percentile points are to the reference line, the more the observed distribution matches a normal distribution:

Using a QQ plot to determine whether the observed distribution is a normal distribution or not

👉 Over to you: What other plots do you typically struggle with and want me to cover?

Thanks for reading!

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